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

    An Inequality with Angle Trisectors

  196. An Inequality with Arctangents in Triangle
  197. An Inequality with Circumradii And Distances to the Vertices
  198. An inequality with Cosines and a Sine
  199. An Inequality with Inradius and Side Lengths
  200. An Inequality with Cotangents And the Circumradius
  201. An Inequality with Tangents and Sides
  202. An Inequality with One Tangent and Six Sines
  203. An inequality with Three Points
  204. An Inequality in Triangle with Differences of the Medians
  205. An Inequality with Inradius and Circumradii
  206. An Inequality in Triangle with the Medians, Sines and Cube Roots
  207. An Inequality with Powers of Six
  208. An Inequality with Sides, Altitudes, Angle Bisectors and Medians
  209. An Inequality with Sides, Cosines, and Semiperimeter
  210. An Inequality with Sin, Cos, Tan, Cot, and Some
  211. An Inequality with Sines
  212. An Inequality with Tangents and Cotangents
  213. An Inequality with the Most Important Cevians
  214. An Inradii Relation in Inscriptible Quadrilateral [JavaScript]
  215. An Isoperimetric Problem in Quadrilateral
  216. An Isoperimetric Theorem [Java]
  217. An Old Japanese Theorem
  218. An Unexpected Pair of Similar Triangles Which Are Equal [JavaScript, GeoGebra]
  219. An Unexpected Rhombus [JavaScript, GeoGebra]
  220. An Universal Inequality for Cevians
  221. An Unusual Generalization of the Pythagorean Theorem
  222. An Unusual Generalization of the Pythagorean Theorem, a Variant
  223. Angle: An Illustrated Classification [Java]
  224. Angle Bisector in Square
  225. Angle Bisectors Cross Circumcircle
  226. Angle Bisector in Equilateral Trapezoid
  227. Angle Bisector in Parallelogram [Java]
  228. Angle Bisectors In Rectangle [Java]
  229. Angle Bisector in Touching Circles [Java]
  230. Angle Bisectors [Java]
  231. Angle Bisectors and Perpendiculars in a Quadrilateral [Java]
  232. Angle Bisectors in Ellipse [Java]
  233. Angle Bisectors in Ellipse II [Java]
  234. Angle Bisectors in a Quadrilateral [Java]
  235. Angle Bisectors in a Quadrilateral - Cyclic and Otherwise [Java]
  236. Angle Bisectors On Circumcircle [Java]
  237. Angle Chasing on Radical Axis [JacaScritp, GeoGebra]
  238. Angle Chasing in a 75-30-75 triangle
  239. Angle in Square
  240. Angle in Right Triangle
  241. An Angle Inequality in Triangle with Perpendicular Medians
  242. Angle Preservation Property [Java]
  243. Angle Subtended by a Diameter [Java]
  244. Angle Trisection, the Impossibility of Thereof
  245. Angle Trisection by Archimedes [Java]
  246. Angle Trisection by Hippocrates [Java]
  247. Angle Trisection by Paul Vjecsner [Java]
  248. Angle Trisectors on Circumcircle [Java]
  249. Angle Trisection by Paper Folding
  250. Angles in 4-5-6 Triangle [JavaScript]
  251. Angles in a Cube I [Java]
  252. Angles in a Cube II [Java]
  253. Angles in a Cube III [Java]
  254. Angles in Triangle Add to 180o
  255. Angles in a Triangle: an Exercise
  256. Angles Inscribed in an Absent Circle [Java]
  257. Another Concurrence on the 9-Point Circle [JavaScript, GeoGebra]
  258. Another Equilateral Triangle in Napoleon's Configuration [JavaScript, GeoGebra]
  259. Another Geometry Problem from 2012 IMO - Problem 1
  260. Another Golden Ratio in Semicircle
  261. Another Identity in Triangle
  262. Another Pair of Archimedean Twins - a Redux [JavaScript, GeoGebra]
  263. Another Property of Points on Incircle
  264. Another Property of the 9-Point Circle [JavaScript, GeoGebra]
  265. Another Refinement of the Ionescu-Weitzenbock Inequality
  266. Another Sangaku in Square
  267. Another Seven Circles Theorem [JavaScript, GeoGebra]
  268. Anticenter and Orthocenters [JavaScript, GeoGebra]
  269. Anticomplementary Triangle Surprise [Java]
  270. Antiparallel [Java]
  271. Antiparallel and Circumradius [JavaSCript, GeoGebra]
  272. Antiparallel via Three Reflections [Java]
  273. APMO 1995 Problem 3
  274. APMO 1998, Problem 4
  275. APMO 2002, Problem 3
  276. APMO 2003, Problem 2
  277. APMO 2004, Problem 2
  278. The Averages of Sides and Angles in a Triangle
  279. The Problem of Apollonius
  280. Approximate Construction of Regular Pentagon by A. Dürer
  281. Arbelos -- the Shoemaker's Knife [Java]
  282. Another Pair of Twins in an Arbelos [Java]
  283. Archimedes' Quadruplets [Java]
  284. Archimedes' Twin Circles and a Brother [Java]
  285. Area and Perimeter of Circle
  286. Area Inequalities in Triangle
  287. Area Inequality in Three Triangles
  288. Area of an Arbelos [Java]
  289. Area of Cevian Triangle
  290. Area of Cutoff Triangles
  291. Area of Rectangle
  292. Area of the Intersection of Two Equal Rectangles [JavaScript, GeoGebra]
  293. Area of Trapezoid
  294. Area Optimization in Trapezoid
  295. Area, Sector Area, and Segment Area of an Ellipse
  296. Areas between Two Parallelograms [JavaScript, GeoGebra]
  297. Areas in Three Squares [JavaScript, GeoGebra]
  298. Average Distance to N Points
  299. Chain of Circles on a Chord [Java]
  300. Chain of Four Intersecting Circles [JavaScript, GeoGebra]
  301. Chain of Inscribed Circles [Java]
  302. Chain of Six Intersecting Circles [JavaScript, GeoGebra]
  303. Characterization of the Symmedian Point with Medians and Orthic Triangle
  304. Characterization of Trapezoid [JavaScript, GeoGebra]
  305. Chasing Secant Angles [JavaScript]
  306. Concurrence in Arbelos [JavaScript, GeoGebra]
  307. Concurrency in Arbelos [Java]
  308. Concurrence on Angle Bisector [JavaScript, GeoGebra]
  309. Concurrent Chords in a Circle, Equally Inclined
  310. Concyclic Points in Arbelos [Java]
  311. Rectangle in Arbelos [Java]
  312. Rectangular Areas in Circle [JavaScript, GeoGebra]
  313. Red and Pink Areas
  314. Reuleaux's Triangle, Extended [GeoGebra]
  315. Small Triangle from Small Triangle
  316. Square, 45 Degrees Angle and Pythagoras' Look-alike
  317. Square, Semicircle, and Other Curves [JavaScript, GeoGebra]
  318. Squares in Arbelos [Java]
  319. Twin Segments in Arbelos [Java]
  320. Archimedean Siblings out of Wedlock, i.e., Arbelos (JavaScript, GeoGebra)
  321. Archimedes'Book of Lemmas
  322. Arbelos' Morsels [JavaScript, GeoGebra]
  323. Archimedes' Law of the Lever [Java]
  324. Archimedes' Method
  325. Archimedes' Twins in the Edo Period
  326. Area and Perimeter Splitters in a Triangle
  327. Area Inequality in Trapezoid
  328. Area Inequality in Triangle
  329. Area Inequality in Triangle II
  330. Area of a Bicentric Quadrilateral
  331. Area of a Circle by Leonardo da Vinci [Java]
  332. Area of a Circle by Rabbi Abraham bar Hiyya Hanasi [Java]
  333. Area of Isosceles Triangle
  334. Area of Median Triangle [Java]
  335. Area of Parallelogram [Java]
  336. Area of Parallelogram Formula by Shearing
  337. Area of the Union of Two Squares [Java]
  338. Area of Triangle [Java]
  339. Areas and Centroid in a Triangle [Java]
  340. Areas In Circle
  341. Areas in Square by Dissection [Java]
  342. Areas in Two Parallelograms and a Translation [JavaScript, GeoGebra]
  343. Arithmetic-Geometric Mean Inequality
  344. Arithmetic Mean Sangaku [Java]
  345. Arithmetic Mean Sangaku II [Java]
  346. Around the Incircle [Java]
  347. Around the Incircle in a Polygon [Java]
  348. Artisans vs Mathematicians
  349. Asian Pacific Kite [Java]
  350. Assigning Numbers to Points in the Plane
  351. Assimilation Illusion [Java]
  352. Axis of Similitude of Three Circles
  353. Barbier, The Theorem of [Java]
  354. Barycenter of Cevian Triangle
  355. Barycentric coordinates
  356. Batman's Problem [JavaScript, GeoGebra]
  357. Bender: A Visual Illusion [Java]
  358. Bespectacled Eyeballs Extension [JavaSCript, GeoGebra]
  359. Between a Cross and a Square (lies a Golden Ratio)
  360. Between Major and Minor Circles [Java]
  361. Bevan's Point and Theorem [Java]
  362. Beyond Pythagoras
  363. Beyond Viviani [JavaScript]
  364. Bimedians and Diagonals in a Quadrilateral
  365. Bimedians in a Regular Tetrahedron [Java]
  366. Bisectal Circle [Java]
  367. Bisecting arcs
  368. Bisecting a shape
  369. Bisection of Yin and Yang
  370. Bisector of an imaginary angle may be real
  371. Bisectors and Proportions [JavaScript]
  372. BMO 2014, Problem 3 [JavaScript, GeoGebra]
  373. Bottema Shatters Japan's Seclusion [Java]
  374. Bottema's theorem [Java]
  375. Bottles in a Wine Rack [Java]
  376. Bounded Distance
  377. Bounds for the Sum of Distances to the Vertices [JavaScript]
  378. Brahmagupta's Formula and Theorem
  379. Brahmagupta's Theorem [Java]
  380. Brahmagupta-Mahavira Identities
  381. Brianchon in Ellipse [Java]
  382. Brianchon's theorem [Java]
  383. Brick Wall Illusion [Java]
  384. Bride's Chair [Java]
  385. Brief introduction to Rational Trigonometry
  386. Brocard Point and a Relation of Circumradii
  387. Broken Chord Theorem [Java]
  388. Broken Line in Triangle
  389. Building a Bridge [Java]
  390. Building Bridges [Java]
  391. Bulging lines illusion [Java]
  392. Butterfly Theorem
  393. Cabart's Collinearity
  394. Camouflaged Butterfly
  395. Cantor Set and Function
