Geometry articles, theorems, problems

What Is Geometry?
What Is Analytic Geometry?

Pictorial Geometry Index

  1. 1 + 27 = 12 + 16 Sangaku
  2. 120° Breeds 90° [Java]
  3. 3-4-5, Golden Ratio
  4. 3 Roads, 3 Travelers [Java]
  5. 3 Utilities Puzzle
  6. 3D Concurrency Of Altitudes
  7. 3D Quadrilateral - a Coffin Problem
  8. 3-4-5 Triangle by a Kid
  9. 4 Travelers problem
  10. 5-Step Construction of the Golden Ratio, One of Many
  11. 5x5 Square Grid and 5 Circes [Java, GeoGebra]
  12. 6 to 9 Point Circle [Java]
  13. 60° Angle And Importance of Being The Other End of a Diameter
  14. 60o Breeds 90o [Java]
  15. 7 = 2 + 5 Sangaku
  16. 9-point Circle as a Locus of Concurrency [Java]
  17. 9 Point Center on Angle Bisector [GeoGebra]
  18. A 60° Rhombus in a 60° Isosceles Trapezoid
  19. A better solution to a difficult sangaku problem
  20. A Broken Line in 3D
  21. A Case of Similarity [Java]
  22. A Chain of Touching Circles in a Polygon (a la Bui Quang Tuan) [Java]
  23. A Chain of Touching Circles in a Polygon (à la Evelyn) [Java]
  24. A Characterization of the Euler Line [Java]
  25. A Circle in an Isosceles triangle from the 2006 Irish MO
  26. A Circle Related to Incenter and Circumcenter [Java]
  27. A Circle Rolling in an Equilateral Triangle [Java]
  28. A Circle With Two Centers [Java]
  29. A Conic in a Triangle [JavaScript, GeoGebra]
  30. A Combinaton Locus
  31. A Corrected Version of the Calculus Proof of the Pythagorean Theorem
  32. A Curious Identity in Triangle
  33. A Cyclic Inequality in Triangle
  34. A Cyclic Inequality in Triangle II
  35. A Cyclic Inequality in Triangle for Integer Powers
  36. A Degenerate Case of Bottema's Configuration [Java, GeoGebra]
  37. A Diameter As a Diagonal of Inscribed Quadrilateral [Java, GeoGebra]
  38. A Discovery of Hirotaka Ebisui And Thanos Kalogerakis
  39. A dissection puzzle. Proof #99 of the Pythagorean theorem
  40. A Double Meaning of an Arc's Midpoint [Java, GeoGebra]
  41. A Family of Cyclic Quadrilaterals [JavaScript, GeoGebra]
  42. A Generalization of Simson Line [JavaScript, GeoGebra]
  43. A Generalization of the Pythagorean Theorem
  44. A Generalization of Van Aubel's Theorem
  45. A Generalized Cavalieri-Zu Principle
  46. A Geometric Limit
  47. A Geometry Problem from 2012 IMO - Problem 5
  48. A Hard but Important Sangaku
  49. A Hinged Realization of a Plane Tessellation [Java]
  50. A Lemma of Equal Areas [Java]
  51. A Lemma on the Road to Sawayama
  52. A Line in a Square Grid [Java]
  53. A Line in Triangle Through the Circumcenter [Java]
  54. A Matter of Collinearity: Metamorphosis of a Problem
  55. A Modified Sangaku
  56. A Multiplicative Identity of Areas in a Triangle [Java]
  57. A Note on Cavalieri's Indivisibles
  58. A Parallelogram in Triangle [Java]
  59. A Plane Filling Curve for the Year 2017
  60. A Possibly First Proof of the Concurrence of Altitudes
  61. A Problem from Greece via Peru
  62. A Problem from the 1985 Balkan Mathematical Olympiad (Shortlist)
  63. A Problem in a Configuration of Three Squares
  64. A Problem in a Special Tangential Quadrilateral
  65. A Problem In an Isosceles Right Triangle [Java]
  66. A Problem in Pentagon with Right Angles
  67. A Problem in Pentagon with Supplementary Angles
  68. A Problem in Three Pentagons [JavaScript, GeoGebra]
  69. A Problem of Acute Triangle
  70. A Problem of Two Incircles by Miguel Ochoa Sanchez
  71. A Problem on an Icy Cone
  72. A problem with equilateral triangles [Java]
  73. A Problem with Right Isosceles Triangles [JavaScript]
  74. A Problem with Three Equilateral Triangles
  75. A Problem with Two Isosceles Triangles [JavaScript]
  76. A Problem with Two Similar Rectangles
  77. A Proof Perigal and All Others After Him Missed
  78. A Property of a Median [JavaScript, GeoGebra]
  79. A Property of Angle Bisectors
  80. A Property of Circle Through the Incenter [JavaScript]
  81. A Property of Incenter Relative to Circumcircle
  82. A Property of Cyclic Quadrilateral
  83. A Property of Equiangular Polygons [Java]
  84. A Property of Inscriptible Quadrilaterals [JavaScript]
  85. A Property of Isogonal Lines [JavaScript, GeoGebra]
  86. A Property of Orthic Triangle [JavaScript, GeoGebra]
  87. A Property of Pascal's Hexagon Pascal May Have Overlooked
  88. A Property of Perspective Triangles [JavaScript, GeoGebra]
  89. A Property of Points on Excircle
  90. A Property of Points on Incircle
  91. A Property of Rhombi [Java]
  92. A Property of the Line IO [Java]
  93. A Property of the Line IO: A Bundled Statement and Proof [Java]
  94. A Property of the Line IO: a proof from the Book [Java]
  95. A Property of Trapezoid with a Right Angle
  96. A Quick Proof of cos(pi/7)cos(2.pi/7)cos(3.pi/7)=1/8
  97. A Rectangle in Three Circles by Hirotaka Ebisui
  98. A Relation in Inscribed Tetrahedra
  99. A Relation in Triangle
  100. A Restored Sangaku
  101. A Sangaku Follow-Up on an Archimedes' Lemma [Java]
  102. A Sangaku: Two Unrelated Circles [Java]
  103. A Sangaku with an Egyptian Attachment [Java]
  104. A Sangaku with Many Circles and Some [Java]
  105. A Simple Solution to a Difficult Sangaku Problem
  106. A Special Point: Intersection of the Diagonals in Quadrilateral
  107. A Special Triangle with a Line Through the Lemoine Point
  108. A square in parallel lines
  109. A Straightedge Construction of the Midpoint of a Chord Common to Two Circles
  110. A Stronger Triangle Inequality [Java]
  111. A Sushi Morsel
  112. A Theorem of M. Mansion
  113. A Three Pegs Question [Java]
  114. A Triangle in a Rhombus with a 60 Degrees Angle
  115. A Triangle of Antreas Hatzipolakis [Java]
  116. A Triangle Problem from Caucasus
  117. A Triangle With a 45 Degrees Angle in Square
  118. A Trigonometric Identity in a Right Triangle from the 1960 IMO
  119. A Trigonometric Solution to a Difficult Sangaku Problem
  120. A Two-Triangle Inequality
  121. A Two-Triangle Inequality II
  122. A View on the Circle of Apollonius [JavaScript,GeoGebra]
  123. About a Line and a Triangle [Java]
  124. Abul Wafa al-Buzjani's Proof of the Pythagorean Theorem [Java]
  125. Abutting Equilateral Triangles on a Line I [JavaScript, GeoGebra]
  126. Acute Angle Bisectors in a Right Triangle [Java]
  127. Adams' Circle [Java]
  128. Addition and Subtraction Formulas for Sine and Cosine
  129. Addition and Subtraction Formulas for Sine and Cosine II
  130. Adil Abdulayev's Inequality With Angles, Medians, Inradius and Circumradius
  131. Adil Abdullayev's Inequality With Roots and Powers
  132. Alexandru Lupas' Property of the Incenter
  133. Algebraic proof of the theorem of butterflies in quadrilaterals
  134. Algebraic-Geometric Equation
  135. All about altitudes
  136. All Triangles Are Isosceles [Java]
  137. All Trigonometric Inequality in Triangle
  138. Altitudes and the Euler Line [GeoGebra]
  139. Altitudes and the Power of a Point [Java]
  140. Altitudes Concur at a Point: a Second Look
  141. Altitudes have ears, foot, stem, and root
  142. An Affine Property of Barycenter
  143. An Algebraic Lemma with Geometric Consequences [JavaScript]
  144. An All-Inclusive Inequality
  145. An All-Inclusive Inequality II
  146. An Angle in Square Conjoint with Regular Pentagon
  147. An Angle Inequality in Simple Polygons
  148. An Appearance of a 30-60-90 Triangle
  149. An Area Inequality
  150. An Area Inequality in Right Triangle
  151. An Asymmetric Inequality
  152. An Equilateral Triangle In Parallel Lines
  153. An Euclidean Construction with Inversion [Java, GeoGebra]
  154. An Extension of a Sangaku with Touching Circles
  155. An Extension of van Schooten's Theorem
  156. An Extra Triple of Equilateral Triangles for Napoleon [JavaScript, GeoGebra]
  157. An Identity for Regular Tetrahedra
  158. An Identity in a Regular Heptagon
  159. An Identity in Bicentric Isosceles Trapezoid
  160. An Identity in (Cyclic) Quadrilaterals [JavaScript, GeoGebra]
  161. An Identity in Cyclic Quadrilateral
  162. An Identity in Triangle
  163. An Identity in Triangle II
  164. An Identity in Triangle with a 135 Degrees Angle
  165. An Inequality for the Tangent to the Incircle
  166. An Inequality in a Convex Quadrilateral
  167. An Inequality in a Nonobtuse Triangle
  168. An Inequality in Triangle for Side Lengths, Cycled in Two Ways
  169. An Inequality in Triangle with a Constraint
  170. An Inequality in Triangle with Radicals, Semiperimeter, Incenter and Inradius
  171. An Inequality in Triangle with Side Lengths and Circumradius
  172. An Inequality with Exradii and an Altitude
  173. An Identity with Inradius and Circumradii
  174. An Inequality for Sides and Area
  175. An Inequality for the Cevians through Circumcenter
  176. An Inequality for the Cevians through Spieker Point via Brocard Angle
  177. An Inequality from the 2015 Romanian TST
  178. An Inequality in Triangle with Radicals, Semiperimeter and Inradius
  179. A Cyclic Inequality from the 6th IMO, 1964
  180. A Property of Nagel Cevians
  181. An Inequality in Acute Triangle, Courtesy of Ceva's Theorem
  182. An Inequality in Cyclic Quadrilateral
  183. An Inequality in Cyclic Quadrilateral II
  184. An Inequality in Cyclic Quadrilateral III
  185. An Inequality in Cyclic Quadrilateral IV
  186. An Inequality of the Areas of Triangles Formed by Circumcenter And Orthocenter
  187. An Inequality on Circumscribed Quadrilateral
  188. An Inequality in Triangle
  189. An Inequality in Triangle II
  190. An Inequality in Triangle III
  191. An Inequality in Triangle IV
  192. An Inequality in Triangle, V
  193. An Inequality in Triangle, VI
  194. An Inequality in Triangle XI
  195. An Inequality in Triangle, Mostly with the Medians
  196. An Inequality In Triangle That Involves the Four Basic Centers
  197. An Inequality in Triangle with Altitudes, Medians And Symmedians
  198. An Inequality in Triangle, with Integrals
  199. An Inequality in Triangle with Roots and Circumradius
  200. An Inequality in Triangle, with Sines
  201. An Inequality in Triangle, with Sines II
  202. An Inequality in Triangle with the Circumradius, Inradius and Angle Bisectors
  203. An Inequality in Triangle with the Sines of Half-Angles and Cube Roots
  204. An Inequality Involving Fermat Point
  205. An Inequality Not in Triangle
  206. An Inequality of Degree 3 with Inradius
  207. An Inequality with Altitudes and Angle Bisectors
  208. An Inequality with Altitudes and Medians

    An Inequality with Angle Trisectors