  396. Cantor's Theorem [Java]
  397. Carnot's Theorem
  398. Carnot's Theorem
  399. Carnot's Theorem from Ptolemy's Theorem
  400. Carnot's Theorem (Generalization of Wallace's theorem) [Java]
  401. Carnot's Theorem for Conics
  402. Carpet With a Hole [Java]
  403. Carpets Theorem [Java]
  404. Casey's Theorem [Java]
  405. Cassini's Ovals and Geometric Optimization [JavaScript, GeoGebra]
  406. centers of similitude
  407. Centroid, a Characteristic Property Of
  408. Centroid and Circumcenter in Isosceles Tetrahedra
  409. Centroid and Incenter in Isosceles Tetrahedra
  410. Centroid on the Incircle in Isosceles Triangle
  411. Centroid on the Incircle in Right Triangle
  412. Centroids and Circumcenters
  413. Centroids in a Polygon [Java]
  414. Cevian Parallelogram [JavScript, GeoGebra]
  415. Chasing Angles Among Angle Bisectors [JavaScript]
  416. Chasing Angles in Pascal's Hexagon [Java]
  417. Circle, Isosceles Triangle and Fixed Point [Java]
  418. Circle Center by Paperfolding
  419. Circle Centers on Radical Axes [Java]
  420. Circle Chains on Napoleon Triangles [Java]
  421. Circle Concurrence on Circumcircle/a> [JavaScript, GeoGebra]
  422. Circle in a Square Inscribed in a Circle [Java]
  423. Circle Rotations and Fixed Points
  424. Circles in Barycentric Coordinates
  425. Circles on the sides of a triangle from the 2005 Austrian MO
  426. Circles Tangent to Circumcircle [Java]
  427. Circles Tangent to Medians at the Centroid [JavaScript, GeoGebra]
  428. Circles with Tangent Diameters [Java]
  429. Ceva and Menelaus Meet on the Roads
  430. Ceva in Circumscribed Quadrilateral
  431. Ceva's Theorem
  432. Ceva's Theorem and Fibonacci Bamboozlement [Java]
  433. Cevian Cradle [Java]
  434. Cevian Cradle II [JavaScript, GeoGebra]
  435. Cevian Nest [Java]
  436. Cevian Triangle [Java]
  437. Cevians And Semicircles [JavaScript]
  438. Cevians Through the Circumcenter
  439. Chain of Inscribed Circles [Java]
  440. Chaos, Emergence of [Java]
  441. Characteristic Property Of Right Triangles
  442. Chasles' Theorem
  443. Cherchez le quadrilatère cyclique [Java]
  444. Cherchez le quadrilatère cyclique II [Java]
  445. Chords, Concurrency and Orthic Triangle [Java]
  446. Chromatic Number of the Plane
  447. Chvatal's Art Gallery Theorem [Java]
  448. Circle and Hyperbola as Lighthouse Curves
  449. Circle and Hyperbola as Lighthouse Curves II
  450. Circle Crosses Triangle [Java]
  451. Circle Concurrency and Spiral Similarity [Java]
  452. Circle Division by Euclid and Leonardo [Java]
  453. Circle of Apollonius in Equilateral Triangle
  454. Circle of Similitude [Java]
  455. Circle Rotations and Fixed Points [JavaScript, GeoGebra]
  456. Circle through the Circumcenter [Java]
  457. Circle through the Incenter [Java]
  458. Circle through the Incenter And Antiparallels [Java]
  459. Circle-Stacking Theorem [Java]
  460. Circles And Parallels [Java]
  461. Circles and Semicircles in Rectangle [Java]
  462. Circles Cover a Quadrilateral [Java]
  463. Circles in a Circular Segment
  464. Circles in a Regular Polygon [Java]
  465. Circles in Morley's Triangles [Java]
  466. Circles Lined on the Legs of a Right Triangle [Java]
  467. Circles On Cevians [Java]
  468. Circles through the Orthocenter [Java]
  469. Circles with Equal Collinear Chords [Java]
  470. Circular Poggendorff Illusion [Java]
  471. Circle Inscribed in a Circular Segment [Java]
  472. Circumcenter and Orthocenter
  473. Circumcenter and Orthocenter Are Isogonal Conjugate
  474. Circumcenter on Angle Bisector [Java]
  475. Circumcevian Triangle [Java]
  476. Classification of Quadrilaterals [Java]
  477. Cleavance Center [Java]
  478. Cleaver [Java]
  479. Clifford Algebras
  480. Clifford's Chain [Java]
  481. Climbing Pyramidal Slopes
  482. Clough's theorem: the simplest proof [JavaScript, GeoGebra]
  483. Coaxal Circles on Perpendicular Bisector [Java]
  484. Coaxal Circles Theorem [Java]
  485. Collage Theorem [Java]
  486. Collinear Intersections and Products of Ratios [JavaScript, GeoGebra]
  487. Collinearity from the IMO 2013 (Problem 4) [Javacript, GeoGebra]
  488. Collinearity in Bicentric Quadrilaterals [Java]
  489. Collinearity in Tangent Circles
  490. Collinearity via Concyclicity [Java]
  491. Collinearity with the Orthocenter [Java]
  492. Color Cycling on the Mandelbrot Set [Java]
  493. Coloring Plane with Three Colors
  494. Coloring Points in the Plane
  495. Common Centroids Lead to Equilateral Triangle [JavaScript, GeoGebra]
  496. Common Chord and a Tangent [Java]
  497. Common Tangents to Two Circles I [Java]
  498. Common Tangents to Two Circles II [Java]
  499. Compass Only Construction - A Chord Tangent to an Inner circle [Java, GeoGebra]
  500. Complete Quadrilateral [Java]
  501. Complex Numbers and Geometry
  502. >Concurrence in Right Triangle
  503. Concurrence on a Circle [JavaScript, GeoGebra]
  504. Concurrence Not from School Geometry [Java, GeoGebra]
  505. Concurrency of Medians and Medial Triangles
  506. Concurrency of the Altitudes in a Triangle - Trigonometric Proof
  507. Concyclic Points at the IMO 2014 [JavaScript, GeoGebra[
  508. Concyclicity in Rectangle [Java]
  509. Concurrence in Equilateral Triangle [JavaScript,GeoGebra]
  510. Concurrence of Ten Nine-Point Circles [JavScript, GeoGebra]
  511. Concurrency in the Intouch Triangle [Java]
  512. Concurrent and Parallel Lines in Parallelogram [JavaScript, GeoGebra]
  513. Concurrent Cevians and a Conic through Their Feet [JavaScript, GeoGebra]
  514. Concyclic Points from Midpoint of an Arc [GeoGebra, JavaScript]
  515. Concyclic Incenters in Bicentric Quadrilateral [JavaScript, GeoGebra]
  516. Concyclic Points in Inscriptible Quadrilateral [JavaScript, GeoGebra]
  517. Concyclicity from Collinearity [JavaScript,GeoGebra]
  518. Concyclicity in Two Semicircles [JavaScript, GeoGebra]
  519. Concyclic Points of Two Ellipses with Orthogonal Axes [JavaScript, GeoGebra]
  520. Condition to Have a 60 Degrees Angle
  521. Concyclic Circumcenters: A Dynamic View [Java]
  522. Concyclic Points in a Triangle
  523. Concyclic Points in Bride's Chair [Java]
  524. Concyclic Points in Equilateral Bumps [Java]
  525. Conic from Parallel Chords [JavaScript, GeoGebra]
  526. Conic in Hexagon [Javascript, GeoGebra]
  527. Conic in Mixtilinear Incircles [JavaScript, GeoGebra]
  528. Conic Sections
  529. Conic Sections as Loci of Points [Java]
  530. Conics Intersecting Sides Of A Triangle [JavaScript, GeoGebra]
  531. Conics in Triangle [JavaScript, GeoGebra]
  532. Conics Related To In- and Excircles [JavaScript, GeoGebra]
  533. Conjugate Diameters in Ellipse [Java]
  534. Consecutive Isosceles Decomposition [Java]
  535. Constant Chord
  536. Constrained Area in Triangle
  537. Constant Ratio on Circle [JavaScript, GeoGebra]
  538. Construct Triangle from Angle, Inradius, and Altitude [JavaScript, GeoGebra]
  539. Construct Triangle by Angle, Median, and Circumradius [JavaScript, GeoGebra]
  540. Construct Triangle by Angle Bisector, Altitude, and Side [JavaScript, GeoGebra]
  541. Construct Triangle by Angle, Altitude and Median [JavaScript, GeoGebra]
  542. Construct Triangle from Altitude, Median and Inradius [JavaScript, GeoGebra]
  543. Constructing a triangle from its angle bisectors is in general impossible
  544. Construction: Parallel Line through Point
  545. Construction and Properties of Mixtilinear Incircles [JavaScript, GeoGebra]
  546. Construction and Properties of Mixtilinear Incircles 2 [JavaScript, GeoGebra]
  547. Construction of a Cyclic Quadrilateral
  548. Construction of a Square from the 2008 Austrian MO
  549. Construction of a Triangle from an Angle, Circumcenter and Incenter
  550. Construction of a Triangle from the Circumcenter, Orthocenter and Incenter
  551. Construction of a Triangle from the Circumradius, Inradius, and an Altitude
  552. Construction of a Triangle from a Side, the Median and the Angle Bisector
  553. Construction of a Triangle from Two Vertices and the Centroid
  554. Construction of an Oval - the Roman Way [Java, GeoGebra]
  555. Construction of Conics from Pascal's Theorem [Java]
  556. Construction of Regular Pentagon by H. W. Richmond
  557. Construction of Thebault Circles [JavaScript, GeoGebra]
  558. Construction of the Angle Bisector [Java]
  559. Construction of the Perpendicular Bisector [Java]
  560. Construction of Triangle from Side, Angle, and that Angle's Bisector
  561. Construction problem [Java]
  562. Constructions Related To An Inaccessible Point
  563. Construction with the Compass Only
  564. Continuous Line Illusion [Java]
  565. Convex Polygon Is the Intersection of Half Planes [Java]
  566. Copernicus' Theorem [Java]
  567. Construction with Optimization in Angle - Problem the 1979 USA Mathematical Olympiad
  568. cos(36°) = (1 +5)/4
  569. cos 75 + cos 45 = cos 15
  570. Cosine Law
  571. Counting Triangles and Segments in a Polygon [Java]
  572. Cross Points in a Polygon [Java]
  573. Cross-Ratio
  574. Crossed-Lines Construction of Shapes of Constant Width [Java]
  575. Crossing Number of a Graph
  576. Cube Counting Ambiguity [Java]
  577. Cultivating Regular Pentagons
  578. Curious Irrationality in Square
  579. Curry's Paradox [Java]
  580. Cut the Cone [Java]
  581. Cut the Cube [Java]
  582. Cutting a Hole in Half [JavaScript, GeoGebra]
  583. Cut the Cylinder [Java]
  584. Cutting Circle to Rearrange Two Dots [JavaScript]
  585. Cutting Squares
  586. Cutting Triangle in Two by a Line through a Point [Java, GeoGebra]
  587. Cutting Triangles off Regular Hexagon
  588. Cyclic Hexagon [Java]
  589. Cyclic Quadrilateral, Angle Bisector And Isosceles Triangle
  590. Cyclic Quadrilateral, Concurrent Circles and Collinear Points [Java]
  591. Cyclic Quadrilateral from the USAMO
  592. Cycloids [Java]
  593. Dan Sitaru's Inequality with Tangents II
  594. Dancing Rectangles Model Auxetic Behavior [Java]
  595. Dancing Squares or a Hinged Plane Tessellation [Java]
  596. Dao's Archimedean Twins [JavaScript, GeoGebra]
  597. Dao's Archimedean Twins - Second Pair [JavaScript]
  598. Dao's Archimedean Twins - Third Pair [JavaScript]
  599. Dao Thanh Oai's Invariant
  600. Dao's Variant of Thébault's First Problem [JavaScript, GeoGebra]
  601. David Richeson's Extention of an Old Japanses Theorem [Java]
  602. Day's Sine Illusion [Java]
  603. Decompose Cyclic Quadrilaterals into k≥4 Cyclic Quadrilaterals
  604. A Decomposition of Isosceles Triangles into 4 Isosecles Triangles
  605. Delboeuf Illusion [Java]
  606. Delian Problem Solved [Java]
  607. Desargues' Hexagon [Java, GeoGebra]
  608. Desargues in the Bride's Chair (with Pythagoras)
  609. Desargues' Theorem [Java]
  610. Determination ofπ
  611. Diagonal Count [Java]
  612. Diagonals in a Cyclic Quadrilateral
  613. Diameters and Chords [Java]
  614. Dimensionless Inequality in the Euclidean Plane
  615. Directly Similar Figures [Java]
  616. Disappearing Lines puzzle [Java]
  617. Discovery of Duane DeTemple [Java]
  618. Dissection of a 10×13 Rectangle into Two Chessboards
  619. Dissection of a Vase [Java]
  620. Dissection of Cyclic Quadrilateral [Java]
  621. Dissection of Triangle into Rhombus [Java]
  622. Dissection of Triangle into Rhombus by Hubert Shutrick [Java]
  623. Distance
  624. Distance Between Projections
  625. Distance between the Orthocenter and Circumcenter
  626. Distance Formula
  627. Distorted Lines Illusion [Java]
  628. Divergent Spirals Illusion [Java]
  629. Divide a Circle into N Parts of Equal Area
  630. Divide a segment into n equal parts
  631. Divide Triangle by Lines Parallel to Base [JavaScript, GeoGebra]
  632. Dividing Evenly a Quadrilateral [Java]
  633. Dividing Evenly a Quadrilateral II [Java]
  634. Dorin Marghidanu's Inequality with Maximum Side
  635. Double Generation Theorem [Java]
  636. Drawing circles [Java]
  637. Droz-Farny Circles [Java]
  638. Droz-Farny Line Theorem [Java]
  639. Droz-Farny Theorem - an Analytic Solution [JavaScript, GeoGebra]
  640. Dual of Maxwell's Theorem
  641. Duplication of the Cube
  642. Dynamic Construction of Ellipse and Other Curves [Java]
  643. Dynamic Software as Serendipity Enhancement [Java, GeoGebra]
  644. A. G. Samosvat's Proof by Dissection of the Pythagorean Theorem (#104) [GeoGebra]
  645. E. W. Dijkstra's Proof of the Pythagorean Theorem [Java]
  646. Early Refinement of the Ionescu-Weitzenbock Inequality
  647. Easy Construction of Bicentric Quadrilateral [Java]
  648. Easy Construction of Bicentric Quadrilateral II [Java]
  649. Egyptian Triangle By Paper Folding
  650. Egyptian Triangle By Paper Folding II
  651. Egyptian Triangle By Paper Folding III
  652. Eight Equal Tangents [Java]
  653. Eight Point Circle [Java]
  654. Elementary Introduction into the Concept of Area
  655. Ellipse Between Two Circles [Java]
  656. Ellipse in Arbelos [Java]
  657. Ellipse Touching Sides of Triangle at Midpoints [Java, GeoGebra]
  658. Emil Stoyanov's From Reflections to Altitudes
  659. Emil Stoyanov's New Year's Problem
  660. Emil Stoyanov's New Year's Problem, a Sequel
  661. Equal And Perpendicular Segments in a Square
  662. Equal Angles in Two Circles [Java]
  663. Equal Angles in Two Circles II [Java]
  664. Equal areas In Circle [JavaScript]
  665. Equal Areas in Equilateral Triangle [Java]
  666. Equal Areas In Parallelogram à la Pythagoras [Java]
  667. Equal Areas in Regular 2n-gons [Java]
  668. Equal Chords in Crossing Circles [Java]
  669. Equal Circles, Medial Triangle and Orthocenter [Java]
  670. Equal Incircles Theorem [Java]
  671. Equiangular p-gons
  672. Equichordal points: Just Do It [Java]
  673. Equidecomposition of a Rectangle and a Square [Java]
  674. Equidecomposition of Two Rectangles [Java]
  675. Equidecomposition of a Triangle and a Rectangle [Java]
  676. Equidecomposition of a Triangle and a Rectangle II [Java]
  677. Equidecomposition of Two Parallelograms [Java]
  678. Equilateral and 3-4-5 Triangles [Java]
  679. Equilateral triangle and squares
  680. Equilateral Triangle from Equilateral Triangle
  681. Equilateral Triangle in Equilateral Triangle [JavaScript, GeoGebra]
  682. Equilateral Triangle on a Closed Curve [JavaScript, GeoGebra]
  683. Equilateral Triangle on Angle Bisectors
  684. Equilateral Triangle on Parallel Lines [Java]
  685. Equilateral Triangle on Parallel Lines II
  686. Equilateral Triangle on Three Lines [JavaScript, GeoGebra]
  687. Equilateral Triangle in Square and Its Circumcircle
  688. Equilateral Triangle in Square with the Cevians through Its Apex
  689. Equilateral Triangle in Square And the Pedal Circle of Its Apex
  690. Equilateral Triangle, Straight Line and Tangent Circles [Java]
  691. Equilateral Triangles and Incircles in a Square
  692. Equilateral Triangles formed by Circumcenters [JavaScript, GeoGebra]
  693. Equilateral Triangles on Diagonals of Antiequilic Quadrilateral [Java]
  694. Equilateral Triangles On Sides of a Parallelogram [Java]
  695. Equilateral Triangles On Sides of a Parallelogram II [Java]
  696. Equilateral Triangles on Sides of a Parallelogram III [JavaScript, GeoGebra]
  697. Equilateral Triangles on Sides of a Quadrilateral [Java]
  698. Equilic Quadrilateral I, a Flawed Proof [Java]
  699. Equilic Quadrilateral I, A Variation [Java]
  700. Equilic Quadrilateral II [Java]
  701. Erdös-Mordell Inequality
  702. Escher's Theorem [Java]
  703. Euclid's Fifth Postulate
  704. Euclid'sElements Reference Page
  705. Euclid I.43 [Java]
  706. Euclid I.43 Extended [Java]
  707. Euclidean Construction of Center of Ellipse [Java]
  708. Euclidean Construction of Tangent to Ellipse
  709. Euler Inequality in Triangle
  710. Euler Line Cuts Off Equilateral Triangle [Java]
  711. Euler Line and 9-Point Circle [Java]
  712. Euler Line Through a Vertex
  713. Euler's Formula and Poncelet Porism
  714. Euler Line in a Triangle with a 60 Degrees Angle
  715. Every Parallelogram Is a Rectangle
  716. Excircle in Equilateral Triangle
  717. Excircles in Trapezoid
  718. Exeter Point [Java, GeoGebra]
  719. Existence of the Circumcenter [Java]
  720. Existence of the Orthocenter [GeoGebra]
  721. Existence of the Euler Line: An Elementary Proof [Java]
  722. Existence of the Incenter: a Second Look
  723. Experimentation with Dynamic Geometry Software: An Example [Java]
  724. Exploring Vecten's Wreaths with Linear Algebra
  725. Expressions Invariant under Projecive Mappings
  726. Exterior Angle Theorem - an appreciation
  727. External Angle Bisector [Java]
  728. Extouch Triangle in Poncelet Porism [Java]
  729. Extra Feature of Van Aubel Configuration [JavaScript,GeoGebra]
  730. Extras in Bottema's Configuration [JavaScritpt, GeoGebra]
  731. Extremal Problem in a Quadrilateral
  732. Extremal Distance Ratio [GeoGebra]
  733. Extremal Problem in a Circular Segment
  734. The Extreme Principle
  735. Eye-to-Eye Theorem I [JavaScript, GeoGebra]
  736. Eye-to-Eye Theorem II [JavaScript, GeoGebra]
  737. Eyeball Theorem [JavaScript, GeoGebra]
  738. Eyeball Theorem Rectified [JavaScript]
  739. Eyeballing a Ball [JavaScript, GeoGebra]
  740. Eyeballs Projected [JavaScript, GeoGebra]
  741. Fagnano's problem [Java]
  742. Faulty Symmetry
  743. Fermat's Hexagon [JavaScript, GeoGebra]
  744. Fermat in a Triangle with a 60 Degrees Angle
  745. Fermat point and 9-point Centers [Java]
  746. Fermat Point Several Times Over
  747. Feuerbach's Theorem: A Proof [Java]
  748. Find a Common Chord of Given Length [Java]
  749. Find the Angle! [Java]
  750. Finding a Parallelogram in 3D
  751. Finding Circle Center By Ruler Alone [Java]
  752. Finding the Circumradius of the Excentral Triangle
  753. Five Concyclic Points [Java]
  754. Five Incircles in a Square [Java]
  755. Five Incircles Theorem [Java]
  756. Five Squares in Complex Numbers [Java, GeoGebra]
  757. Fixed Point in a Kite - Problem from the 1993 Asian Pacific MO
  758. Fixed Point in Isosceles and Equilateral Triangles
  759. Fixed Point on Perpendicular Bisector [GeoGebra, JavaScript]
  760. Fixed Point of Circles Orthogonal to the Given One [Java]
  761. Fixed points from 2007 Irish Mathematical Olympiad
  762. Fleury's Algorithm and Euler's Paths and Cycles [Java]
  763. FJG Capitan's Sangaku
  764. Focal Definition of Ellipse [Java]