  209. An Inequality with Arctangents in Triangle
  210. An Inequality with Circumradii And Distances to the Vertices
  211. An inequality with Cosines and a Sine
  212. An Inequality with Inradius and Side Lengths
  213. An Inequality with Cotangents And the Circumradius
  214. An Inequality with Tangents and Sides
  215. An Inequality with One Tangent and Six Sines
  216. An inequality with Three Points
  217. An Inequality in Triangle with Differences of the Medians
  218. An Inequality with Inradius and Circumradii
  219. An Inequality in Triangle with the Medians, Sines and Cube Roots
  220. An Inequality with Powers of Six
  221. An Inequality with Sides, Altitudes, Angle Bisectors and Medians
  222. An Inequality with Sides, Cosines, and Semiperimeter
  223. An Inequality with Sin, Cos, Tan, Cot, and Some
  224. An Inequality with Sines
  225. An Inequality with Tangents and Cotangents
  226. An Inequality with the Most Important Cevians
  227. An Inradii Relation in Inscriptible Quadrilateral [JavaScript]
  228. An Isoperimetric Problem in Quadrilateral
  229. An Isoperimetric Theorem [Java]
  230. An Old Japanese Theorem
  231. An Unexpected Pair of Similar Triangles Which Are Equal [JavaScript, GeoGebra]
  232. An Unexpected Rhombus [JavaScript, GeoGebra]
  233. An Universal Inequality for Cevians
  234. An Unusual Generalization of the Pythagorean Theorem
  235. An Unusual Generalization of the Pythagorean Theorem, a Variant
  236. Angle: An Illustrated Classification [Java]
  237. Angle Bisector in Square
  238. Angle Bisectors Cross Circumcircle
  239. Angle Bisector in Equilateral Trapezoid
  240. Angle Bisector in Parallelogram [Java]
  241. Angle Bisectors In Rectangle [Java]
  242. Angle Bisector in Touching Circles [Java]
  243. Angle Bisectors [Java]
  244. Angle Bisectors and Perpendiculars in a Quadrilateral [Java]
  245. Angle Bisectors in Ellipse [Java]
  246. Angle Bisectors in Ellipse II [Java]
  247. Angle Bisectors in a Quadrilateral [Java]
  248. Angle Bisectors in a Quadrilateral - Cyclic and Otherwise [Java]
  249. Angle Bisectors On Circumcircle [Java]
  250. Angle Chasing on Radical Axis [JacaScritp, GeoGebra]
  251. Angle Chasing in a 75-30-75 triangle
  252. Angle in Square
  253. Angle in Right Triangle
  254. An Angle Inequality in Triangle with Perpendicular Medians
  255. Angle Preservation Property [Java]
  256. Angle Subtended by a Diameter [Java]
  257. Angle Trisection, the Impossibility of Thereof
  258. Angle Trisection by Archimedes [Java]
  259. Angle Trisection by Hippocrates [Java]
  260. Angle Trisection by Paul Vjecsner [Java]
  261. Angle Trisectors on Circumcircle [Java]
  262. Angle Trisection by Paper Folding
  263. Angles in 4-5-6 Triangle [JavaScript]
  264. Angles in a Cube I [Java]
  265. Angles in a Cube II [Java]
  266. Angles in a Cube III [Java]
  267. Angles in Triangle Add to 180o
  268. Angles in a Triangle: an Exercise
  269. Angles Inscribed in an Absent Circle [Java]
  270. Another Concurrence on the 9-Point Circle [JavaScript, GeoGebra]
  271. Another Equilateral Triangle in Napoleon's Configuration [JavaScript, GeoGebra]
  272. Another Geometry Problem from 2012 IMO - Problem 1
  273. Another Golden Ratio in Semicircle
  274. Another Identity in Triangle
  275. Another Pair of Archimedean Twins - a Redux [JavaScript, GeoGebra]
  276. Another Property of Points on Incircle
  277. Another Property of the 9-Point Circle [JavaScript, GeoGebra]
  278. Another Refinement of the Ionescu-Weitzenbock Inequality
  279. Another Sangaku in Square
  280. Another Seven Circles Theorem [JavaScript, GeoGebra]
  281. Anticenter and Orthocenters [JavaScript, GeoGebra]
  282. Anticomplementary Triangle Surprise [Java]
  283. Antiparallel [Java]
  284. Antiparallel and Circumradius [JavaSCript, GeoGebra]
  285. Antiparallel via Three Reflections [Java]
  286. APMO 1995 Problem 3
  287. APMO 1998, Problem 4
  288. APMO 2002, Problem 3
  289. APMO 2003, Problem 2
  290. APMO 2004, Problem 2
  291. The Averages of Sides and Angles in a Triangle
  292. The Problem of Apollonius
  293. Approximate Construction of Regular Pentagon by A. Dürer
  294. Arbelos -- the Shoemaker's Knife [Java]
  295. Another Pair of Twins in an Arbelos [Java]
  296. Archimedes' Quadruplets [Java]
  297. Archimedes' Twin Circles and a Brother [Java]
  298. Area and Perimeter of Circle
  299. Area Inequalities in Triangle
  300. Area Inequality in Three Triangles
  301. Area of an Arbelos [Java]
  302. Area of Cevian Triangle
  303. Area of Cutoff Triangles
  304. Area of Rectangle
  305. Area of the Intersection of Two Equal Rectangles [JavaScript, GeoGebra]
  306. Area of Trapezoid
  307. Area Optimization in Trapezoid
  308. Area, Sector Area, and Segment Area of an Ellipse
  309. Areas between Two Parallelograms [JavaScript, GeoGebra]
  310. Areas in Three Squares [JavaScript, GeoGebra]
  311. Average Distance to N Points
  312. Chain of Circles on a Chord [Java]
  313. Chain of Four Intersecting Circles [JavaScript, GeoGebra]
  314. Chain of Inscribed Circles [Java]
  315. Chain of Six Intersecting Circles [JavaScript, GeoGebra]
  316. Characterization of the Symmedian Point with Medians and Orthic Triangle
  317. Characterization of Trapezoid [JavaScript, GeoGebra]
  318. Chasing Secant Angles [JavaScript]
  319. Concurrence in Arbelos [JavaScript, GeoGebra]
  320. Concurrency in Arbelos [Java]
  321. Concurrence on Angle Bisector [JavaScript, GeoGebra]
  322. Concurrent Chords in a Circle, Equally Inclined
  323. Concyclic Points in Arbelos [Java]
  324. Rectangle in Arbelos [Java]
  325. Rectangular Areas in Circle [JavaScript, GeoGebra]
  326. Red and Pink Areas
  327. Reuleaux's Triangle, Extended [GeoGebra]
  328. Small Triangle from Small Triangle
  329. Square, 45 Degrees Angle and Pythagoras' Look-alike
  330. Square, Semicircle, and Other Curves [JavaScript, GeoGebra]
  331. Squares in Arbelos [Java]
  332. Twin Segments in Arbelos [Java]
  333. Archimedean Siblings out of Wedlock, i.e., Arbelos (JavaScript, GeoGebra)
  334. Archimedes'Book of Lemmas
  335. Arbelos' Morsels [JavaScript, GeoGebra]
  336. Archimedes' Law of the Lever [Java]
  337. Archimedes' Method
  338. Archimedes' Twins in the Edo Period
  339. Area and Perimeter Splitters in a Triangle
  340. Area Inequality in Trapezoid
  341. Area Inequality in Triangle
  342. Area Inequality in Triangle II
  343. Area of a Bicentric Quadrilateral
  344. Area of a Circle by Leonardo da Vinci [Java]
  345. Area of a Circle by Rabbi Abraham bar Hiyya Hanasi [Java]
  346. Area of Isosceles Triangle
  347. Area of Median Triangle [Java]
  348. Area of Parallelogram [Java]
  349. Area of Parallelogram Formula by Shearing
  350. Area of the Union of Two Squares [Java]
  351. Area of Triangle [Java]
  352. Areas and Centroid in a Triangle [Java]
  353. Areas In Circle
  354. Areas in Square by Dissection [Java]
  355. Areas in Two Parallelograms and a Translation [JavaScript, GeoGebra]
  356. Arithmetic-Geometric Mean Inequality
  357. Arithmetic Mean Sangaku [Java]
  358. Arithmetic Mean Sangaku II [Java]
  359. Around the Incircle [Java]
  360. Around the Incircle in a Polygon [Java]
  361. Artisans vs Mathematicians
  362. Asian Pacific Kite [Java]
  363. Assigning Numbers to Points in the Plane
  364. Assimilation Illusion [Java]
  365. Axis of Similitude of Three Circles
  366. Barbier, The Theorem of [Java]
  367. Barycenter of Cevian Triangle
  368. Barycentric coordinates
  369. Batman's Problem [JavaScript, GeoGebra]
  370. Bender: A Visual Illusion [Java]
  371. Bespectacled Eyeballs Extension [JavaSCript, GeoGebra]
  372. Between a Cross and a Square (lies a Golden Ratio)
  373. Between Major and Minor Circles [Java]
  374. Bevan's Point and Theorem [Java]
  375. Beyond Pythagoras
  376. Beyond Viviani [JavaScript]
  377. Bimedians and Diagonals in a Quadrilateral
  378. Bimedians in a Regular Tetrahedron [Java]
  379. Bisectal Circle [Java]
  380. Bisecting arcs
  381. Bisecting a shape
  382. Bisection of Yin and Yang
  383. Bisector of an imaginary angle may be real
  384. Bisectors and Proportions [JavaScript]
  385. BMO 2014, Problem 3 [JavaScript, GeoGebra]
  386. Bottema Shatters Japan's Seclusion [Java]
  387. Bottema's theorem [Java]
  388. Bottles in a Wine Rack [Java]
  389. Bounded Distance
  390. Bounds for the Sum of Distances to the Vertices [JavaScript]
  391. Brahmagupta's Formula and Theorem
  392. Brahmagupta's Theorem [Java]
  393. Brahmagupta-Mahavira Identities
  394. Brianchon in Ellipse [Java]
  395. Brianchon's theorem [Java]
  396. Brick Wall Illusion [Java]
  397. Bride's Chair [Java]
  398. Brief introduction to Rational Trigonometry
  399. Brocard Point and a Relation of Circumradii
  400. Broken Chord Theorem [Java]
  401. Broken Line in Triangle
  402. Building a Bridge [Java]
  403. Building Bridges [Java]
  404. Bulging lines illusion [Java]
  405. Butterfly Theorem
  406. Cabart's Collinearity
  407. Camouflaged Butterfly
  408. Cantor Set and Function
  409. Cantor's Theorem [Java]
  410. Carnot's Theorem
  411. Carnot's Theorem
  412. Carnot's Theorem from Ptolemy's Theorem
  413. Carnot's Theorem (Generalization of Wallace's theorem) [Java]
  414. Carnot's Theorem for Conics
  415. Carpet With a Hole [Java]
  416. Carpets Theorem [Java]
  417. Casey's Theorem [Java]
  418. Cassini's Ovals and Geometric Optimization [JavaScript, GeoGebra]
  419. centers of similitude
  420. Centroid, a Characteristic Property Of
  421. Centroid and Circumcenter in Isosceles Tetrahedra
  422. Centroid and Incenter in Isosceles Tetrahedra
  423. Centroid on the Incircle in Isosceles Triangle
  424. Centroid on the Incircle in Right Triangle
  425. Centroids and Circumcenters
  426. Centroids in a Polygon [Java]
  427. Cevian Parallelogram [JavScript, GeoGebra]
  428. Chasing Angles Among Angle Bisectors [JavaScript]
  429. Chasing Angles in Pascal's Hexagon [Java]
  430. Circle, Isosceles Triangle and Fixed Point [Java]
  431. Circle Center by Paperfolding
  432. Circle Centers on Radical Axes [Java]
  433. Circle Chains on Napoleon Triangles [Java]
  434. Circle Concurrence on Circumcircle/a> [JavaScript, GeoGebra]
  435. Circle in a Square Inscribed in a Circle [Java]
  436. Circle Rotations and Fixed Points
  437. Circles in Barycentric Coordinates
  438. Circles on the sides of a triangle from the 2005 Austrian MO
  439. Circles Tangent to Circumcircle [Java]
  440. Circles Tangent to Medians at the Centroid [JavaScript, GeoGebra]
  441. Circles with Tangent Diameters [Java]
  442. Ceva and Menelaus Meet on the Roads
  443. Ceva in Circumscribed Quadrilateral
  444. Ceva's Theorem
  445. Ceva's Theorem and Fibonacci Bamboozlement [Java]
  446. Cevian Cradle [Java]
  447. Cevian Cradle II [JavaScript, GeoGebra]
  448. Cevian Nest [Java]
  449. Cevian Triangle [Java]
  450. Cevians And Semicircles [JavaScript]
  451. Cevians Through the Circumcenter
  452. Chain of Inscribed Circles [Java]
  453. Chaos, Emergence of [Java]
  454. Characteristic Property Of Right Triangles