  765. Focal Definition of Parabola [Java, GeoGebra]
  766. Focus and Directrix of Ellipse [Java]
  767. Focus on the Eyeball Theorem [JavaScript, GeoGebra]
  768. Folding Square in a Line through the Center [Java, GeoGebra]
  769. Fold Square into Equilateral Triangle [JavaScript]
  770. Following the Hilbert Curve [Java]
  771. Foot of Altitude and Minimum Distance [Java]
  772. For Equality Choose Angle Bisector [JavaScript, GeoGebra]
  773. For every object there is a distance at which it looks its best.
  774. Ford's touching circles
  775. Four Centroids and Parallels [Java]
  776. Four Circles and a Line [GeoGebra]
  777. Four Circles In a Triangle [Java]
  778. Four Concurrent Lines in a Cyclic Quadrilateral [Java]
  779. Four Construction Problems [Java]
  780. Four Crossing Circles [Java]
  781. Four Geometric Problems of Antiquity
  782. Four Golden Circles
  783. Four Hinged Squares [Java]
  784. Four Incident Circles [Java]
  785. Four Incircles in Equilateral Triangle [Java]
  786. Four Isosceles Triangles Hinged at Vertices [JavaScript, GeoGebra]
  787. Four 9-Point Circles in a Quadrilateral [Java]
  788. Four Pedal Circles [Java]
  789. Four Touching Circles [Java]
  790. Four Touching Circles II [Java]
  791. Four Touching Circles III [Java]
  792. The Four Touching Circles Problem IV [Java, GeoGebra]
  793. Four Triangles, One Circle [Java]
  794. Four Turtles (or Bugs, or Dogs, etc.) [Java]
  795. Fractal curves and dimension [Java]
  796. François Viète's Reduction of CCC to PCC [Java, GeoGebra]
  797. Friendly Kiepert's Perspectors [Java]
  798. From 3 to Golden Ratio in Semicircle
  799. From Angle Bisector to 120°120 degrees Angle
  800. From Arbitrary Hexagon to Regular One [JavaScript, GeoGebra]
  801. From Arbitrary Pentagon to Regular One [JavaScript, GeoGebra]
  802. From Equilateral Triangle and Square to Golden Ratio
  803. From Foci to a Tangent in Ellipse [Java]
  804. From One Collinearity to Another
  805. From Perpendicular Center Lines to Concyclic Points
  806. From Straight Line to Regular Hexagon [JavaScript, GeoGebra]
  807. From Triangle Inequality to Inequality in Triangle
  808. Fun Identity in Right Triangle
  809. Functions And Triangles
  810. Fundamental Theorem of 3-Bar Motion [Java]
  811. Further Arithmetic Progression in 30-60-90 Triangle
  812. Further Properties of Peculiar Circles
  813. Further properties of Van Aubel Configuration [JavaScript, GeoGebra]
  814. Fuss' Theorem [Java]
  815. Garcia's Archimedean Quadruplets [JavaScript, GeoGebra]
  816. Garcia's Two Circles Lemmas [JavaScript, GeoGebra]
  817. Garcia-Feuerbach Collinearity [JvaScript, GeoGebra]
  818. Garfield's Ghost Revisited - by Tony Foster
  819. Generalizing a Romanian Olympiad Problem [Java]
  820. Geometric/Trigonometric Observation/Exercise
  821. Geometric Illustration of a Convergent Series
  822. Geometric Mean In Trapezoid
  823. Geometric Mean Sangaku
  824. Geometric Meaning of the Geometric Mean
  825. Geometric Optimization from the Asian Pacific Mathematical Olympiad [Java]
  826. Geometric Proof of Hlawka's Inequality
  827. Geometric Proofs Of the Irrationality of Square Roots
  828. Geometry, Algebra, and Illustrations
  829. Gergonne and Medial Triangles Are Orthologic [Java]
  830. Gergonne and Soddy Lines Are Perpendicular [Java]
  831. Gergonne in Ellipse [Java]
  832. Gergonne and Van Obel Theorems
  833. Getting the first digits of Pi by counting collisions
  834. Gion Shrine Problem
  835. Given Parabola, Find Axis
  836. Glide Reflection [Java]
  837. Golden Ratio in Geometry
  838. Golomb's inductive proof of a tromino theorem [Java]
  839. Gothic Arc [Java]
  840. Graph Theory [Java]
  841. Grebe: from Ladies' Diary to Carroll's Pillow [Java]
  842. Grebe's Theorem
  843. Greg Markowsky's Problem for Parabola [Java]
  844. Gregoie Nicollier's Proof of Napoleon's Theorem
  845. Griffiths Points in Cyclic Quadrilateral [Java]
  846. Griffiths' Theorem
  847. Half Turn, Reflection in Point [Java]
  848. Halving a square
  849. Harmonic Mean in Geometry
  850. Harmonic Mean Sangaku [Java]
  851. Harmonic Ratio
  852. Harmonic Ratio in Complex Domain
  853. Hart Circle [Java]
  854. Hart's Inversor [Java]
  855. Haruki's Lemma [Java]
  856. Haruki's Theorem
  857. Hausdorff Distance
  858. Hearty Munching on Cardioids [Java]
  859. Height/Width Interplay Illusion [Java]
  860. Helly's Theorem
  861. Hering Illusion [Java]
  862. Hermann Grid Illusion [Java]
  863. Heron's formula
  864. Heron's Formula: a Proof [Java]
  865. Heron's Problem [Java]
  866. Heron in Trapezoid [JavaScript, GeoGebra]
  867. Hexagon Parallel to Medial Triangle [Java]
  868. Hexagon Parallel to Orthic Triangle [Java]
  869. Hexagons in a Square
  870. Hidden Orthogonality [JavaScript, GeoGebra]
  871. Hinged Greek Cross Tessellation [Java]
  872. Hinged Squares [Java]
  873. Hinged Squares II [JavaScript, GeoGebra]
  874. Hippocrates' Squaring of a Lune [Java]
  875. Hippocrates' Squaring of Lunes
  876. Hjelmslev Theorem [Java]
  877. Hlawka in Convex Quadrilateral
  878. Homologous Lines under Three Spiral Similarities [Java]
  879. Homothety [Java]
  880. Homothety between In- and Excircles [Java]
  881. Homothety in Equilateral Triangles [JavaScript, GeoGebra]
  882. Homothety in Three Tangent Circles
  883. Homothety in Three Tangent Circles II
  884. Hooper's Paradox [Java]
  885. How Do Angle Trisectors Divide the Area?
  886. How Fast Does One's Shadow Grow?
  887. How Long Are the Angle Bisectors of a Degenerate Triangle?
  888. How to Construct a Radical Axis [Java, GeoGebra]
  889. How to Construct Tangents from a Point to a Circle [Java, GeoGebra]
  890. Hung Nguyen Viet's Inequality with Radicals and Chebyshev
  891. Hunting Right Angles [Java]
  892. Huygens' Problem
  893. Ian McGee's Observation [Java]
  894. IMO 1998 Problem 1
  895. IMO 2004, Problem 5
  896. IMO 2006, Problem 1
  897. Impossible Fork [Java]
  898. Impossible Frame [Java]
  899. Impossiblity Condition in Concurrent Cevians
  900. Importance of Having an Angle of 60 Degrees
  901. Importance of Occluders: Motion Binding [Java]
  902. In the Spirit of Thebault I [Java, GeoGebra]
  903. In the Wasan Spirit
  904. Incenters in Cyclic Quadrilateral [Java]
  905. Incidence in Feuerbach's Theorem [Java]
  906. Incircle in Equilateral Triangle
  907. Inequalities in Triangle
  908. Inequality in Quadrilateral
  909. Inequality in Rectangle
  910. An Inequality with a Variety of Circumradii
  911. Inequality with Cubes and Cube Roots
  912. An Inequality with Inradius and Excenters
  913. Inequality with Roots, Squares and the Area
  914. An Inequality with Two Sets of Cevians
  915. Infinitude of Primes - A Topological Proof
  916. Inradii Relation in Right Triangle
  917. Inscribed and Central Angles in a Circle [Java]
  918. Inscribed Angles [Java]
  919. Inscriptible and Exscriptible Quadrilaterals [Java]
  920. Inscriptible Quadrilateral: An Illustration [Java]
  921. Inscriptible Quadrilateral of Triangle Incenters [JavaScript, GeoGebra]
  922. Integer Chord in a Polynomial Graph
  923. Integer Triangles with Two Angles in the Ratio 1 : 2 [JavaScript, GeoGebra]
  924. Internal Tangents to Three Circles [Java]
  925. Interpretation of the coordinate formula for the dot product in 3D
  926. Intersecting Chords Theorem
  927. Intersections of a Circle with the Four Quadrants [Java]
  928. Intouch Triangle in Poncelet Porism [Java]
  929. Invariance in Orthodiagonal Quadrilaterals [Java]
  930. Invariant Area Sweep Implies Pythagorean Theorem [Java]
  931. Inverse Similarity through Reflections
  932. Inversion: Reflection in a Circle [Java]
  933. Involution on the Projective Line
  934. Is Every Trapezoid Parallelogram? [Java]
  935. Is X a Midpoint of a Chord [JavaScript, GeoGebra]
  936. Isosceles Tetrahedra Characterization via Inequalities
  937. Isogonal Concurrencies [JavaScript, GeoGebra]
  938. Isogonal Lemma [JavaSCript, GeoGebra]
  939. Isosceles Configuration in Triangle [JavaScript, GeoGebra]
  940. Isosceles Tetrahedron
  941. Isosceles Trapezoid In Cyclic Quadrilateral [JavaScript, GeoGebra]
  942. Isosceles Triangle with Two Points on Base
  943. Isogonal and Isotomic Conjugalities [Java]
  944. Isogonal Concurrency [Java]
  945. Isogonal image of the circumcircle [Java]
  946. Isoperimetric Theorem and Inequality
  947. Isosceles on the Sides of a Triangle [Java]
  948. Isotomic Reciprocity [JavaScript, GeoGebra]
  949. Isotomy and Isogonality Hand-in-Hand [Java]
  950. Iterations and the Mandelbrot Set [Java]
  951. Iterations on a Circle Through Three Points [Java]
  952. Iterations on Euler Lines [Java]
  953. Igor Sharygin's Problem in Circumscribed Quadrilateral
  954. J. Casey's Additions to Euclid I.47
  955. Jan Stevens' proof of E. W. Dijkstra's Generalization of the Pythagorean theorem
  956. Joachimsthal's Notations
  957. John Sharp's Paradox [Java]
  958. Johnson Circles [Java]
  959. Join Circles by Given Segment [Java]
  960. Joined Common Chords of Napoleon's Circumcircles [JavaScript, GeoGebra]
  961. Jordan and Kober Inequalities, PWW
  962. Jordan Curve Theorem
  963. Joseph Keech in Bride's Chair [Java]
  964. Judd Illusion [Java]
  965. Julia sets indexing [Java]
  966. K. Knop's Problem with Two Regular Pentagons And an Equilateral Triangle
  967. Kanizsa Triangle [Java]
  968. Kiepert's Centroid [JavaScript, GeoGebra]
  969. Kiepert's Theorem [Java]
  970. Kiepert's Triangles Graduate to Ears of Arbitrary Shape [JavaScript, GeoGebra]
  971. Klamkin's Quickie via Peru Geometrico
  972. Knots [avi movie]
  973. Knots on a Torus [Java]
  974. Kürschak's Tile and Theorem [Java]
  975. La Hire's Theorem [Java]
  976. Langman's Paradox [Java]
  977. LCC: Apollonius' Problem with Two Circles and a Line [Java, GeoGebra]
  978. Lean Napoleon's Triangles [Java]
  979. Length of a Median
  980. Length of the diagonal of the unit square equals the square root of 2
  981. Lennes' Polyhedron [Java]
  982. Leo's Lemma, Second Application
  983. Leo Giugiuc's Inequality for the Medians
  984. Leo Giugiuc's Inequality in Triangle, Solely with Cotangents
  985. Leo Giugiuc's Proof of Napoleon's Theorem
  986. Leo Giugiuc's Trigonometric Lemma
  987. Leo Giugiuc's Second Lemma And Applications
  988. Leonardo's Petals
  989. Lepidoptera of the Circles [Java]
  990. Leuenberger's Inequality for Medians, Inradius and Circumradius
  991. Lighthouse at Fermat Points [JavaScript, GeoGebra]
  992. Line IO in Bicentric Quadrilaterals
  993. Line Not Through a Center of Similarity [JavaScript, GeoGebra]
  994. Line Through a Center of Similarity [JavaScript, GeoGebra]
  995. Line through a Point in an Angle
  996. Line, Circle, and Fixed Points [Java]
  997. Linear Function with Coefficients in Arithmetic Progression [Java, GeoGebra]
  998. Lines Crossing Circles at Vertices of Equilateral Triangle
  999. Lines through Circles at Vertices of Equilateral Triangle [JavaScript]
  1000. LLC: Apollonius' Problem with Two Lines and a Circle [Java, GeoGebra]
  1001. Lipogrammatic Proof of the Pythagorean Theorem
  1002. Loci of points in a cube
  1003. Locus of Points in a Given Ratio to Two Points [Java]
  1004. Longest segment
  1005. Longitude, Latitude and Distance to the Equator
  1006. Looking Back at Bottema [JavaScript, GeoGebra]
  1007. Luca Moroni's Problem In Equilateral Triangle
  1008. Mach's Conservation of Area and the Pythagorean Theorem
  1009. MacLaurin's Construction of Conics [Java]
  1010. Maimed Cake [Java]
  1011. Malfatti's Problem [Java]
  1012. Malfatti's Problem, Hart's Solution [Java]
  1013. Marian Cucoanes' Inequality With Roots and Powers
  1014. Marian Dinca's Inequality
  1015. Mascheroni Construction of a Regular Pentagon
  1016. Mathematical Droodles [Java]
  1017. Mathematics in Pizzeria [Java]
  1018. MathPro Logo [Java]
  1019. Maximal Properties of the Pythagorean Relation
  1020. Maximum Area Property of Equilateral Triangles
  1021. Maximum Area Property of the Medial Triangle
  1022. Maximum Perimeter Property of the Incircle [Java]
  1023. Maximum Ratio of Similarity - Belarus Olympiad Problem
  1024. Maxwell's Theorem [Java]
  1025. May the Product of Planes Be a Sphere?
  1026. McDougall's Generalization of Ptolemy's Theorem
  1027. Mechanical Proofs of the Pythagorean Theorem
  1028. Median in Touching Circles [Java]
  1029. Medians
  1030. Medians in a Quadrilateral [Java]
  1031. Medians in a Triangle Meet at the Center: a Second Look
  1032. Meisters' Two Ears Theorem
  1033. Menelaus Theorem [Java]
  1034. Metric Relations in a Triangle
  1035. Mickey Might Be a Red Herring in the Mickey Mouse Theorem
  1036. Midline in Quadrilateral [Java, GeoGebra]
  1037. Midline in Similar Triangles [Java]
  1038. Midline in Trapezoid [Java, GeoGebra]
  1039. Midline in Triangle [Java, GeoGebra]
  1040. Midpoint Reciprocity in Napoleon's Configuration [JavaScript,GeoGebra]
  1041. Midpoints and Orthogonality in Isosceles Triangles [Java]
  1042. Midpoints from Gergonne Triangle [Java]
  1043. Midpoints of the Lines Joining In- and Excenters [Java]
  1044. Miguel's Area of Square [JavaScript, GeoGebra]
  1045. Miguel's Tangents: Modern Day Sangaku [JavaScript, GeoGebra]
  1046. Miguel Ochoa's Chords And Tangents [JavScript, GeoGebra]
  1047. Miguel Ochoa's van Schooten Is a Slanted Viviani [JavScript, GeoGebra]
  1048. Miguel Ochoa's van Schooten Like Theorem [JavaScript, GeoGebra]
  1049. Miguel Ochoa's van Schooten Like Theorem II [JavaScript, GeoGebra]
  1050. Miguel Ochoa's van Schooten Like Theorem III [JavaScript, GeoGebra]
  1051. Miguel's Special Trapezoid
  1052. Mikhalev's Octahedrons
  1053. Minesweeper Theorem
  1054. Miquel's Point [Java]
  1055. Miquel's Point of a 4-line Via Spiral Similarity [Java]
  1056. Miquel's Theorem for Circles [Java]
  1057. Miquel Circumcenters [JavaScrirpt, GeoGebra]
  1058. Mirror on the Wall [Java]
  1059. Mirror property of the altitudes [Java]
  1060. Mirror Property of Altitudes via Pascal's Hexagram [Java]
  1061. Mixing Incenter And Orthocenter in Greece
  1062. Mixtilinear Circles and Concurrence [Java]
  1063. Modern Day Sangaku
  1064. Moebius Strip [avi movie]
  1065. Möbius' Strip [Java]
  1066. Models and Metamathematics
  1067. Moment of Inertia of a Regular Polygon [JavaScript]
  1068. Moments in a Peculiar Cyclic Polygon
  1069. Monge via Desargues [Java]
  1070. Monge via Desargues II [Java]
  1071. More of More of Gloden Ratio in Equilateral Triangles
  1072. Morley Constellation [Java]
  1073. Morley's Miracle [Java]
  1074. Morphing [Java]
  1075. Müller-Lyer Illusion [Java]
  1076. Multifaceted Cork [Java]
  1077. Multiplication of Points on a Circle [JavaScript,GeoGebra]
  1078. Multiplication of Points on an Ellipse [JavaScript, GeoGebra]
  1079. Munching on Circles
  1080. Munching on Inscribed Angles
  1081. My logo
  1082. Nagel Line [Java]
  1083. Nagel point [Java]
  1084. Nagel Point and Centroid on Adjacent Isosceles Triangles
  1085. Nagel Point of the Medial Triangle [Java]
  1086. Nagel Point on the Incircle in Isosceles Triangle
  1087. Nagel's Theorem [Java]
  1088. Napoleon's Hexagon [JavaScript, GeoGebra]
  1089. Napoleon's Theorem
  1090. Necker Cube [Java]
  1091. Neuberg Cubic [Java, GeoGebra]
  1092. Neuberg Sangaku [Java]
  1093. Newly Born Pair of Siblings to Archimedes' Twins [Java]
  1094. Newton's Construction of Conics [Java]
  1095. Newton's Theorem [Java]
  1096. Nine Point Center in Square
  1097. Nine Point Circle [Java]
  1098. Nine Point Circle: an Elementary Proof [Java]
  1099. No Equilateral Triangles, Please [Java]
  1100. Nobbs' Points, Gergonne Line [Java]
  1101. Non-Eclidean Geometries
  1102. No-Pedal Collinearity [Java]
  1103. Not So Hidden Homotheties [JavaScript, GeoGebra]
  1104. Novel Concurrency of Perpendicular Bisectors [JavaScript, GeoGebra]
  1105. Number of Regions N Lines Divide Plane
  1106. Occluded Wheel Illusion [Java]
  1107. Olof Hanner's Jigsaw Puzzle [Java]
  1108. On the Difference of Areas
  1109. One More Property of Equilateral Triangles
  1110. One More Seven Circles Theorem [JavaScript, GeoGebra]
  1111. One Sheet Hyperboloid [Java]
  1112. A One-Sided Inequality in Triangle
  1113. One Triangle from Another
  1114. One Triangle from Another II
  1115. Optimal Quadrilateral Inscribed in a Square
  1116. Optimization in a Crooked Trapezoid
  1117. Optimization in Parallelepiped
  1118. Optimization Problem in Acute Angle [Java]
  1119. Octagon in Parallelogram: Overlapping Regions [Java]
  1120. Octagon in Parallelogram [Java]
  1121. Optical Property of Ellipse [Java]
  1122. Orbison illusion [Java]
  1123. Orthic Semiperimeter [Java, GeoGebra]
  1124. Orthic Triangle in a Triangle with a 120 degrees angle
  1125. Orthogonal Lines, Midpoints, and Collinearity [Java, GeoGebra]
  1126. Orthogonality in Isogonal Conjugacy [JavaScript, GeoGebra]
  1127. Orthocenter and Three Equal Circles [Java]
  1128. Orthocenters
  1129. Orthocenters of Two Triangles Sharing Circumcenter and Base [Java]
  1130. Orthocentric System From Rectangle [Java]
  1131. Orthodiagonal and Cyclic Quadrilaterals [Java]
  1132. Orthogonality in Isosceles Triangles [Java]
  1133. Orthogonality in Two Squares [JavaScript, GeoGebra]
  1134. Orthologic Triangles in a Quadrilateral [Java]
  1135. Orthopole [Java]
  1136. Out of Pentagon Sangaku
  1137. Packing shapes in a plane
  1138. Padoa's Inequality
  1139. Pairs of Areas in Equilateral Triangle
  1140. Pairs of Homologous Lines under Spiral Similarities [Java]
  1141. Pairs of Incircles in a Quadrilateral [Java]
  1142. Pantograph [Java]
  1143. Paper Folding & Cutting Sangaku
  1144. Paper Folding Geometry
  1145. Paper strip activities [avi movies]
  1146. Paper strip activities, two strips
  1147. Pappus' Generalization of Euclid I.47 [Java]
  1148. Pappus' Theorem [Java]
  1149. Parabola [Java]
  1150. Parabola and Abutting Equilateral Triangles
  1151. Parabolas Related to the Orthic Triangle [JavaScript, GeoGebra]
  1152. Parabolic Mirror, Illustration [Java]
  1153. Parabolic Mirror, Theory [Java]
  1154. Parabolic Reciprocity [JavaScript, GeoGebra]
  1155. Parabolic Sieve of Prime Numbers
  1156. Paragon [Java]
  1157. Parahexagon [Java]
  1158. Parallel Chords [Java]