  455. Chasles' Theorem
  456. Cherchez le quadrilatère cyclique [Java]
  457. Cherchez le quadrilatère cyclique II [Java]
  458. Chords, Concurrency and Orthic Triangle [Java]
  459. Chromatic Number of the Plane
  460. Chvatal's Art Gallery Theorem [Java]
  461. Circle and Hyperbola as Lighthouse Curves
  462. Circle and Hyperbola as Lighthouse Curves II
  463. Circle Crosses Triangle [Java]
  464. Circle Concurrency and Spiral Similarity [Java]
  465. Circle Division by Euclid and Leonardo [Java]
  466. Circle of Apollonius in Equilateral Triangle
  467. Circle of Similitude [Java]
  468. Circle Rotations and Fixed Points [JavaScript, GeoGebra]
  469. Circle through the Circumcenter [Java]
  470. Circle through the Incenter [Java]
  471. Circle through the Incenter And Antiparallels [Java]
  472. Circle-Stacking Theorem [Java]
  473. Circles And Parallels [Java]
  474. Circles and Semicircles in Rectangle [Java]
  475. Circles Cover a Quadrilateral [Java]
  476. Circles in a Circular Segment
  477. Circles in a Regular Polygon [Java]
  478. Circles in Morley's Triangles [Java]
  479. Circles Lined on the Legs of a Right Triangle [Java]
  480. Circles On Cevians [Java]
  481. Circles through the Orthocenter [Java]
  482. Circles with Equal Collinear Chords [Java]
  483. Circular Poggendorff Illusion [Java]
  484. Circle Inscribed in a Circular Segment [Java]
  485. Circumcenter and Orthocenter
  486. Circumcenter and Orthocenter Are Isogonal Conjugate
  487. Circumcenter on Angle Bisector [Java]
  488. Circumcevian Triangle [Java]
  489. Classification of Quadrilaterals [Java]
  490. Cleavance Center [Java]
  491. Cleaver [Java]
  492. Clifford Algebras
  493. Clifford's Chain [Java]
  494. Climbing Pyramidal Slopes
  495. Clough's theorem: the simplest proof [JavaScript, GeoGebra]
  496. Coaxal Circles on Perpendicular Bisector [Java]
  497. Coaxal Circles Theorem [Java]
  498. Collage Theorem [Java]
  499. Collinear Intersections and Products of Ratios [JavaScript, GeoGebra]
  500. Collinearity from the IMO 2013 (Problem 4) [Javacript, GeoGebra]
  501. Collinearity in Bicentric Quadrilaterals [Java]
  502. Collinearity in Tangent Circles
  503. Collinearity via Concyclicity [Java]
  504. Collinearity with the Orthocenter [Java]
  505. Color Cycling on the Mandelbrot Set [Java]
  506. Coloring Plane with Three Colors
  507. Coloring Points in the Plane
  508. Common Centroids Lead to Equilateral Triangle [JavaScript, GeoGebra]
  509. Common Chord and a Tangent [Java]
  510. Common Tangents to Two Circles I [Java]
  511. Common Tangents to Two Circles II [Java]
  512. Compass Only Construction - A Chord Tangent to an Inner circle [Java, GeoGebra]
  513. Complete Quadrilateral [Java]
  514. Complex Numbers and Geometry
  515. >Concurrence in Right Triangle
  516. Concurrence on a Circle [JavaScript, GeoGebra]
  517. Concurrence Not from School Geometry [Java, GeoGebra]
  518. Concurrency of Medians and Medial Triangles
  519. Concurrency of the Altitudes in a Triangle - Trigonometric Proof
  520. Concyclic Points at the IMO 2014 [JavaScript, GeoGebra[
  521. Concyclicity in Rectangle [Java]
  522. Concurrence in Equilateral Triangle [JavaScript,GeoGebra]
  523. Concurrence of Ten Nine-Point Circles [JavScript, GeoGebra]
  524. Concurrency in the Intouch Triangle [Java]
  525. Concurrent and Parallel Lines in Parallelogram [JavaScript, GeoGebra]
  526. Concurrent Cevians and a Conic through Their Feet [JavaScript, GeoGebra]
  527. Concyclic Points from Midpoint of an Arc [GeoGebra, JavaScript]
  528. Concyclic Incenters in Bicentric Quadrilateral [JavaScript, GeoGebra]
  529. Concyclic Points in Inscriptible Quadrilateral [JavaScript, GeoGebra]
  530. Concyclicity from Collinearity [JavaScript,GeoGebra]
  531. Concyclicity in Two Semicircles [JavaScript, GeoGebra]
  532. Concyclic Points of Two Ellipses with Orthogonal Axes [JavaScript, GeoGebra]
  533. Condition to Have a 60 Degrees Angle
  534. Concyclic Circumcenters: A Dynamic View [Java]
  535. Concyclic Points in a Triangle
  536. Concyclic Points in Bride's Chair [Java]
  537. Concyclic Points in Equilateral Bumps [Java]
  538. Conic from Parallel Chords [JavaScript, GeoGebra]
  539. Conic in Hexagon [Javascript, GeoGebra]
  540. Conic in Mixtilinear Incircles [JavaScript, GeoGebra]
  541. Conic Sections
  542. Conic Sections as Loci of Points [Java]
  543. Conics Intersecting Sides Of A Triangle [JavaScript, GeoGebra]
  544. Conics in Triangle [JavaScript, GeoGebra]
  545. Conics Related To In- and Excircles [JavaScript, GeoGebra]
  546. Conjugate Diameters in Ellipse [Java]
  547. Consecutive Isosceles Decomposition [Java]
  548. Constant Chord
  549. Constrained Area in Triangle
  550. Constant Ratio on Circle [JavaScript, GeoGebra]
  551. Construct Triangle from Angle, Inradius, and Altitude [JavaScript, GeoGebra]
  552. Construct Triangle by Angle, Median, and Circumradius [JavaScript, GeoGebra]
  553. Construct Triangle by Angle Bisector, Altitude, and Side [JavaScript, GeoGebra]
  554. Construct Triangle by Angle, Altitude and Median [JavaScript, GeoGebra]
  555. Construct Triangle from Altitude, Median and Inradius [JavaScript, GeoGebra]
  556. Constructing a triangle from its angle bisectors is in general impossible
  557. Construction: Parallel Line through Point
  558. Construction and Properties of Mixtilinear Incircles [JavaScript, GeoGebra]
  559. Construction and Properties of Mixtilinear Incircles 2 [JavaScript, GeoGebra]
  560. Construction of a Cyclic Quadrilateral
  561. Construction of a Square from the 2008 Austrian MO
  562. Construction of a Triangle from an Angle, Circumcenter and Incenter
  563. Construction of a Triangle from the Circumcenter, Orthocenter and Incenter
  564. Construction of a Triangle from the Circumradius, Inradius, and an Altitude
  565. Construction of a Triangle from a Side, the Median and the Angle Bisector
  566. Construction of a Triangle from Two Vertices and the Centroid
  567. Construction of an Oval - the Roman Way [Java, GeoGebra]
  568. Construction of Conics from Pascal's Theorem [Java]
  569. Construction of Regular Pentagon by H. W. Richmond
  570. Construction of Thebault Circles [JavaScript, GeoGebra]
  571. Construction of the Angle Bisector [Java]
  572. Construction of the Perpendicular Bisector [Java]
  573. Construction of Triangle from Side, Angle, and that Angle's Bisector
  574. Construction problem [Java]
  575. Constructions Related To An Inaccessible Point
  576. Construction with the Compass Only
  577. Continuous Line Illusion [Java]
  578. Convex Polygon Is the Intersection of Half Planes [Java]
  579. Copernicus' Theorem [Java]
  580. Construction with Optimization in Angle - Problem the 1979 USA Mathematical Olympiad
  581. cos(36°) = (1 +5)/4
  582. cos 75 + cos 45 = cos 15
  583. Cosine Law
  584. Counting Triangles and Segments in a Polygon [Java]
  585. Cross Points in a Polygon [Java]
  586. Cross-Ratio
  587. Crossed-Lines Construction of Shapes of Constant Width [Java]
  588. Crossing Number of a Graph
  589. Cube Counting Ambiguity [Java]
  590. Cultivating Regular Pentagons
  591. Curious Irrationality in Square
  592. Curry's Paradox [Java]
  593. Cut the Cone [Java]
  594. Cut the Cube [Java]
  595. Cutting a Cube into Smaller Ones
  596. Cutting a Hole in Half [JavaScript, GeoGebra]
  597. Cut the Cylinder [Java]
  598. Cutting Circle to Rearrange Two Dots [JavaScript]
  599. Cutting Squares
  600. Cutting Triangle in Two by a Line through a Point [Java, GeoGebra]
  601. Cutting Triangles off Regular Hexagon
  602. Cyclic Hexagon [Java]
  603. Cyclic Quadrilateral, Angle Bisector And Isosceles Triangle
  604. Cyclic Quadrilateral, Concurrent Circles and Collinear Points [Java]
  605. Cyclic Quadrilateral from the USAMO
  606. Cycloids [Java]
  607. Dan Sitaru's Inequality with Radicals and Cosines
  608. Dan Sitaru's Inequality with Tangents II
  609. Dancing Rectangles Model Auxetic Behavior [Java]
  610. Dancing Squares or a Hinged Plane Tessellation [Java]
  611. Dao's Archimedean Twins [JavaScript, GeoGebra]
  612. Dao's Archimedean Twins - Second Pair [JavaScript]
  613. Dao's Archimedean Twins - Third Pair [JavaScript]
  614. Dao Thanh Oai's Invariant
  615. Dao's Variant of Thébault's First Problem [JavaScript, GeoGebra]
  616. David Richeson's Extention of an Old Japanses Theorem [Java]
  617. Day's Sine Illusion [Java]
  618. Decompose Cyclic Quadrilaterals into k≥4 Cyclic Quadrilaterals
  619. A Decomposition of Isosceles Triangles into 4 Isosecles Triangles
  620. Delboeuf Illusion [Java]
  621. Delian Problem Solved [Java]
  622. Desargues' Hexagon [Java, GeoGebra]
  623. Desargues in the Bride's Chair (with Pythagoras)
  624. Desargues' Theorem [Java]
  625. Determination ofπ
  626. Diagonal Count [Java]
  627. Diagonals in a Cyclic Quadrilateralli>Diagonals in a Polygon Parallel to Sides <
  628. Diameters and Chords [Java]
  629. Dimensionless Inequality in the Euclidean Plane
  630. Directly Similar Figures [Java]
  631. Disappearing Lines puzzle [Java]
  632. Discovery of Duane DeTemple [Java]
  633. Dissection of a 10×13 Rectangle into Two Chessboards
  634. Dissection of a Vase [Java]
  635. Dissection of Cyclic Quadrilateral [Java]
  636. Dissection of Triangle into Rhombus [Java]
  637. Dissection of Triangle into Rhombus by Hubert Shutrick [Java]
  638. Distance
  639. Distance Between Projections
  640. Distance between the Orthocenter and Circumcenter
  641. Distance Formula
  642. Distorted Lines Illusion [Java]
  643. Divergent Spirals Illusion [Java]
  644. Divide a Circle into N Parts of Equal Area
  645. Divide a segment into n equal parts
  646. Divide Triangle by Lines Parallel to Base [JavaScript, GeoGebra]
  647. Dividing Evenly a Quadrilateral [Java]
  648. Dividing Evenly a Quadrilateral II [Java]
  649. Dorin Marghidanu's Inequality with Maximum Side
  650. Double Generation Theorem [Java]
  651. Drawing circles [Java]
  652. Droz-Farny Circles [Java]
  653. Droz-Farny Line Theorem [Java]
  654. Droz-Farny Theorem - an Analytic Solution [JavaScript, GeoGebra]
  655. Dual of Maxwell's Theorem
  656. Duplication of the Cube
  657. Dynamic Construction of Ellipse and Other Curves [Java]
  658. Dynamic Software as Serendipity Enhancement [Java, GeoGebra]
  659. A. G. Samosvat's Proof by Dissection of the Pythagorean Theorem (#104) [GeoGebra]
  660. E. W. Dijkstra's Proof of the Pythagorean Theorem [Java]
  661. Early Refinement of the Ionescu-Weitzenbock Inequality
  662. Easy Construction of Bicentric Quadrilateral [Java]
  663. Easy Construction of Bicentric Quadrilateral II [Java]
  664. Egyptian Triangle By Paper Folding
  665. Egyptian Triangle By Paper Folding II
  666. Egyptian Triangle By Paper Folding III
  667. Eight Equal Tangents [Java]
  668. Eight Point Circle [Java]
  669. Elementary Introduction into the Concept of Area
  670. Ellipse Between Two Circles [Java]
  671. Ellipse in Arbelos [Java]
  672. Ellipse Touching Sides of Triangle at Midpoints [Java, GeoGebra]
  673. Emil Stoyanov's From Reflections to Altitudes
  674. Emil Stoyanov's New Year's Problem
  675. Emil Stoyanov's New Year's Problem, a Sequel
  676. Equal And Perpendicular Segments in a Square
  677. Equal Angles in Two Circles [Java]
  678. Equal Angles in Two Circles II [Java]
  679. Equal areas In Circle [JavaScript]
  680. Equal Areas in Equilateral Triangle [Java]
  681. Equal Areas In Parallelogram à la Pythagoras [Java]
  682. Equal Areas in Regular 2n-gons [Java]
  683. Equal Chords in Crossing Circles [Java]
  684. Equal Circles, Medial Triangle and Orthocenter [Java]
  685. Equal Incircles Theorem [Java]
  686. Equiangular p-gons
  687. Equichordal points: Just Do It [Java]
  688. Equidecomposition of a Rectangle and a Square [Java]
  689. Equidecomposition of Two Rectangles [Java]
  690. Equidecomposition of a Triangle and a Rectangle [Java]
  691. Equidecomposition of a Triangle and a Rectangle II [Java]
  692. Equidecomposition of Two Parallelograms [Java]
  693. Equilateral and 3-4-5 Triangles [Java]
  694. Equilateral triangle and squares
  695. Equilateral Triangle from Equilateral Triangle
  696. Equilateral Triangle from Three Centroids
  697. Equilateral Triangle In a Pretty Diagram
  698. Equilateral Triangle in Equilateral Triangle [JavaScript, GeoGebra]
  699. Equilateral Triangle on a Closed Curve [JavaScript, GeoGebra]
  700. Equilateral Triangle on Angle Bisectors
  701. Equilateral Triangle on Parallel Lines [Java]
  702. Equilateral Triangle on Parallel Lines II
  703. Equilateral Triangle on Three Lines [JavaScript, GeoGebra]
  704. Equilateral Triangle in Square and Its Circumcircle
  705. Equilateral Triangle in Square with the Cevians through Its Apex
  706. Equilateral Triangle in Square And the Pedal Circle of Its Apex
  707. Equilateral Triangle, Straight Line and Tangent Circles [Java]
  708. Equilateral Triangles and Incircles in a Square
  709. Equilateral Triangles formed by Circumcenters [JavaScript, GeoGebra]
  710. Equilateral Triangles on Diagonals of Antiequilic Quadrilateral [Java]
  711. Equilateral Triangles On Sides of a Parallelogram [Java]
  712. Equilateral Triangles On Sides of a Parallelogram II [Java]
  713. Equilateral Triangles on Sides of a Parallelogram III [JavaScript, GeoGebra]
  714. Equilateral Triangles on Sides of a Quadrilateral [Java]
  715. Equilic Quadrilateral I, a Flawed Proof [Java]
  716. Equilic Quadrilateral I, A Variation [Java]
  717. Equilic Quadrilateral II [Java]
  718. Erdös-Mordell Inequality
  719. Escher's Theorem [Java]
  720. Euclid's Fifth Postulate
  721. Euclid'sElements Reference Page
  722. Euclid I.43 [Java]
  723. Euclid I.43 Extended [Java]
  724. Euclidean Construction of Center of Ellipse [Java]
  725. Euclidean Construction of Tangent to Ellipse
  726. Euler Inequality in Triangle
  727. Euler Line Cuts Off Equilateral Triangle [Java]
  728. Euler Line and 9-Point Circle [Java]
  729. Euler Line Through a Vertex
  730. Euler's Formula and Poncelet Porism
  731. Euler Line in a Triangle with a 60 Degrees Angle
  732. Every Parallelogram Is a Rectangle
  733. Excircle in Equilateral Triangle
  734. Excircles in Trapezoid
  735. Exeter Point [Java, GeoGebra]
  736. Existence of the Circumcenter [Java]
  737. Existence of the Orthocenter [GeoGebra]
  738. Existence of the Euler Line: An Elementary Proof [Java]
  739. Existence of the Incenter: a Second Look
  740. Experimentation with Dynamic Geometry Software: An Example [Java]
  741. Exploring Vecten's Wreaths with Linear Algebra
  742. Expressions Invariant under Projecive Mappings
  743. Exterior Angle Theorem - an appreciation
  744. External Angle Bisector [Java]
  745. Extouch Triangle in Poncelet Porism [Java]
  746. Extra Feature of Van Aubel Configuration [JavaScript,GeoGebra]
  747. Extras in Bottema's Configuration [JavaScritpt, GeoGebra]
  748. Extremal Problem in a Quadrilateral
  749. Extremal Distance Ratio [GeoGebra]
  750. Extremal Problem in a Circular Segment
  751. The Extreme Principle
  752. Eye-to-Eye Theorem I [JavaScript, GeoGebra]
  753. Eye-to-Eye Theorem II [JavaScript, GeoGebra]
  754. Eyeball Theorem [JavaScript, GeoGebra]
  755. Eyeball Theorem Rectified [JavaScript]
  756. Eyeballing a Ball [JavaScript, GeoGebra]
  757. Eyeballs Projected [JavaScript, GeoGebra]
  758. Fagnano's problem [Java]
  759. Faulty Symmetry
  760. Fermat's Hexagon [JavaScript, GeoGebra]
  761. Fermat in a Triangle with a 60 Degrees Angle
  762. Fermat point and 9-point Centers [Java]
  763. Fermat Point Several Times Over
  764. Feuerbach's Theorem: A Proof [Java]
  765. Find a Common Chord of Given Length [Java]
  766. Find the Angle! [Java]
  767. Finding a Parallelogram in 3D
  768. Finding Circle Center By Ruler Alone [Java]
  769. Finding the Circumradius of the Excentral Triangle
  770. Five Concyclic Points [Java]
  771. Five Incircles in a Square [Java]
  772. Five Incircles Theorem [Java]
  773. Five Squares in Complex Numbers [Java, GeoGebra]
  774. Fixed Point in a Kite - Problem from the 1993 Asian Pacific MO
  775. Fixed Point in Isosceles and Equilateral Triangles
  776. Fixed Point on Perpendicular Bisector [GeoGebra, JavaScript]
  777. Fixed Point of Circles Orthogonal to the Given One [Java]
  778. Fixed points from 2007 Irish Mathematical Olympiad
  779. Fleury's Algorithm and Euler's Paths and Cycles [Java]
  780. FJG Capitan's Sangaku
  781. Focal Definition of Ellipse [Java]
  782. Focal Definition of Parabola [Java, GeoGebra]
  783. Focus and Directrix of Ellipse [Java]
  784. Focus on the Eyeball Theorem [JavaScript, GeoGebra]
  785. Folding and Cutting a Square
  786. Folding Square in a Line through the Center [Java, GeoGebra]
  787. Fold Square into Equilateral Triangle [JavaScript]
  788. Following the Hilbert Curve [Java]
  789. Foot of Altitude and Minimum Distance [Java]
  790. For Equality Choose Angle Bisector [JavaScript, GeoGebra]
  791. For every object there is a distance at which it looks its best.
  792. Ford's touching circles
  793. Four Centroids and Parallels [Java]
  794. Four Circles and a Line [GeoGebra]
  795. Four Circles In a Triangle [Java]
  796. Four Concurrent Lines in a Cyclic Quadrilateral [Java]
  797. Four Construction Problems [Java]
  798. Four Crossing Circles [Java]
  799. Four Geometric Problems of Antiquity
  800. Four Golden Circles
  801. Four Hinged Squares [Java]
  802. Four Incident Circles [Java]
  803. Four Incircles in Equilateral Triangle [Java]
  804. Four Isosceles Triangles Hinged at Vertices [JavaScript, GeoGebra]
  805. Four 9-Point Circles in a Quadrilateral [Java]
  806. Four Pedal Circles [Java]
  807. Four Touching Circles [Java]
  808. Four Touching Circles II [Java]
  809. Four Touching Circles III [Java]
  810. The Four Touching Circles Problem IV [Java, GeoGebra]
  811. Four Triangles, One Circle [Java]
  812. Four Turtles (or Bugs, or Dogs, etc.) [Java]
  813. Fractal curves and dimension [Java]
  814. François Viète's Reduction of CCC to PCC [Java, GeoGebra]
  815. Friendly Kiepert's Perspectors [Java]
  816. From 3 to Golden Ratio in Semicircle
  817. From Angle Bisector to 120°120 degrees Angle
  818. From Arbitrary Hexagon to Regular One [JavaScript, GeoGebra]
  819. From Arbitrary Pentagon to Regular One [JavaScript, GeoGebra]
  820. From Equilateral Triangle and Square to Golden Ratio
  821. From Foci to a Tangent in Ellipse [Java]
  822. From One Collinearity to Another
  823. From Perpendicular Center Lines to Concyclic Points
  824. From Straight Line to Regular Hexagon [JavaScript, GeoGebra]
  825. From Triangle Inequality to Inequality in Triangle
  826. Fun Identity in Right Triangle
  827. Functions And Triangles
  828. Fundamental Theorem of 3-Bar Motion [Java]
  829. Further Arithmetic Progression in 30-60-90 Triangle
  830. Further Properties of Peculiar Circles
  831. Further properties of Van Aubel Configuration [JavaScript, GeoGebra]
  832. Fuss' Theorem [Java]
  833. Garcia's Archimedean Quadruplets [JavaScript, GeoGebra]
  834. Garcia's Two Circles Lemmas [JavaScript, GeoGebra]
  835. Garcia-Feuerbach Collinearity [JvaScript, GeoGebra]
  836. Garfield's Ghost Revisited - by Tony Foster
  837. Generalizing a Romanian Olympiad Problem [Java]
  838. Geometric/Trigonometric Observation/Exercise
  839. Geometric Illustration of a Convergent Series
  840. Geometric Mean In Trapezoid
  841. Geometric Mean Sangaku
  842. Geometric Meaning of the Geometric Mean
  843. Geometric Optimization from the Asian Pacific Mathematical Olympiad [Java]
  844. Geometric Proof of Hlawka's Inequality
  845. Geometric Proofs Of the Irrationality of Square Roots
  846. Geometry, Algebra, and Illustrations
  847. Gergonne and Medial Triangles Are Orthologic [Java]
  848. Gergonne and Soddy Lines Are Perpendicular [Java]
  849. Gergonne in Ellipse [Java]
  850. Gergonne and Van Obel Theorems
  851. Getting the first digits of Pi by counting collisions
  852. Gion Shrine Problem
  853. Given Parabola, Find Axis
  854. Glide Reflection [Java]
  855. Golden Ratio in Geometry
  856. Golomb's inductive proof of a tromino theorem [Java]
  857. Gothic Arc [Java]
  858. Graph Theory [Java]
  859. Grebe: from Ladies' Diary to Carroll's Pillow [Java]
  860. Grebe's Theorem
  861. Greg Markowsky's Problem for Parabola [Java]
  862. Gregoie Nicollier's Proof of Napoleon's Theorem
  863. Griffiths Points in Cyclic Quadrilateral [Java]
  864. Griffiths' Theorem
  865. Half Turn, Reflection in Point [Java]
  866. Halving a square
  867. Harmonic Mean in Geometry
  868. Harmonic Mean Sangaku [Java]
  869. Harmonic Ratio
  870. Harmonic Ratio in Complex Domain
  871. Hart Circle [Java]
  872. Hart's Inversor [Java]
  873. Haruki's Lemma [Java]
  874. Haruki's Theorem
  875. Hausdorff Distance
  876. Hearty Munching on Cardioids [Java]
  877. Height/Width Interplay Illusion [Java]
  878. Helly's Theorem
  879. Hering Illusion [Java]
  880. Hermann Grid Illusion [Java]
  881. Heron's formula
  882. Heron's Formula: a Proof [Java]
  883. Heron's Problem [Java]
  884. Heron in Trapezoid [JavaScript, GeoGebra]
  885. Hexagon Parallel to Medial Triangle [Java]
  886. Hexagon Parallel to Orthic Triangle [Java]
  887. Hexagons in a Square
  888. Hidden Orthogonality [JavaScript, GeoGebra]
  889. Hinged Greek Cross Tessellation [Java]
  890. Hinged Squares [Java]
  891. Hinged Squares II [JavaScript, GeoGebra]
  892. Hippocrates' Squaring of a Lune [Java]
  893. Hippocrates' Squaring of Lunes
  894. Hjelmslev Theorem [Java]
  895. Hlawka in Convex Quadrilateral
  896. Homologous Lines under Three Spiral Similarities [Java]
  897. Homothety [Java]
  898. Homothety between In- and Excircles [Java]
  899. Homothety in Equilateral Triangles [JavaScript, GeoGebra]
  900. Homothety in Three Tangent Circles
  901. Homothety in Three Tangent Circles II
  902. Hooper's Paradox [Java]
  903. How Do Angle Trisectors Divide the Area?
  904. How Fast Does One's Shadow Grow?
  905. How Long Are the Angle Bisectors of a Degenerate Triangle?