  1159. Parallel Chords II [Java]
  1160. Parallel Chords in Conics [Java, GeoGebra]
  1161. Parallel Chords in Ellipse [Java]
  1162. Parallel Chords in Crossing Circles [Java]
  1163. Parallel Lines in a Cyclic Quadrilateral [Java]
  1164. Parallel Lines in a Quadrilateral II [Java] Parallel Lines in a Quadrilateral
  1165. Parallel Lines in Rhombus
  1166. Parallel Lines in a Triangle [Java, GeoGebra]
  1167. Parallels through the Vertices of Equilateral Triangle
  1168. Parallelogram and Ellipses [Java, GeoGebra]
  1169. Parallelogram and Four Equilateral Triangles [JavaScript, GeoGebra]
  1170. Parallelogram and Similar Triangles [Java]
  1171. Parallelogram Illusion [Java]
  1172. Parallelogram in Four Circles [JavaScript, GeoGebra]
  1173. Parallelogram in Parallelogram And in Projection [JavaScript, GeoGebra]
  1174. Parallelogram in Trapezoid
  1175. Parallelogram Iterations [Java]
  1176. Parallelogram Law [Java]
  1177. Parallelogram Law: A PWW [Java]
  1178. Parallelogram Law: A Tessellation [Java]
  1179. Parallelogram with Side Lines through Fixed Points [JavaScript, GeoGebra]
  1180. Partition of point sets in a plane
  1181. Partitioning 3-Space with Circles
  1182. Partitioning a Circle
  1183. Pascal: Necessary and Sufficient [Java]
  1184. Pascal in a Cyclic Quadrilateral [Java]
  1185. Pascal Lines: Steiner and Kirkman Theorems [Java]
  1186. Pascal Lines: Steiner and Kirkman Theorems II [Java]
  1187. Pascal's theorem [Java]
  1188. Peacock's Tail Sangaku
  1189. Peaucellier Linkage [Java]
  1190. Pedal Collinearities [Java]
  1191. Pedal Parallelogram [JavScript, GeoGebra]
  1192. Pedal Polygons [Java]
  1193. Pedal Property in Equilateral Triangle
  1194. Pedal SimilarityPedal Triangle and Isogonal Conjugacy [Java]
  1195. Pedal Triangles of Inverse Points [JavaScript, GeoGebra]
  1196. Pedoe's Theorem [Java]
  1197. Pencils of Cubics
  1198. Pentagon, construction of
  1199. Pentagon And Decagon, Both Regular
  1200. Pentagon in a Semicircle [Java]
  1201. Pentagon Proportions Sangaku
  1202. Perimeters of Convex Polygons, One within the Other
  1203. Perimeters of Parallelogram And Rhombus [JavaScript, GeoGebra]
  1204. Periodic patterns in sin(N) [Java]
  1205. Perpendicular Bisectors in an Inscriptible Quadrilateral [Java]
  1206. Perpendicular Bisectors in an Inscriptible Quadrilateral II [Java]
  1207. Perpendicular lines in a cyclic quadrilateral from 1975 Canadian Mathematical Olympiad
  1208. Perpendiculars in Parallelogram [JavaScript, GeoGebra]
  1209. Perspective Triangles in Circle
  1210. Pick's Theorem [Java]
  1211. Phantom Circle and Recaptured Symmetry
  1212. Plane Filling Curves [Java]
  1213. Plane Isometries
  1214. Plane Isometries As Complex Functions
  1215. Plato's Geometric Numbers: can you better Sam Loyd?
  1216. Pleasant Proportions in Triangle
  1217. Poggendorff's Illusion
  1218. Point common to two similar rectangles [Java]
  1219. Point in a Square
  1220. Point on Bisector in Right Angle
  1221. Points Generated by the Nine Points
  1222. Points on Incircle: Another Look
  1223. Polar Circle [Java]
  1224. Poles and Polars [Java]
  1225. Polygon in a Rectangle
  1226. Polygons: formality and intuition [Java]
  1227. Polygons Formed by Perpendicular Bisectors [Java]
  1228. Pompeiu's Theorem
  1229. Poncelet's Porism [Java]
  1230. Poncelet's Porism in Ellipses [Java]
  1231. Poncelet's Theorem [Java]
  1232. Ponzo Illusion [Java]
  1233. Ponzo Illusion II [Java]
  1234. Possible or Impossible? [Java]
  1235. Power of a point with respect to a circle
  1236. PCC: Apollonius' Problem with Two Circles and a Point [Java, GeoGebra]
  1237. PLC: Apollonius Problem with a point, a line, and a circle [Java, GeoGebra]
  1238. PLL: Apollonius' Problem with Two Lines and a Point [Java, GeoGebra]
  1239. PPC: Apollonius' Problem with Two Points and a Circle [Java, GeoGebra]
  1240. PPL: An Elementary Solution [Java, GeoGebra]
  1241. PPL: Apollonius' Problem with Two Points and a Line [Java, GeoGebra]
  1242. Prasolov's Pythagorean Identity
  1243. Praying Eyes Theorem [JavaScript, GeoGebra]
  1244. Problem 1 from the 2006 IMO
  1245. Problem 1 from the EGMO2017
  1246. Problem 1 from the Ninth Nordic Mathematical Contest (1994)
  1247. Problem 11984 From the American Mathematical Monthly
  1248. Problem 3 from the EGMO2017
  1249. Problem 4 from the 1959 IMO: Construction of a Right Triangle [Java, GeoGebra]
  1250. Problem 4, 1975 USA Math Olympiad and the Radical Axis [Java]
  1251. Problem 4, 1975 USA Math Olympiad and Isosceles Triangles [Java]
  1252. Problem 4, 1975 USA Math Olympiad: Normals and Tangents [Java]
  1253. Problem 4, 1975 USA Math Olympiad: Problem 4, 1975 USA Math Olympiad: The Final Touch [Java]
  1254. Problem 4 from the 2016 OBJM TST
  1255. Problem 4 from the IMO 2009
  1256. Problem 4 from the 4th BJMO Team Selection Test
  1257. Problem 4087 from Crux Mathematicorum
  1258. Problem 4096 from Crux Mathematicorum
  1259. Problem in an Equilateral Triangle [Java]
  1260. Problem 4 from the IMO 2013 - Synthetic Solution [Javacript, GeoGebra]
  1261. Problem 4160 from the Crux Mathematicorum
  1262. Problem A-2 from the 2002 Putnam Math Competition
  1263. Problem A-6 from the 1992 Putnam Math Competition
  1264. Problem CC156 From Crux Mathematicorum
  1265. Problem in a Special Trapezoid
  1266. Problem in an Equilateral Triangle II [Java]
  1267. Problem in Direct Similarity [JavaScript, GeoGebra]
  1268. Problem in Three Squares [Java]
  1269. Problem of Equal Steps [Java]
  1270. Problem of Equal Steps II [Java]
  1271. Problem on a Pentagonal Star
  1272. Problem with angle bisector from 1975 Canadian Mathematical Olympiad
  1273. Problem with equal angles from 1987 IberoAmerican Mathematical Olympiad
  1274. Proclivity of Conjoint Archimedean Twins for Proliferation [JabvaScript, GeoGebra]
  1275. Projections of Convex Quadrilateral [JavaScript, GeoGebra]
  1276. Projections of Isogonal Conjugate are Concyclic [JavaScript, GeoGebra]
  1277. Projections on Internal and External Angle Bisectors [Java]
  1278. Projective Collinearity in a Quadrilateral [Java]
  1279. Projective infinity
  1280. Projective Invariants for Pascal And Desargues
  1281. Properties of Flank Triangles
  1282. Properties of the Circle of Similitude [Java]
  1283. Properties of Circle Through the Incenter
  1284. Properties of the Figures in Euclid I.47
  1285. Properties of the Harmonic Ratio
  1286. Property of 6-Parpolygon [Java]
  1287. Property of Angle Bisectors [Java]
  1288. Property of Circumscribed Quadrilaterals [Java]
  1289. Property of Points Where In- and Excircles Touch a Triangle [Java]
  1290. Property of Right Isosceles Triangle [Java, GeoGebra]
  1291. Property of Right Trapezoids [GeoGrebra]
  1292. Property of Semicircles [Java]
  1293. Property of Thébault Circles [JavaScript, GeoGebra]
  1294. Property of Two Pencils of Parallel Lines
  1295. Proportions and the Incenter [JavaScript]
  1296. Proportions in Square
  1297. Proportions with Two Orthocenters [JavaScript, GeoGebra]
  1298. Ptolemy's Theorem
  1299. Pure Angle Chasing [JavaScript, GeoGebra]
  1300. Pure Angle Chasing II [JavaScript, GeoGebra]
  1301. Pure Angle Chasing III [JavScript, GeoGebra]
  1302. Puzzles on graphs.
  1303. Pythagorean Theorem (121 proofs)
  1304. Pythagorean Perimeter Theorem
  1305. Pythagoras and Vecten Break Japan's Isolation [Java]
  1306. Pythagorean Triples [Java]
  1307. Quadrature: A Child's Play
  1308. Quadrilateral from a Segment
  1309. Quadrilateral Inequality
  1310. Quadrilateral Inscribed into Parallelogram
  1311. Quadrilateral With Equal Opposite Sides And Angles [Java]
  1312. Quadrilateral with 3 Equal Sides [Java]
  1313. Quadrilaterals Formed by Perpendicular Bisectors [Java]
  1314. Quest for Paragon [Java]
  1315. R and r When G on Incircle
  1316. Radical Axis and Center, an Application [Java]
  1317. Radical Axis of Circles Inscribed in a Circular Segment [Java]
  1318. Radical Center [Java]
  1319. Radius and Construction of a Mixtilinear Circle [Java]
  1320. Radius of a Circle by Paper Folding [Java]
  1321. Random Dot Stereograms [Java]
  1322. The Range of r/R in Triangle with Centroid on the Incircle
  1323. Ratios and Orthogonality in a Triangle - Problem from the 2006 Romania MO
  1324. Rational Points On a Circle
  1325. Rectangle Inscribed in Triangle [JavaScript, GeoGebra]
  1326. Rectified, Halved, Sheared, Eyeballs Still Surprise [JavaScript, GeoGebra]
  1327. Reflection in a Triangle Tangent to Parabola [JavaScript, GeoGebra]
  1328. Reflection In Line [Java]
  1329. Reflection in the Circumcenter
  1330. Reflections in Ellipse [Java]
  1331. Reflections of a Line Through the Orthocenter [Java]
  1332. Reflections of a Point on the Circumcircle [Java]
  1333. Reflections of the Orthocenter
  1334. Reflections of the Orthocenter [Java]
  1335. Reflections of the Orthocenter II Regular Hexagon and Triangle Joined at Vertex [JavaScript, GeoGebra]
  1336. Regular Hexagon from Arbitrary Triangle [JavaScript, GeoGebra]
  1337. Regular Octagon by Paper Folding