  906. How to Construct a Radical Axis [Java, GeoGebra]
  907. How to Construct Tangents from a Point to a Circle [Java, GeoGebra]
  908. Hung Nguyen Viet's Inequality with Radicals and Chebyshev
  909. Hunting Right Angles [Java]
  910. Huygens' Problem
  911. Ian McGee's Observation [Java]
  912. IMO 1998 Problem 1
  913. IMO 2004, Problem 5
  914. IMO 2006, Problem 1
  915. Impossible Fork [Java]
  916. Impossible Frame [Java]
  917. Impossiblity Condition in Concurrent Cevians
  918. Importance of Having an Angle of 60 Degrees
  919. Importance of Occluders: Motion Binding [Java]
  920. In the Spirit of Thebault I [Java, GeoGebra]
  921. In the Wasan Spirit
  922. Incenters in Cyclic Quadrilateral [Java]
  923. Incidence in Feuerbach's Theorem [Java]
  924. Incircle in Equilateral Triangle
  925. Inequalities in Triangle
  926. Inequality in Quadrilateral
  927. Inequality in Rectangle
  928. An Inequality with a Variety of Circumradii
  929. Inequality with Cubes and Cube Roots
  930. An Inequality with Inradius and Excenters
  931. Inequality with Roots, Squares and the Area
  932. An Inequality with Two Sets of Cevians
  933. Infinitude of Primes - A Topological Proof
  934. Inradii Relation in Right Triangle
  935. Inscribed and Central Angles in a Circle [Java]
  936. Inscribed Angles [Java]
  937. Inscriptible and Exscriptible Quadrilaterals [Java]
  938. Inscriptible Quadrilateral: An Illustration [Java]
  939. Inscriptible Quadrilateral of Triangle Incenters [JavaScript, GeoGebra]
  940. Integer Chord in a Polynomial Graph
  941. Integer Triangles with Two Angles in the Ratio 1 : 2 [JavaScript, GeoGebra]
  942. Internal Tangents to Three Circles [Java]
  943. Interpretation of the coordinate formula for the dot product in 3D
  944. Intersecting Chords Theorem
  945. Intersections of a Circle with the Four Quadrants [Java]
  946. Intouch Triangle in Poncelet Porism [Java]
  947. Invariance in Orthodiagonal Quadrilaterals [Java]
  948. Invariant Area Sweep Implies Pythagorean Theorem [Java]
  949. Inverse Similarity through Reflections
  950. Inversion: Reflection in a Circle [Java]
  951. Involution on the Projective Line
  952. Is Every Trapezoid Parallelogram? [Java]
  953. Is X a Midpoint of a Chord [JavaScript, GeoGebra]
  954. Isosceles Tetrahedra Characterization via Inequalities
  955. Isogonal Concurrencies [JavaScript, GeoGebra]
  956. Isogonal Lemma [JavaSCript, GeoGebra]
  957. Isosceles Configuration in Triangle [JavaScript, GeoGebra]
  958. Isosceles Tetrahedron
  959. Isosceles Trapezoid In Cyclic Quadrilateral [JavaScript, GeoGebra]
  960. Isosceles Triangle with Two Points on Base
  961. Isogonal and Isotomic Conjugalities [Java]
  962. Isogonal Concurrency [Java]
  963. Isogonal image of the circumcircle [Java]
  964. Isoperimetric Theorem and Inequality
  965. Isosceles on the Sides of a Triangle [Java]
  966. Isotomic Reciprocity [JavaScript, GeoGebra]
  967. Isotomy and Isogonality Hand-in-Hand [Java]
  968. Iterations and the Mandelbrot Set [Java]
  969. Iterations on a Circle Through Three Points [Java]
  970. Iterations on Euler Lines [Java]
  971. Igor Sharygin's Problem in Circumscribed Quadrilateral
  972. J. Casey's Additions to Euclid I.47
  973. Jan Stevens' proof of E. W. Dijkstra's Generalization of the Pythagorean theorem
  974. Joachimsthal's Notations
  975. John Sharp's Paradox [Java]
  976. Johnson Circles [Java]
  977. Join Circles by Given Segment [Java]
  978. Joined Common Chords of Napoleon's Circumcircles [JavaScript, GeoGebra]
  979. Jordan and Kober Inequalities, PWW
  980. Jordan Curve Theorem
  981. Joseph Keech in Bride's Chair [Java]
  982. Judd Illusion [Java]
  983. Julia sets indexing [Java]
  984. K. Knop's Problem with Two Regular Pentagons And an Equilateral Triangle
  985. Kanizsa Triangle [Java]
  986. Kiepert's Centroid [JavaScript, GeoGebra]
  987. Kiepert's Theorem [Java]
  988. Kiepert's Triangles Graduate to Ears of Arbitrary Shape [JavaScript, GeoGebra]
  989. Klamkin's Quickie via Peru Geometrico
  990. Knots [avi movie]
  991. Knots on a Torus [Java]
  992. Kürschak's Tile and Theorem [Java]
  993. La Hire's Theorem [Java]
  994. Langman's Paradox [Java]
  995. LCC: Apollonius' Problem with Two Circles and a Line [Java, GeoGebra]
  996. Lean Napoleon's Triangles [Java]
  997. Length of a Median
  998. Length of the diagonal of the unit square equals the square root of 2
  999. Lennes' Polyhedron [Java]
  1000. Leo's Lemma, Second Application
  1001. Leo Giugiuc's Inequality for the Medians
  1002. Leo Giugiuc's Inequality in Triangle, Solely with Cotangents
  1003. Leo Giugiuc's Proof of Napoleon's Theorem
  1004. Leo Giugiuc's Trigonometric Lemma
  1005. Leo Giugiuc's Second Lemma And Applications
  1006. Leonardo's Petals
  1007. Lepidoptera of the Circles [Java]
  1008. Leuenberger's Inequality for Medians, Inradius and Circumradius
  1009. Lighthouse at Fermat Points [JavaScript, GeoGebra]
  1010. Line IO in Bicentric Quadrilaterals
  1011. Line Not Through a Center of Similarity [JavaScript, GeoGebra]
  1012. Line Through a Center of Similarity [JavaScript, GeoGebra]
  1013. Line through a Point in an Angle
  1014. Line, Circle, and Fixed Points [Java]
  1015. Linear Function with Coefficients in Arithmetic Progression [Java, GeoGebra]
  1016. Lines Crossing Circles at Vertices of Equilateral Triangle
  1017. Lines through Circles at Vertices of Equilateral Triangle [JavaScript]
  1018. LLC: Apollonius' Problem with Two Lines and a Circle [Java, GeoGebra]
  1019. Lipogrammatic Proof of the Pythagorean Theorem
  1020. Loci of points in a cube
  1021. Locus of Points in a Given Ratio to Two Points [Java]
  1022. Longest segment
  1023. Longitude, Latitude and Distance to the Equator
  1024. Looking Back at Bottema [JavaScript, GeoGebra]
  1025. Lorian Saceanu's Inequality for All Triangles
  1026. Lorian Saceanu's Sides And Angles Inequality
  1027. Luca Moroni's Problem In Equilateral Triangle
  1028. Mach's Conservation of Area and the Pythagorean Theorem
  1029. MacLaurin's Construction of Conics [Java]
  1030. Maimed Cake [Java]
  1031. Malfatti's Problem [Java]
  1032. Malfatti's Problem, Hart's Solution [Java]
  1033. Marian Cucoanes' Inequality With Roots and Powers
  1034. Marian Dinca's Inequality
  1035. Mascheroni Construction of a Regular Pentagon
  1036. Mathematical Droodles [Java]
  1037. Mathematics in Pizzeria [Java]
  1038. MathPro Logo [Java]
  1039. Maximal Properties of the Pythagorean Relation
  1040. Maximum Area Property of Equilateral Triangles
  1041. Maximum Area Property of the Medial Triangle
  1042. Maximum Perimeter Property of the Incircle [Java]
  1043. Maximum Ratio of Similarity - Belarus Olympiad Problem
  1044. Maxwell's Theorem [Java]
  1045. May the Product of Planes Be a Sphere?
  1046. McDougall's Generalization of Ptolemy's Theorem
  1047. Mechanical Proofs of the Pythagorean Theorem
  1048. Median in Touching Circles [Java]
  1049. Medians
  1050. Medians in a Quadrilateral [Java]
  1051. Medians in a Triangle Meet at the Center: a Second Look
  1052. Mehmet Sahin's Identity in Triangle
  1053. Meisters' Two Ears Theorem
  1054. Menelaus Theorem [Java]
  1055. Metric Relations in a Triangle
  1056. Mickey Might Be a Red Herring in the Mickey Mouse Theorem
  1057. Midline in Quadrilateral [Java, GeoGebra]
  1058. Midline in Similar Triangles [Java]
  1059. Midline in Trapezoid [Java, GeoGebra]
  1060. Midline in Triangle [Java, GeoGebra]
  1061. Midpoint Reciprocity in Napoleon's Configuration [JavaScript,GeoGebra]
  1062. Midpoints and Orthogonality in Isosceles Triangles [Java]
  1063. Midpoints from Gergonne Triangle [Java]
  1064. Midpoints of the Lines Joining In- and Excenters [Java]
  1065. Miguel's Area of Square [JavaScript, GeoGebra]
  1066. Miguel's Tangents: Modern Day Sangaku [JavaScript, GeoGebra]
  1067. Miguel Ochoa's Chords And Tangents [JavScript, GeoGebra]
  1068. Miguel Ochoa's van Schooten Is a Slanted Viviani [JavScript, GeoGebra]
  1069. Miguel Ochoa's van Schooten Like Theorem [JavaScript, GeoGebra]
  1070. Miguel Ochoa's van Schooten Like Theorem II [JavaScript, GeoGebra]
  1071. Miguel Ochoa's van Schooten Like Theorem III [JavaScript, GeoGebra]
  1072. Miguel's Special Trapezoid
  1073. Mikhalev's Octahedrons
  1074. Minesweeper Theorem
  1075. Miquel's Point [Java]
  1076. Miquel's Point of a 4-line Via Spiral Similarity [Java]
  1077. Miquel's Theorem for Circles [Java]
  1078. Miquel Circumcenters [JavaScrirpt, GeoGebra]
  1079. Mirror on the Wall [Java]
  1080. Mirror property of the altitudes [Java]
  1081. Mirror Property of Altitudes via Pascal's Hexagram [Java]
  1082. Mixing Incenter And Orthocenter in Greece
  1083. Mixtilinear Circles and Concurrence [Java]
  1084. Modern Day Sangaku
  1085. Moebius Strip [avi movie]
  1086. Möbius' Strip [Java]
  1087. Models and Metamathematics
  1088. Moment of Inertia of a Regular Polygon [JavaScript]
  1089. Moments in a Peculiar Cyclic Polygon
  1090. Monge via Desargues [Java]
  1091. Monge via Desargues II [Java]
  1092. More of More of Gloden Ratio in Equilateral Triangles
  1093. Morley Constellation [Java]
  1094. Morley's Miracle [Java]
  1095. Morphing [Java]
  1096. Müller-Lyer Illusion [Java]
  1097. Multifaceted Cork [Java]
  1098. Multiplication of Points on a Circle [JavaScript,GeoGebra]
  1099. Multiplication of Points on an Ellipse [JavaScript, GeoGebra]
  1100. Munching on Circles
  1101. Munching on Inscribed Angles
  1102. My logo
  1103. Nagel Line [Java]
  1104. Nagel point [Java]
  1105. Nagel Point and Centroid on Adjacent Isosceles Triangles
  1106. Nagel Point of the Medial Triangle [Java]
  1107. Nagel Point on the Incircle in Isosceles Triangle
  1108. Nagel's Theorem [Java]
  1109. Napoleon's Hexagon [JavaScript, GeoGebra]
  1110. Napoleon's Theorem
  1111. Necker Cube [Java]
  1112. Neuberg Cubic [Java, GeoGebra]
  1113. Neuberg Sangaku [Java]
  1114. Newly Born Pair of Siblings to Archimedes' Twins [Java]
  1115. Newton's Construction of Conics [Java]
  1116. Newton's Theorem [Java]
  1117. Nine Point Center in Square
  1118. Nine Point Circle [Java]
  1119. Nine Point Circle: an Elementary Proof [Java]
  1120. No Equilateral Triangles, Please [Java]
  1121. Nobbs' Points, Gergonne Line [Java]
  1122. Non-Eclidean Geometries
  1123. No-Pedal Collinearity [Java]
  1124. Not So Hidden Homotheties [JavaScript, GeoGebra]
  1125. Novel Concurrency of Perpendicular Bisectors [JavaScript, GeoGebra]
  1126. Number of Regions N Lines Divide Plane
  1127. Occluded Wheel Illusion [Java]
  1128. Olof Hanner's Jigsaw Puzzle [Java]
  1129. On the Difference of Areas
  1130. One More Property of Equilateral Triangles
  1131. One More Seven Circles Theorem [JavaScript, GeoGebra]
  1132. One Sheet Hyperboloid [Java]
  1133. A One-Sided Inequality in Triangle
  1134. One Triangle from Another
  1135. One Triangle from Another II
  1136. Optimal Quadrilateral Inscribed in a Square
  1137. Optimization in a Crooked Trapezoid
  1138. Optimization in Parallelepiped