  1338. Regular Polygons in a Triangular Grid [Java]
  1339. Regular Polyhedra - Platonic Solids
  1340. Other Solids
  1341. Regular Pentagon Inscribed in Circle by Paper Folding
  1342. Regular polyhedra and Euler's Theorem
  1343. Reim's Similar Coins I
  1344. Reim's Similar Coins II
  1345. Reim's Similar Coins III
  1346. Reim's Similar Coins IV
  1347. Relation Engendered By Altitudes
  1348. Relation Engendered By Medians
  1349. Relations in a Cyclic Polygon
  1350. Remarkable Line in a Quadrilateral [Java]
  1351. Remarkable Line in Cyclic Quadrilateral [Java]
  1352. Rendezvous [Java]
  1353. Reverse Spoke Illusion [Java]
  1354. Revolving Circles Illusion [Java]
  1355. Rhombus in a Cyclic Quadrilateral [Java]
  1356. Rhombus in Circles [Java, GeoGebra]
  1357. Riemann Sphere and Möbius Transformation
  1358. Surprise: Right Angle in Circle [JavaScript, GeoGebra]
  1359. Surprising Length Dependence In Equilateral Triangle by Miguel Ochoa Sanchez
  1360. Right Triangles on Sides of a Square [Java]

    Rotating Square in Search of the Golden Ratio

  1361. Rotating Top Illusion [Java]
  1362. Rotating Gears [Java]
  1363. Rotation Transform [Java]
  1364. Rouse Ball's Fallacy [Java]
  1365. Rusty Compass Construction of Equilateral Triangle [Java]
  1366. Salinon: From Archimedes'Book of Lemmas [Java]
  1367. Sam Loyd's Geometric Puzzle
  1368. Sam Loyd's Son's Dissection [Java]
  1369. Sanchez's Areas in Bottema's Configuration [JavaScript]
  1370. Sangaku: Reflections and the Phenomenon
  1371. Sangaku: Critique of My View and a Response
  1372. Sangaku and The Egyptian Triangle
  1373. Sangaku in a Square
  1374. Sangaku Iterations, Is it Wasan? [Java]
  1375. Sangaku via Peru
  1376. Sangaku with 8 Circles
  1377. Sangaku with Angle between a Tangent and a Chord [Java]
  1378. Sangaku with Quadratic Optimization
  1379. Sangaku with Three Mixtilinear Circles [Java]
  1380. Sangaku with Versines [Java]
  1381. Sangakus with a Mixtilinear Circle [Java]
  1382. Scintillating Grid Illusion [Java]
  1383. Schwarz Lantern [Java]
  1384. Secant Angles [Java]
  1385. Secant Angles II [Java]
  1386. Secant, Normal, Tangent [Java]
  1387. Secant, Tangents and Orthogonality [Java]
  1388. See-Saw Lemma [Java]
  1389. Segment Projections in Equilateral Triangle
  1390. Segment Trisection [Java]
  1391. Segment Trisection II
  1392. Segment Trisection Induced by Parallels to Medians [Java]
  1393. Semicircle on Square [JavaScript]
  1394. Semi-regular Tessellation on Hinges A [Java]
  1395. Semi-regular Tessellation on Hinges B [Java]
  1396. Separating point sets with a circle
  1397. Sequences of Concyclic Points on a Conic
  1398. Sequences of Touching Circles
  1399. Serendipitous Beauty [Java]
  1400. Serendipitous Proofs Of The Pythagorean Theorem
  1401. Seven and the Eighth Circle Theorem
  1402. Seven Circles Theorem [Java]
  1403. Seven Concyclic Points [Java, GeoGebra]
  1404. Seven Equal Circles [JavaScript, GeoGebra]
  1405. 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
  1406. Seyran Ibrahimov's Inequality
  1407. Shaggy Dog Theorem
  1408. Shapes in a lattice
  1409. Shapes of constant width [Java]
  1410. Shearing and Translation in Pythagorean Pants [Java]
  1411. Shearing a Polygon into a Triangle of Equal Area [Java]
  1412. Shearing Butterflies in Quadrilaterals [Java]
  1413. Shedding Light on the Ball for Eyeballing
  1414. Shepard's Parallelogram Illusion [Java]
  1415. Shifted by the Inradius Tangent Collinearities [JavaScript, GeoGebra]
  1416. Shifting Cube Illusion [Java]
  1417. Shimmer Illusion [Java]
  1418. Short Construction of the Geometric Mean
  1419. Shortest Fence in a Quarter-Circle Pasture
  1420. Shredding the torus
  1421. Sides and Area of Pedal Triangle
  1422. Sierpinski Gasket By Common Trema Removal [Java]
  1423. Sierpinski Gasket Via Chaos Game [Java]
  1424. Sierpinski Gasket by Trema Removal [Java]
  1425. Similar Parallelograms on Sides of a Triangle
  1426. Similar Triangles And More
  1427. Similar Triangles in Crossing Circles [JavaScript, GeoGebra]
  1428. Similar Triangles on Sides of a Quadrilateral [Java]
  1429. Similar Triangles on Sides and Diagonals of a Quadrilateral [Java]
  1430. Similarity Is About Proportion - And Ways to Look at It
  1431. Simple Construction of the Circle of Apollonius
  1432. Simple dissection of an acute triangle
  1433. Simple Property of Circle Through the Incenter [JavaScript]
  1434. Simple Quadrilaterals Tessellate the Plane [Java]
  1435. Simson Line [Java]
  1436. Simsons and 9-Point Circles in Cyclic Quadrilateral [Java]
  1437. Simultaneous Contrast Illusion [Java]
  1438. Simultaneous Contrast Illusion II [Java]
  1439. Simultaneous Contrast: Koffka's Illusion [Java]
  1440. Simultaneous Contrast: White's Illusion [Java]
  1441. Simultaneous Contrast: White's Illusion, V-Variant [Java]
  1442. Three Concurrent Chords at 60 Degrees Angles
  1443. Simultaneous Diameters in Concurrent Circles [Java]
  1444. Simultaneous Generalization of the Theorems of Ceva and Menelaus
  1445. Sine and Cosine of 15 Degrees Angle
  1446. Sine, Cosine, and Ptolemy's Theorem
  1447. Six Circles with Concurrent Pairwise Radical Axes
  1448. Six Circles Theorem (Bui Quang Tuan) [Java]
  1449. Six Circles Theorem (Elkies) [Java]
  1450. Six Circles Theorem (Evelyn) [Java]
  1451. Six Concyclic Circumcenters in Fermat's Configuration [JavaScript, GeoGebra]
  1452. Six Concyclic Points [Java]
  1453. Six Concyclic Points on Sides of a Triangle
  1454. Six Concyclic Points II [Java]
  1455. Six Concyclic Points via Antipedal Triangle [JavaScript, GeoGebra]
  1456. Six Incircles in an Equilateral Triangle [Java]
  1457. Six Point Circle [Java]
  1458. SixPoints, ThreeLines [Java]
  1459. Soddy Circles and David Eppstein's Centers [Java]
  1460. Some Properties of Common Tangents [JavaScript, GeoGebra]
  1461. Some Properties of Napoleon's Configuration [Java]
  1462. Spectral Decomposition of a Planar Quadrilateral
  1463. Sperner's Lemma [Java]
  1464. Spiral Similarity [Java]
  1465. Spiral Similarity and CollinearitySpiral Similarity and Collinearity [Java, GeoGebra]
  1466. Spiral Similarity Leads to Equilateral Triangle [JavaScript, GeoGebra]
  1467. Square and Circle in a Gothic Cupola
  1468. Square from Four Points, One on Each Side
  1469. Square From Nowhere [Java]
  1470. Square in a Circle Inscribed in a Square [Java]
  1471. Square in a Right Triangle [Java]
  1472. Square in Chair [Java]
  1473. Square Inscribed in a Triangle [Java]
  1474. Square Inscribed in a Triangle II [Java]
  1475. Square, Similarity and Slopes [Java]
  1476. Squares and Straight Tetrominoes
  1477. Squares in Circles [Java]
  1478. Squares in Semicircle and Circle
  1479. Squares in Triangles
  1480. Squares Inscribed In a Triangle III [Java]
  1481. Squares on Sides of a Parallelogram [JavaScript, GeoGebra]
  1482. Squares on Sides of a Quadrilateral [Java]
  1483. Squares on Sides of a Quadrilateral II [JavaScript, GeoGebra]
  1484. Square out of a Quadrilateral
  1485. Squaring a circle
  1486. Squaring a Rectangle [Java]
  1487. Squinting Eyes Theorem [Java]
  1488. SSA
  1489. SSS
  1490. Staircase Illusion [Java]
  1491. Stan Fulger's Observation in Right Triangle
  1492. Star of David [Java]
  1493. Stathis Koutras' Butterfly
  1494. Stathis Koutras' Theorem
  1495. Stathis Koutras' Theorem II
  1496. Steiner's Circumellipse in Barycentric Coordinates [GeoGebra]
  1497. Steiner's Inellipse
  1498. Steiner's Sangaku
  1499. Steiner's Ratio Theorem
  1500. Steiner's Theorem
  1501. Stereographic Projection [Java]
  1502. Stereographic Projection and Inversion
  1503. Stereographic Projection and Radical Axes
  1504. Stewart's theorem
  1505. Straight Edge Only Construction of Polar
  1506. Structural Constellation [Java]
  1507. Sums of Squares in Circle
  1508. Sum of Squares in Equilateral Triangle
  1509. Sum of Squares of Distances to Vertices
  1510. Sum of Two Squares [JavaScript, GeoGebra]
  1511. Sums of Unit Vectors
  1512. Surprising 60° in Equilateral Triangle [JavaScript, GeoGebra]
  1513. Sylvester's Problem
  1514. Symmedians
  1515. Symmetries in a Triangle
  1516. Symmetries in Triangle II [JavaScript, GeoGebra]
  1517. Symmetry in an Asymmetric Configuration [JavaScript, GeoGebra]
  1518. (tan(72°)±tan( 60°)sin(30°$\mp$18°)= 1
  1519. Tangency Point of Two Circles [Java]
  1520. Tangent and Secant [Java]
  1521. Tangent as a Radical Axis [Java]
  1522. Tangent Circles, Similarity and Equal Segments [JavaScript, GeoGebra]
  1523. Tangent Circles and an Isosceles Triangle [Java]
  1524. Tangent Circles in a Parallelogram [Java]
  1525. Tangent, Cotangent and Square Roots Inequality
  1526. Tangent Curiosity in Equilateral Triangle [JavaScript, GeoGebra]
  1527. Tangent in Concurrency [Java]
  1528. Tangent Lines and Circles in Convex Quadrilateral [Java]
  1529. Tangent of 22.5° - Proof Wthout Words
  1530. Tangent to Circle in Three Steps
  1531. Tangent to the Incircle [JavaScript]
  1532. Tangent to two circles
  1533. Tangents And Bisectors
  1534. Tangents and Diagonals in Cyclic Quadrilateral [Java]