  1139. Optimization Problem in Acute Angle [Java]
  1140. Octagon in Parallelogram: Overlapping Regions [Java]
  1141. Octagon in Parallelogram [Java]
  1142. Optical Property of Ellipse [Java]
  1143. Orbison illusion [Java]
  1144. Orthic Semiperimeter [Java, GeoGebra]
  1145. Orthic Triangle in a Triangle with a 120 degrees angle
  1146. Orthogonal Lines, Midpoints, and Collinearity [Java, GeoGebra]
  1147. Orthogonality in Isogonal Conjugacy [JavaScript, GeoGebra]
  1148. Orthocenter and Three Equal Circles [Java]
  1149. Orthocenters
  1150. Orthocenters of Two Triangles Sharing Circumcenter and Base [Java]
  1151. Orthocentric System From Rectangle [Java]
  1152. Orthodiagonal and Cyclic Quadrilaterals [Java]
  1153. Orthogonality in Isosceles Triangles [Java]
  1154. Orthogonality in Two Squares [JavaScript, GeoGebra]
  1155. Orthologic Triangles in a Quadrilateral [Java]
  1156. Orthopole [Java]
  1157. Out of Pentagon Sangaku
  1158. Packing shapes in a plane
  1159. Padoa's Inequality
  1160. Pairs of Areas in Equilateral Triangle
  1161. Pairs of Homologous Lines under Spiral Similarities [Java]
  1162. Pairs of Incircles in a Quadrilateral [Java]
  1163. Pantograph [Java]
  1164. Paper Folding & Cutting Sangaku
  1165. Paper Folding Geometry
  1166. Paper strip activities [avi movies]
  1167. Paper strip activities, two strips
  1168. Pappus' Generalization of Euclid I.47 [Java]
  1169. Pappus' Theorem [Java]
  1170. Parabola [Java]
  1171. Parabola and Abutting Equilateral Triangles
  1172. Parabolas Related to the Orthic Triangle [JavaScript, GeoGebra]
  1173. Parabolic Mirror, Illustration [Java]
  1174. Parabolic Mirror, Theory [Java]
  1175. Parabolic Reciprocity [JavaScript, GeoGebra]
  1176. Parabolic Sieve of Prime Numbers
  1177. Paragon [Java]
  1178. Parahexagon [Java]
  1179. Parallel Chords [Java]
  1180. Parallel Chords II [Java]
  1181. Parallel Chords in Conics [Java, GeoGebra]
  1182. Parallel Chords in Ellipse [Java]
  1183. Parallel Chords in Crossing Circles [Java]
  1184. Parallel Lines in a Cyclic Quadrilateral [Java]
  1185. Parallel Lines in a Quadrilateral II [Java] Parallel Lines in a Quadrilateral
  1186. Parallel Lines in Rhombus
  1187. Parallel Lines in a Triangle [Java, GeoGebra]
  1188. Parallels through the Vertices of Equilateral Triangle
  1189. Parallelogram and Ellipses [Java, GeoGebra]
  1190. Parallelogram and Four Equilateral Triangles [JavaScript, GeoGebra]
  1191. Parallelogram and Similar Triangles [Java]
  1192. Parallelogram Illusion [Java]
  1193. Parallelogram in Four Circles [JavaScript, GeoGebra]
  1194. Parallelogram in Parallelogram And in Projection [JavaScript, GeoGebra]
  1195. Parallelogram in Trapezoid
  1196. Parallelogram Iterations [Java]
  1197. Parallelogram Law [Java]
  1198. Parallelogram Law: A PWW [Java]
  1199. Parallelogram Law: A Tessellation [Java]
  1200. Parallelogram with Side Lines through Fixed Points [JavaScript, GeoGebra]
  1201. Partition of point sets in a plane
  1202. Partitioning 3-Space with Circles
  1203. Partitioning a Circle
  1204. Pascal: Necessary and Sufficient [Java]
  1205. Pascal in a Cyclic Quadrilateral [Java]
  1206. Pascal Lines: Steiner and Kirkman Theorems [Java]
  1207. Pascal Lines: Steiner and Kirkman Theorems II [Java]
  1208. Pascal's theorem [Java]
  1209. Peacock's Tail Sangaku
  1210. Peaucellier Linkage [Java]
  1211. Pedal Collinearities [Java]
  1212. Pedal Parallelogram [JavScript, GeoGebra]
  1213. Pedal Polygons [Java]
  1214. Pedal Property in Equilateral Triangle
  1215. Pedal SimilarityPedal Triangle and Isogonal Conjugacy [Java]
  1216. Pedal Triangles of Inverse Points [JavaScript, GeoGebra]
  1217. Pedoe's Theorem [Java]
  1218. Pencils of Cubics
  1219. Pentagon, construction of
  1220. Pentagon And Decagon, Both Regular
  1221. Pentagon in a Semicircle [Java]
  1222. Pentagon Proportions Sangaku
  1223. Perimeters of Convex Polygons, One within the Other
  1224. Perimeters of Parallelogram And Rhombus [JavaScript, GeoGebra]
  1225. Periodic patterns in sin(N) [Java]
  1226. Perpendicular Bisectors in an Inscriptible Quadrilateral [Java]
  1227. Perpendicular Bisectors in an Inscriptible Quadrilateral II [Java]
  1228. Perpendicular lines in a cyclic quadrilateral from 1975 Canadian Mathematical Olympiad
  1229. Perpendiculars in Parallelogram [JavaScript, GeoGebra]
  1230. Perspective Triangles in Circle
  1231. Pick's Theorem [Java]
  1232. Phantom Circle and Recaptured Symmetry
  1233. Planar Sets with Integer Distances between Points
  1234. Plane Filling Curves [Java]
  1235. Plane Isometries
  1236. Plane Isometries As Complex Functions
  1237. Plato's Geometric Numbers: can you better Sam Loyd?
  1238. Pleasant Proportions in Triangle
  1239. Poggendorff's Illusion
  1240. Point between Two Roads
  1241. Point common to two similar rectangles [Java]
  1242. Point in a Square
  1243. Point on Bisector in Right Angle
  1244. Points Generated by the Nine Points
  1245. Points on Incircle: Another Look
  1246. Polar Circle [Java]
  1247. Poles and Polars [Java]
  1248. Polygon in a Rectangle
  1249. Polygons: formality and intuition [Java]
  1250. Polygons Formed by Perpendicular Bisectors [Java]
  1251. Pompeiu's Theorem
  1252. Poncelet's Porism [Java]
  1253. Poncelet's Porism in Ellipses [Java]
  1254. Poncelet's Theorem [Java]
  1255. Ponzo Illusion [Java]
  1256. Ponzo Illusion II [Java]
  1257. Possible or Impossible? [Java]
  1258. Power of a point with respect to a circle
  1259. PCC: Apollonius' Problem with Two Circles and a Point [Java, GeoGebra]
  1260. PLC: Apollonius Problem with a point, a line, and a circle [Java, GeoGebra]
  1261. PLL: Apollonius' Problem with Two Lines and a Point [Java, GeoGebra]
  1262. PPC: Apollonius' Problem with Two Points and a Circle [Java, GeoGebra]
  1263. PPL: An Elementary Solution [Java, GeoGebra]
  1264. PPL: Apollonius' Problem with Two Points and a Line [Java, GeoGebra]
  1265. Prasolov's Pythagorean Identity
  1266. Praying Eyes Theorem [JavaScript, GeoGebra]
  1267. Probability in Triangle
  1268. Problem 1 from the 2006 IMO
  1269. Problem 1 from the EGMO2017
  1270. Problem 1 from the Ninth Nordic Mathematical Contest (1994)
  1271. Problem 11984 From the American Mathematical Monthly
  1272. Problem 3 from the EGMO2017
  1273. Problem 4 from the 1959 IMO: Construction of a Right Triangle [Java, GeoGebra]
  1274. Problem 4, 1975 USA Math Olympiad and the Radical Axis [Java]
  1275. Problem 4, 1975 USA Math Olympiad and Isosceles Triangles [Java]
  1276. Problem 4, 1975 USA Math Olympiad: Normals and Tangents [Java]
  1277. Problem 4, 1975 USA Math Olympiad: Problem 4, 1975 USA Math Olympiad: The Final Touch [Java]
  1278. Problem 4 from the 2016 OBJM TST
  1279. Problem 4 from the IMO 2009
  1280. Problem 4 from the 4th BJMO Team Selection Test
  1281. Problem 4087 from Crux Mathematicorum
  1282. Problem 4096 from Crux Mathematicorum
  1283. Problem in an Equilateral Triangle [Java]
  1284. Problem 4 from the IMO 2013 - Synthetic Solution [Javacript, GeoGebra]
  1285. Problem 4160 from the Crux Mathematicorum
  1286. Problem A-2 from the 2002 Putnam Math Competition
  1287. Problem A-6 from the 1992 Putnam Math Competition
  1288. Problem CC156 From Crux Mathematicorum
  1289. Problem in a Special Trapezoid
  1290. Problem in an Equilateral Triangle II [Java]
  1291. Problem in Direct Similarity [JavaScript, GeoGebra]
  1292. Problem in Three Squares [Java]
  1293. Problem of Equal Steps [Java]
  1294. Problem of Equal Steps II [Java]
  1295. Problem on a Pentagonal Star
  1296. Problem with angle bisector from 1975 Canadian Mathematical Olympiad
  1297. Problem with equal angles from 1987 IberoAmerican Mathematical Olympiad
  1298. Proclivity of Conjoint Archimedean Twins for Proliferation [JabvaScript, GeoGebra]
  1299. Projections of Convex Quadrilateral [JavaScript, GeoGebra]
  1300. Projections of Isogonal Conjugate are Concyclic [JavaScript, GeoGebra]
  1301. Projections on Internal and External Angle Bisectors [Java]
  1302. Projective Collinearity in a Quadrilateral [Java]
  1303. Projective infinity
  1304. Projective Invariants for Pascal And Desargues
  1305. Properties of Flank Triangles
  1306. Properties of the Circle of Similitude [Java]
  1307. Properties of Circle Through the Incenter
  1308. Properties of the Figures in Euclid I.47
  1309. Properties of the Harmonic Ratio
  1310. Property of 6-Parpolygon [Java]
  1311. Property of Angle Bisectors [Java]
  1312. Property of Circumscribed Quadrilaterals [Java]
  1313. Property of Points Where In- and Excircles Touch a Triangle [Java]
  1314. Property of Right Isosceles Triangle [Java, GeoGebra]
  1315. Property of Right Trapezoids [GeoGrebra]
  1316. Property of Semicircles [Java]
  1317. Property of Thébault Circles [JavaScript, GeoGebra]
  1318. Property of Two Pencils of Parallel Lines
  1319. Proportions and the Incenter [JavaScript]
  1320. Proportions in Square
  1321. Proportions with Two Orthocenters [JavaScript, GeoGebra]
  1322. Ptolemy's Theorem
  1323. Pure Angle Chasing [JavaScript, GeoGebra]
  1324. Pure Angle Chasing II [JavaScript, GeoGebra]
  1325. Pure Angle Chasing III [JavScript, GeoGebra]
  1326. Puzzles on graphs.
  1327. Pythagorean Theorem (122 proofs)
  1328. Pythagorean Perimeter Theorem
  1329. Pythagoras and Vecten Break Japan's Isolation [Java]
  1330. Pythagorean Triples [Java]
  1331. Quadrature: A Child's Play
  1332. Quadrilateral from a Segment
  1333. Quadrilateral Inequality
  1334. Quadrilateral Inscribed into Parallelogram
  1335. Quadrilateral With Equal Opposite Sides And Angles [Java]
  1336. Quadrilateral with 3 Equal Sides [Java]
  1337. Quadrilaterals Formed by Perpendicular Bisectors [Java]
  1338. Quest for Paragon [Java]
  1339. R and r When G on Incircle
  1340. Radical Axis and Center, an Application [Java]
  1341. Radical Axis of Circles Inscribed in a Circular Segment [Java]
  1342. Radical Center [Java]
  1343. Radius and Construction of a Mixtilinear Circle [Java]
  1344. Radius of a Circle by Paper Folding [Java]
  1345. Random Dot Stereograms [Java]
  1346. The Range of r/R in Triangle with Centroid on the Incircle
  1347. Ratios and Orthogonality in a Triangle - Problem from the 2006 Romania MO
  1348. Rational Points On a Circle
  1349. Rectangle Inscribed in Triangle [JavaScript, GeoGebra]
  1350. Rectified, Halved, Sheared, Eyeballs Still Surprise [JavaScript, GeoGebra]
  1351. Reflection in a Triangle Tangent to Parabola [JavaScript, GeoGebra]
  1352. Reflection In Line [Java]
  1353. Reflection in the Circumcenter
  1354. Reflections in Ellipse [Java]
  1355. Reflections of a Line Through the Orthocenter [Java]
  1356. Reflections of a Point on the Circumcircle [Java]
  1357. Reflections of the Orthocenter
  1358. Reflections of the Orthocenter [Java]
  1359. Reflections of the Orthocenter II Regular Hexagon and Triangle Joined at Vertex [JavaScript, GeoGebra]
  1360. Regular Hexagon from Arbitrary Triangle [JavaScript, GeoGebra]
  1361. Regular Octagon by Paper Folding
  1362. Regular Polygons in a Triangular Grid [Java]
  1363. Regular Polyhedra - Platonic Solids
  1364. Other Solids
  1365. Regular Pentagon Inscribed in Circle by Paper Folding
  1366. Regular polyhedra and Euler's Theorem
  1367. Reim's Similar Coins I
  1368. Reim's Similar Coins II
  1369. Reim's Similar Coins III
  1370. Reim's Similar Coins IV
  1371. Relation Engendered By Altitudes
  1372. Relation Engendered By Medians
  1373. Relations in a Cyclic Polygon
  1374. Remarkable Line in a Quadrilateral [Java]
  1375. Remarkable Line in Cyclic Quadrilateral [Java]
  1376. Rendezvous [Java]
  1377. Reverse Spoke Illusion [Java]
  1378. Revolving Circles Illusion [Java]
  1379. Rhombus in a Cyclic Quadrilateral [Java]
  1380. Rhombus in Circles [Java, GeoGebra]
  1381. Riemann Sphere and Möbius Transformation
  1382. Surprise: Right Angle in Circle [JavaScript, GeoGebra]
  1383. Surprising Length Dependence In Equilateral Triangle by Miguel Ochoa Sanchez
  1384. Right Triangles on Sides of a Square [Java]

    Rotating Square in Search of the Golden Ratio

  1385. Rotating Top Illusion [Java]
  1386. Rotating Gears [Java]
  1387. Rotation Transform [Java]
  1388. Rouse Ball's Fallacy [Java]
  1389. Rusty Compass Construction of Equilateral Triangle [Java]
  1390. Salinon: From Archimedes'Book of Lemmas [Java]
  1391. Sam Loyd's Geometric Puzzle
  1392. Sam Loyd's Son's Dissection [Java]
  1393. Sanchez's Areas in Bottema's Configuration [JavaScript]
  1394. Sangaku: Reflections and the Phenomenon
  1395. Sangaku: Critique of My View and a Response
  1396. Sangaku and The Egyptian Triangle
  1397. Sangaku in a Square
  1398. Sangaku Iterations, Is it Wasan? [Java]
  1399. Sangaku via Peru
  1400. Sangaku with 8 Circles
  1401. Sangaku with Angle between a Tangent and a Chord [Java]
  1402. Sangaku with Quadratic Optimization
  1403. Sangaku with Three Mixtilinear Circles [Java]
  1404. Sangaku with Versines [Java]
  1405. Sangakus with a Mixtilinear Circle [Java]
  1406. Scintillating Grid Illusion [Java]
  1407. Schwarz Lantern [Java]
  1408. Secant Angles [Java]
  1409. Secant Angles II [Java]
  1410. Secant, Normal, Tangent [Java]
  1411. Secant, Tangents and Orthogonality [Java]
  1412. See-Saw Lemma [Java]
  1413. Segment Projections in Equilateral Triangle
  1414. Segment Trisection [Java]
  1415. Segment Trisection II
  1416. Segment Trisection Induced by Parallels to Medians [Java]
  1417. Semicircle on Square [JavaScript]
  1418. Semi-regular Tessellation on Hinges A [Java]
  1419. Semi-regular Tessellation on Hinges B [Java]
  1420. Separating point sets with a circle
  1421. Sequences of Concyclic Points on a Conic
  1422. Sequences of Touching Circles
  1423. Serendipitous Beauty [Java]
  1424. Serendipitous Proofs Of The Pythagorean Theorem
  1425. Seven and the Eighth Circle Theorem
  1426. Seven Circles Theorem [Java]
  1427. Seven Concyclic Points [Java, GeoGebra]
  1428. Seven Equal Circles [JavaScript, GeoGebra]
  1429. Seven Problems in Equilateral Triangle
    1. Seven Problems in Equilateral Triangle, Solution to Problem 1
    2. Seven Problems in Equilateral Triangle, Solution to Problem 2
    3. Seven Problems in Equilateral Triangle, Solution to Problem 3
    4. Seven Problems in Equilateral Triangle, Solution to Problem 4
    5. Seven Problems in Equilateral Triangle, Solution to Problems 5, 6, 7
  1430. Seyran Ibrahimov's Inequality
  1431. Shaggy Dog Theorem
  1432. Shapes in a lattice
  1433. Shapes of constant width [Java]
  1434. Shearing and Translation in Pythagorean Pants [Java]
  1435. Shearing a Polygon into a Triangle of Equal Area [Java]
  1436. Shearing Butterflies in Quadrilaterals [Java]
  1437. Shedding Light on the Ball for Eyeballing
  1438. Shepard's Parallelogram Illusion [Java]
  1439. Shifted by the Inradius Tangent Collinearities [JavaScript, GeoGebra]
  1440. Shifting Cube Illusion [Java]
  1441. Shimmer Illusion [Java]
  1442. Short Construction of the Geometric Mean
  1443. Shortest Fence in a Quarter-Circle Pasture
  1444. Shredding the torus
  1445. Sides and Area of Pedal Triangle
  1446. Sierpinski Gasket By Common Trema Removal [Java]
  1447. Sierpinski Gasket Via Chaos Game [Java]
  1448. Sierpinski Gasket by Trema Removal [Java]
  1449. Similar Parallelograms on Sides of a Triangle
  1450. Similar Triangles And More
  1451. Similar Triangles in Crossing Circles [JavaScript, GeoGebra]
  1452. Similar Triangles on Sides of a Quadrilateral [Java]
  1453. Similar Triangles on Sides and Diagonals of a Quadrilateral [Java]
  1454. Similarity Is About Proportion - And Ways to Look at It
  1455. Simple Construction of the Circle of Apollonius
  1456. Simple dissection of an acute triangle
  1457. Simple Property of Circle Through the Incenter [JavaScript]
  1458. Simple Quadrilaterals Tessellate the Plane [Java]
  1459. Simson Line [Java]
  1460. Simsons and 9-Point Circles in Cyclic Quadrilateral [Java]
  1461. Simultaneous Contrast Illusion [Java]
  1462. Simultaneous Contrast Illusion II [Java]
  1463. Simultaneous Contrast: Koffka's Illusion [Java]
  1464. Simultaneous Contrast: White's Illusion [Java]
  1465. Simultaneous Contrast: White's Illusion, V-Variant [Java]
  1466. Three Concurrent Chords at 60 Degrees Angles
  1467. Simultaneous Diameters in Concurrent Circles [Java]
  1468. Simultaneous Generalization of the Theorems of Ceva and Menelaus
  1469. Sine and Cosine of 15 Degrees Angle
  1470. Sine, Cosine, and Ptolemy's Theorem
  1471. Six Circles with Concurrent Pairwise Radical Axes
  1472. Six Circles Theorem (Bui Quang Tuan) [Java]
  1473. Six Circles Theorem (Elkies) [Java]
  1474. Six Circles Theorem (Evelyn) [Java]
  1475. Six Concyclic Circumcenters in Fermat's Configuration [JavaScript, GeoGebra]
  1476. Six Concyclic Points [Java]
  1477. Six Concyclic Points on Sides of a Triangle
  1478. Six Concyclic Points II [Java]
  1479. Six Concyclic Points via Antipedal Triangle [JavaScript, GeoGebra]
  1480. Six Incircles in an Equilateral Triangle [Java]
  1481. Six Point Circle [Java]
  1482. SixPoints, ThreeLines [Java]
  1483. Soddy Circles and David Eppstein's Centers [Java]
  1484. Some Properties of Common Tangents [JavaScript, GeoGebra]
  1485. Some Properties of Napoleon's Configuration [Java]
  1486. Spectral Decomposition of a Planar Quadrilateral
  1487. Sperner's Lemma [Java]
  1488. Spiral Similarity [Java]
  1489. Spiral Similarity and CollinearitySpiral Similarity and Collinearity [Java, GeoGebra]
  1490. Spiral Similarity Leads to Equilateral Triangle [JavaScript, GeoGebra]
  1491. Square and Circle in a Gothic Cupola
  1492. Square from Four Points, One on Each Side
  1493. Square From Nowhere [Java]
  1494. Square in a Circle Inscribed in a Square [Java]
  1495. Square in a Right Triangle [Java]
  1496. Square in Chair [Java]
  1497. Square Inscribed in a Triangle [Java]
  1498. Square Inscribed in a Triangle II [Java]
  1499. Square, Similarity and Slopes [Java]
  1500. Squares and Straight Tetrominoes
  1501. Squares in Circles [Java]
  1502. Squares in Semicircle and Circle
  1503. Squares in Triangles
  1504. Squares Inscribed In a Triangle III [Java]
  1505. Squares on Sides of a Parallelogram [JavaScript, GeoGebra]
  1506. Squares on Sides of a Quadrilateral [Java]
  1507. Squares on Sides of a Quadrilateral II [JavaScript, GeoGebra]
  1508. Square out of a Quadrilateral
  1509. Squaring a circle
  1510. Squaring a Rectangle [Java]
  1511. Squinting Eyes Theorem [Java]
  1512. SSA
  1513. SSS
  1514. Staircase Illusion [Java]
  1515. Stan Fulger's Observation in Right Triangle
  1516. Star of David [Java]
  1517. Stathis Koutras' Butterfly
  1518. Stathis Koutras' Theorem
  1519. Stathis Koutras' Theorem II
  1520. Steiner's Circumellipse in Barycentric Coordinates [GeoGebra]
  1521. Steiner's Inellipse
  1522. Steiner's Sangaku
  1523. Steiner's Ratio Theorem
  1524. Steiner's Theorem
  1525. Stereographic Projection [Java]
  1526. Stereographic Projection and Inversion
  1527. Stereographic Projection and Radical Axes
  1528. Stewart's theorem
  1529. Straight Edge Only Construction of Polar
  1530. Structural Constellation [Java]
  1531. Sums of Squares in Circle
  1532. Sum of Squares in Equilateral Triangle
  1533. Sum of Squares of Distances to Vertices
  1534. Sum of Two Squares [JavaScript, GeoGebra]
  1535. Sums of Unit Vectors
  1536. Surprising 60° in Equilateral Triangle [JavaScript, GeoGebra]
  1537. Sylvester's Problem
  1538. Symmedians
  1539. Symmetries in a Triangle
  1540. Symmetries in Triangle II [JavaScript, GeoGebra]
  1541. Symmetry in an Asymmetric Configuration [JavaScript, GeoGebra]
  1542. (tan(72°)±tan( 60°)sin(30°$\mp$18°)= 1
  1543. Tangency Point of Two Circles [Java]
  1544. Tangent and Secant [Java]
  1545. Tangent as a Radical Axis [Java]
  1546. Tangent Circles, Similarity and Equal Segments [JavaScript, GeoGebra]
  1547. Tangent Circles and an Isosceles Triangle [Java]
  1548. Tangent Circles in a Parallelogram [Java]
  1549. Tangent, Cotangent and Square Roots Inequality
  1550. Tangent Curiosity in Equilateral Triangle [JavaScript, GeoGebra]
  1551. Tangent in Concurrency [Java]
  1552. Tangent Lines and Circles in Convex Quadrilateral [Java]
  1553. Tangent of 22.5° - Proof Wthout Words
  1554. Tangent to Circle in Three Steps
  1555. Tangent to the Incircle [JavaScript]
  1556. Tangent to two circles
  1557. Tangents And Bisectors
  1558. Tangents and Diagonals in Cyclic Quadrilateral [Java]
  1559. Tangents, Perpendiculars and Geometric Mean [Java]
  1560. Tarski-Banach Decompositions
  1561. Taylor circle [Java]
  1562. Terquem's Theorem [Java]
  1563. Tesseract [Java]
  1564. Tetrahedron in Parallelepiped
  1565. Tetrahedron with Equiareal Faces
  1566. Tetrahedron with Equiareal Faces, II
  1567. Tetrahedron with Orthogonal Perpendiculars to Opposite Edges
  1568. Thales' Theorem [Java, GeoGebra]
  1569. Thales' Theorems
  1570. Thales on Angle Bisectors [JavaScript, GeoGebra]
  1571. Thanos Kalogerakis' Collinearity in Triangle
  1572. The 80-80-20 Triangle
  1573. The Beauty of Fractions
  1574. The Center of Gravity and Motion of Material Points [JavaScript, GeoGebra]
  1575. The Chaos Game: Address Space vs IFS [Java] The Circle of the Orthocenters
  1576. The Devil is in the Exceptions
  1577. The Eutrigon Theorem [Java, GeoGebra]
  1578. The Golden Pentacross
  1579. The Law of Cosines by Larry Hoehn
  1580. The Midpoint of an Angle Bisector - a Problem by A. A. Zaslavsky
  1581. The only rational triangle
  1582. The Pythagorean Theorem from a Combinatorial Identity
  1583. The Schwarz Lantern Explained [JavaScript]
  1584. The Shape of the Colosseum [Java, GeoGebra]
  1585. The Shortest Crease [JavaScript, GeeoGebra]
  1586. The Shortest Distance in a Circular Segment
  1587. Thébault's Problem I [Java]
  1588. Thébault's Problem II [Java]
  1589. Thébault's Problem III [Java]
  1590. The Triangle of the Medians
  1591. Theorem of Complete Quadrilateral [Java]
  1592. Theorem of Three Tangents to a Conic [JavaScript, GeoGebra]
  1593. Theorems of Ceva and Menelaus, an Illustrated Generalization [Java]
  1594. There is no Difference Between Equilateral Triangles
  1595. Third Unusual Identity in Triangle
  1596. Three Circles and Area [JavaScript]
  1597. Three Circles and Common Tangents
  1598. Three Circles through the Incenter
  1599. Three Collinear and Four Concyclic Points [Java, GeoGebra]
  1600. Three Concurrent Circles [Java]
  1601. Three Common Chords in Three Concurrent Circles [Java, GeoGebra]
  1602. Three Congruent Circles by Reflection [Java]
  1603. Three Congruent Circles by Reflection II [Java]
  1604. Three Congruent Circles by Reflection III [Java]
  1605. Three Equal Circles in a Semicircle
  1606. Three Euler Lines That Are Four [JavaScript]
  1607. Three Incircles In a Right Triangle [Java]
  1608. Three Incircles in a Triangle [Java]
  1609. Three Isosceles Triangles [Java]
  1610. Three Orthogonal Circles Through Three Given Points [Java]
  1611. Three lines at 60 degres and Circumcenters [JavaScript, GeoGebra]
  1612. Three pairs of Parallel Lines and a Conic [JavaScript, GeoGebra]
  1613. Three Parabolas with Common Directrix [JavaScript,GeoGebra]
  1614. Three Parallels in a Triangle [Java]
  1615. Three Points on a Parabola [Java]
  1616. Three Pyramids are Better Than Two [Java]
  1617. Three regions sharing a common boundary
  1618. Three Similar Polygons [Java]
  1619. Three Similar Triangles [Java]
  1620. Three Similar Triangles II [Java]
  1621. Three Squares and Two Ellipses [Java]
  1622. Three Tangent Circles [Java]
  1623. Three Tangents, Three Chords in Ellipse [Java]
  1624. Three Tangent Circles Sangaku
  1625. Three Tangents Theorem [Java]
  1626. Three Tangents, Three Secants [Java]
  1627. Three Touching Circles [Java]
  1628. Three Travelers in Uniform Motion
  1629. Three visions of a fact [GeoGebra]
  1630. Tiling a Chessboard with Dominoes
  1631. Tiling Sphere by Four Equal Triangles
  1632. Toothpick Construction of a Square [Java]
  1633. Topological preliminaries
  1634. Torque as a Mathematical Object
  1635. Touching Circles [Java]
  1636. Touching Circles and Concurrency [Java]
  1637. Touching Circles with Given Centers II [Java]
  1638. Train wheel quandary
  1639. Transitivity in Action [Java]
  1640. Translated Triangles [Java]
  1641. Translation Transform [Java]
  1642. Transversal Trigonometry [JavaScript, GeoGebra]
  1643. Triangle ABC is right iff sin²A + sin²B + sin²C = 2
  1644. Triangle Area in Square with Incircle
  1645. Triangle Areas in a Parallelogram [Java]
  1646. Triangle Areas in a Parallelogram II [Java]
  1647. Triangle by HM segments [JavaScript, GeoGebra]
  1648. Triangle Classification [Java]
  1649. Triangle constructions and facts [Java]
  1650. Triangle Construction from Angle, Altitude and Median
  1651. Triangle from a, A, mc/mb
  1652. Triangle from Angle Bisector, Altitude and Circumradius
  1653. Triangle from Angle Bisector, Altitude and Inradius
  1654. Triangle from Inradius, Circumradius, Side or Angle
  1655. Triangle from Median, Altitude and Circumradius
  1656. Triangle from Side, Circumradius, and Median
  1657. Triangle from Angle, Inradius, and Difference of Sides
  1658. Triangle from Side, Inradius, and Altitude
  1659. Triangle from Side, Median, and Altitude
  1660. Triangle from Two Side Lines and the Euler Line
  1661. Triangle in a 4x4 Square
  1662. Triangle in a 5x5 Square
  1663. Triangle of Maximum Area
  1664. Triangle of Maximum Area II
  1665. Triangle of Minimum Perimeter [JavaScript]
  1666. Triangle on a Rectangular Hyperbola
  1667. Triangle Sliding on Two Straight Lines [Java]
  1668. Triangles, Squares and Areas from Temple Geometry [Java]
  1669. Triangles on HO
  1670. Triangles with Equal Area [Java]
  1671. Triangles with Sides in Geometric Progression [JavaScript]
  1672. Triangular Areas in Circle [JavaScript, GeoGebra]
  1673. Triangular Billiard [Java]
  1674. Triangulating Squares
  1675. Triangle with a 60 degrees angle [JavaScript, GeoGebra]
  1676. Trigonometry by Watching
  1677. Trigonometric Form of Ceva's Theorem [Java]
  1678. Trigonometric Functions [Java]
  1679. Trigonometric Identities with Arctangents
  1680. Trigonometric Identity for the Pi Day
  1681. Trigonometric Proof of the Pythagorean Theorem
  1682. Trigonometry According to Ptolemy
  1683. Trigonometry by Paper Folding
  1684. Trisect Segment: 2 Circles, 4 Lines
  1685. Trisectable angle that is not constructible
  1686. Tucker Circles [Java]
  1687. Tucker Circles Through Homothety [Java]
  1688. Twelve Matchsticks Area Puzzle
  1689. Twin Segments in Four Semicircles
  1690. Twins Beget Twins
  1691. Twisted Cord Illusion [Java]
  1692. Two Altitudes, One Midpoint
  1693. Two Arbelos, Two Chains
  1694. Two Cevians and Proportions in a Triangle
  1695. Two Circles, Two Segments - One Ratio
  1696. Two Circles and a Limit - Analytic Proof
  1697. Two Circles and One More [Java]
  1698. Two Circles and Two More [Java]
  1699. Two Circles, Ellipse, and Parallel Lines
  1700. Two Circles in a Parallelogram [Java]
  1701. Two Circles Inscribed in a Parallelogram [Java]
  1702. Two Circles in a Square [Java]
  1703. Two Circles in a Square II [Java]
  1704. Two Circles in an Angle [Java]
  1705. Two Circles on Angle Bisector [Java]
  1706. Two Circles on a Side of a Triangle [Java]
  1707. Two Circles, Tangents and Two Collinearities [JavaScript, GeoGebra]
  1708. Two Circumcircles And Two Pairs of Parallels [Java]
  1709. Two Circumcircles in Triangle [Java]
  1710. Two Conditions for a Triangle to Be Equilateral
  1711. Two coins puzzle
  1712. Two Colors - Three Points - Any Triangle
  1713. Two Congruent Circles by Reflection [Java]
  1714. Two Conics, Pascal, Chasles, and Cross-Ratio [JavaScript, GeoGebra]
  1715. Two Color Coloring of the Plane [Java]
  1716. Two Common Chords in Three Concurrent Circles [Java, GeoGebra]
  1717. Two Diameters and Longest Common Chord [Java, GeoGebra]
  1718. Two Equilateral Triangles [Java]
  1719. Two Equilateral Triangles on Sides of a Square
  1720. Two Homotheties in a Parallelogram [Java]
  1721. Two Intersecting Circles [Java]
  1722. Two Lines - Two Circles [Java]
  1723. Two Pencils of Parallel Lines [JavaScript, GeoGebra]
  1724. Two Pairs of Parallel Lines in a Triangle [Java, GeoGebra]
  1725. Two Parallels in a Triangle and One More [Java]
  1726. Two Pascals Merge into One [JavaScript, GeoGebra]
  1727. Two Perpendiculars From a Point to a Line [Java]
  1728. Two Planar Constructions Related to a 3D Problem
  1729. Two Perspective Triangles
  1730. Two Quadrilaterals [Java]
  1731. Two Quadruplets of Concyclic Points [JavaSCript,GeoGebra]
  1732. Two Quadruplets of Tangent Circles [Java]
  1733. Two Refinements of Ionescu-Weitzenbock Inequality
  1734. Two Regular Pentagons Joined at Vertex
  1735. Two Related Triangles of Equal Areas
  1736. Two Sangaku with Equal Incircles
  1737. Two Similar Triangles with Parallel Sides [JavaScript, GeoGebra]
  1738. Two Simsons in a Triangle [Java]
  1739. Two Squares and Another Square [Java]
  1740. Two Squares In Circle [JavaScript]
  1741. Two Symmetric Triangles Are Directly Decomposable [Java]
  1742. Two Touching Circles [Java]
  1743. Two Triangles Inscribed in a Conic [Java, GeoGebra]
  1744. Two Triangles Inscribed in a Conic - with Elementary Solution [Java, GeoGebra]
  1745. Two Triangles Inscribed in a Conic - with Solution [Java, GeoGebra]
  1746. Two Triangles With Common Base and Altitude [Java]
  1747. Two Triangles Sharing the Circumcenter
  1748. Two Triples of Concurrent Cevians and a Conic [JavaScript, GeoGebra]
  1749. Two Triples of Concurrent Circles [Java]
  1750. Two Triples of Similar Triangles [Java]
  1751. Uncommon Triangle Constructions
  1752. Unfolding Spirals Illusion [Java]
  1753. Urquhart's Theorem
  1754. USA 1975 Problem 4
  1755. Use of Homogeneous Coordinates for Geometrical Calculations
  1756. Van Aubel's Theorem for Quadrilaterals and Generalization
  1757. Van Khea's Fourth Identity in Triangle
  1758. Van Khea's Quickie
  1759. Van Obel Theorem, Determinants, and Barycentric Coordinates
  1760. Van Schooten's and Pompeiu's Theorems [Java]
  1761. Van Schooten's Locus Problem [Java]
  1762. Variations on the Theme of Tremas [Java]
  1763. Variations on the Theme of Tremas II [Java]
  1764. Varignon's Theorem, Proof Without Words
  1765. Varignon Parallelogram [Java]
  1766. Various Geometries
  1767. Vecten-Nikolin Hexagon [Java]
  1768. Vecten's Collinearity [Java]
  1769. Vecten's Mesh [Java]
  1770. Vector Addition and Subtraction [Flash]
  1771. Vector Algebra in Tetrahedron
  1772. Vector product
  1773. Versatile Theorem [Java]
  1774. Vertical and Horizontal Dominoes on a Chessboard
  1775. Vietnamese Extension of a Japanese Theorem [JavaScript]
  1776. Vietnamese Lemma towards an Extension of a Japanese Theorem [JavaScript, GeoGebra]
  1777. Viewing a Statue
  1778. Viviani's Theorem [Java]
  1779. Viviani's Theorem II [Java]
  1780. Viviani in Isosceles Triangle [Java]
  1781. Viviani by Inversion
  1782. Viviani by Vectors
  1783. Viviani's 3D Analogue
  1784. Sanchez's Viviani's Area Analogue [JavaScript, GeoGebra]
  1785. Volume and Area of Torricelli's Trumpet [JavaScript]

    Volume Inequality in Tetrahedron

  1786. Volume of Fibonacci Tetrahedron
  1787. Volume of Sphere and Volume of an Ellipsoid
  1788. Volumes of Two Pyramids
  1789. Wallace-Bolyai-Gerwien Theorem
  1790. Wallace's Theorem [Java]
  1791. Watt's and Chebyshev's Linkage [Java]
  1792. Weird curves bound normal areas
  1793. Weitzenbock by Sanchez
  1794. Weitzenböck Inequality [Java]
  1795. What does one see inside a spherical mirror? [Java]
  1796. What Is Analytic Geometry?
  1797. What Is Angle?
  1798. What Is Angle Chasing?
  1799. What Is Area?
  1800. What Is Ellipse?
  1801. What Is Indirect Proof?
  1802. What Is Line?
  1803. What Is Point?
  1804. When a Triangle is A-cute
  1805. When a Triangle is Equilateral [Java]
  1806. When Is Triangle Equilateral: Marian Dinca's Criterion
  1807. When Is Triangle Isosceles: Miguel Ochoa Sanchez's Criterion
  1808. When Two Segments Intersect? [JavaScript]
  1809. When index equals content [Java]
  1810. Wonderful Trigonometry In Equilateral Triangle
  1811. Why a Diameter Is the Longest Chord?
  1812. William Wallace's Proof of the Butterfly Theorem
  1813. William Wallace's 1803 Statement of the Butterfly Theorem [JavaScript, GeoGebra]
  1814. Wittenbauer's Parallelogram [Java]
  1815. Wundt Illusion [Java]
  1816. Wundt Block Illusion [Java]
  1817. Y. Sawayama's Lemma [Java]
  1818. Y. Sawayama's Theorem
  1819. YATPOPT, Yet Another Trigonometric Proof of the Pythagorean Theorem
  1820. Yet Another Appearance of the Golden Ratio [JavaScript, GeoGebra]
  1821. Yet Another Concurrence on the 9-Point Circle [JavaScript, GeoGebra]
  1822. Yet Another Seven Circles Theorem [JavaScript, GeoGebra]
  1823. Zaslavsky's theorem [Java]
  1824. Zöllner's Illusion [Java]

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