  1535. Tangents, Perpendiculars and Geometric Mean [Java]
  1536. Tarski-Banach Decompositions
  1537. Taylor circle [Java]
  1538. Terquem's Theorem [Java]
  1539. Tesseract [Java]
  1540. Tetrahedron in Parallelepiped
  1541. Tetrahedron with Equiareal Faces
  1542. Tetrahedron with Equiareal Faces, II
  1543. Tetrahedron with Orthogonal Perpendiculars to Opposite Edges
  1544. Thales' Theorem [Java, GeoGebra]
  1545. Thales' Theorems
  1546. Thales on Angle Bisectors [JavaScript, GeoGebra]
  1547. The 80-80-20 Triangle
  1548. The Beauty of Fractions
  1549. The Center of Gravity and Motion of Material Points [JavaScript, GeoGebra]
  1550. The Chaos Game: Address Space vs IFS [Java]
  1551. The Devil is in the Exceptions
  1552. The Eutrigon Theorem [Java, GeoGebra]
  1553. The Golden Pentacross
  1554. The Law of Cosines by Larry Hoehn
  1555. The Midpoint of an Angle Bisector - a Problem by A. A. Zaslavsky
  1556. The only rational triangle
  1557. The Pythagorean Theorem from a Combinatorial Identity
  1558. The Schwarz Lantern Explained [JavaScript]
  1559. The Shape of the Colosseum [Java, GeoGebra]
  1560. The Shortest Crease [JavaScript, GeeoGebra]
  1561. Thébault's Problem I [Java]
  1562. Thébault's Problem II [Java]
  1563. Thébault's Problem III [Java]
  1564. The Triangle of the Medians
  1565. Theorem of Complete Quadrilateral [Java]
  1566. Theorem of Three Tangents to a Conic [JavaScript, GeoGebra]
  1567. Theorems of Ceva and Menelaus, an Illustrated Generalization [Java]
  1568. There is no Difference Between Equilateral Triangles
  1569. Third Unusual Identity in Triangle
  1570. Three Circles and Area [JavaScript]
  1571. Three Circles and Common Tangents
  1572. Three Circles through the Incenter
  1573. Three Collinear and Four Concyclic Points [Java, GeoGebra]
  1574. Three Concurrent Circles [Java]
  1575. Three Common Chords in Three Concurrent Circles [Java, GeoGebra]
  1576. Three Congruent Circles by Reflection [Java]
  1577. Three Congruent Circles by Reflection II [Java]
  1578. Three Congruent Circles by Reflection III [Java]
  1579. Three Equal Circles in a Semicircle
  1580. Three Euler Lines That Are Four [JavaScript]
  1581. Three Incircles In a Right Triangle [Java]
  1582. Three Incircles in a Triangle [Java]
  1583. Three Isosceles Triangles [Java]
  1584. Three Orthogonal Circles Through Three Given Points [Java]
  1585. Three lines at 60 degres and Circumcenters [JavaScript, GeoGebra]
  1586. Three pairs of Parallel Lines and a Conic [JavaScript, GeoGebra]
  1587. Three Parabolas with Common Directrix [JavaScript,GeoGebra]
  1588. Three Parallels in a Triangle [Java]
  1589. Three Points on a Parabola [Java]
  1590. Three Pyramids are Better Than Two [Java]
  1591. Three regions sharing a common boundary
  1592. Three Similar Polygons [Java]
  1593. Three Similar Triangles [Java]
  1594. Three Similar Triangles II [Java]
  1595. Three Squares and Two Ellipses [Java]
  1596. Three Tangent Circles [Java]
  1597. Three Tangents, Three Chords in Ellipse [Java]
  1598. Three Tangent Circles Sangaku
  1599. Three Tangents Theorem [Java]
  1600. Three Tangents, Three Secants [Java]
  1601. Three Touching Circles [Java]
  1602. Three Travelers in Uniform Motion
  1603. Three visions of a fact [GeoGebra]
  1604. Tiling a Chessboard with Dominoes
  1605. Tiling Sphere by Four Equal Triangles
  1606. Toothpick Construction of a Square [Java]
  1607. Topological preliminaries
  1608. Torque as a Mathematical Object
  1609. Touching Circles [Java]
  1610. Touching Circles and Concurrency [Java]
  1611. Touching Circles with Given Centers II [Java]
  1612. Train wheel quandary
  1613. Transitivity in Action [Java]
  1614. Translated Triangles [Java]
  1615. Translation Transform [Java]
  1616. Transversal Trigonometry [JavaScript, GeoGebra]
  1617. Triangle ABC is right iff sin²A + sin²B + sin²C = 2
  1618. Triangle Area in Square with Incircle
  1619. Triangle Areas in a Parallelogram [Java]
  1620. Triangle Areas in a Parallelogram II [Java]
  1621. Triangle by HM segments [JavaScript, GeoGebra]
  1622. Triangle Classification [Java]
  1623. Triangle constructions and facts [Java]
  1624. Triangle Construction from Angle, Altitude and Median
  1625. Triangle from a, A, mc/mb
  1626. Triangle from Angle Bisector, Altitude and Circumradius
  1627. Triangle from Angle Bisector, Altitude and Inradius
  1628. Triangle from Inradius, Circumradius, Side or Angle
  1629. Triangle from Median, Altitude and Circumradius
  1630. Triangle from Side, Circumradius, and Median
  1631. Triangle from Angle, Inradius, and Difference of Sides
  1632. Triangle from Side, Inradius, and Altitude
  1633. Triangle from Side, Median, and Altitude
  1634. Triangle from Two Side Lines and the Euler Line
  1635. Triangle in a 4x4 Square
  1636. Triangle in a 5x5 Square
  1637. Triangle of Maximum Area
  1638. Triangle of Maximum Area II
  1639. Triangle of Minimum Perimeter [JavaScript]
  1640. Triangle on a Rectangular Hyperbola
  1641. Triangle Sliding on Two Straight Lines [Java]
  1642. Triangles, Squares and Areas from Temple Geometry [Java]
  1643. Triangles on HO
  1644. Triangles with Equal Area [Java]
  1645. Triangles with Sides in Geometric Progression [JavaScript]
  1646. Triangular Areas in Circle [JavaScript, GeoGebra]
  1647. Triangular Billiard [Java]
  1648. Triangulating Squares
  1649. Triangle with a 60 degrees angle [JavaScript, GeoGebra]
  1650. Trigonometry by Watching
  1651. Trigonometric Form of Ceva's Theorem [Java]
  1652. Trigonometric Functions [Java]
  1653. Trigonometric Identities with Arctangents
  1654. Trigonometric Proof of the Pythagorean Theorem
  1655. Trigonometry According to Ptolemy
  1656. Trigonometry by Paper Folding
  1657. Trisect Segment: 2 Circles, 4 Lines
  1658. Trisectable angle that is not constructible
  1659. Tucker Circles [Java]
  1660. Tucker Circles Through Homothety [Java]
  1661. Twelve Matchsticks Area Puzzle
  1662. Twin Segments in Four Semicircles
  1663. Twins Beget Twins
  1664. Twisted Cord Illusion [Java]
  1665. Two Altitudes, One Midpoint
  1666. Two Arbelos, Two Chains
  1667. Two Cevians and Proportions in a Triangle
  1668. Two Circles, Two Segments - One Ratio
  1669. Two Circles and a Limit - Analytic Proof
  1670. Two Circles and One More [Java]
  1671. Two Circles and Two More [Java]
  1672. Two Circles, Ellipse, and Parallel Lines
  1673. Two Circles in a Parallelogram [Java]
  1674. Two Circles Inscribed in a Parallelogram [Java]
  1675. Two Circles in a Square [Java]
  1676. Two Circles in a Square II [Java]
  1677. Two Circles in an Angle [Java]
  1678. Two Circles on Angle Bisector [Java]
  1679. Two Circles on a Side of a Triangle [Java]
  1680. Two Circles, Tangents and Two Collinearities [JavaScript, GeoGebra]
  1681. Two Circumcircles And Two Pairs of Parallels [Java]
  1682. Two Circumcircles in Triangle [Java]
  1683. Two Conditions for a Triangle to Be Equilateral
  1684. Two coins puzzle
  1685. Two Congruent Circles by Reflection [Java]
  1686. Two Conics, Pascal, Chasles, and Cross-Ratio [JavaScript, GeoGebra]
  1687. Two Color Coloring of the Plane [Java]
  1688. Two Common Chords in Three Concurrent Circles [Java, GeoGebra]
  1689. Two Diameters and Longest Common Chord [Java, GeoGebra]
  1690. Two Equilateral Triangles [Java]
  1691. Two Equilateral Triangles on Sides of a Square
  1692. Two Homotheties in a Parallelogram [Java]
  1693. Two Intersecting Circles [Java]
  1694. Two Lines - Two Circles [Java]
  1695. Two Pencils of Parallel Lines [JavaScript, GeoGebra]
  1696. Two Pairs of Parallel Lines in a Triangle [Java, GeoGebra]
  1697. Two Parallels in a Triangle and One More [Java]
  1698. Two Pascals Merge into One [JavaScript, GeoGebra]
  1699. Two Perpendiculars From a Point to a Line [Java]
  1700. Two Planar Constructions Related to a 3D Problem
  1701. Two Perspective Triangles
  1702. Two Quadrilaterals [Java]
  1703. Two Quadruplets of Concyclic Points [JavaSCript,GeoGebra]
  1704. Two Quadruplets of Tangent Circles [Java]
  1705. Two Refinements of Ionescu-Weitzenbock Inequality
  1706. Two Regular Pentagons Joined at Vertex
  1707. Two Related Triangles of Equal Areas
  1708. Two Sangaku with Equal Incircles
  1709. Two Similar Triangles with Parallel Sides [JavaScript, GeoGebra]
  1710. Two Simsons in a Triangle [Java]
  1711. Two Squares and Another Square [Java]
  1712. Two Squares In Circle [JavaScript]
  1713. Two Symmetric Triangles Are Directly Decomposable [Java]
  1714. Two Touching Circles [Java]
  1715. Two Triangles Inscribed in a Conic [Java, GeoGebra]
  1716. Two Triangles Inscribed in a Conic - with Elementary Solution [Java, GeoGebra]
  1717. Two Triangles Inscribed in a Conic - with Solution [Java, GeoGebra]
  1718. Two Triangles With Common Base and Altitude [Java]
  1719. Two Triangles Sharing the Circumcenter
  1720. Two Triples of Concurrent Cevians and a Conic [JavaScript, GeoGebra]
  1721. Two Triples of Concurrent Circles [Java]
  1722. Two Triples of Similar Triangles [Java]
  1723. Uncommon Triangle Constructions
  1724. Unfolding Spirals Illusion [Java]
  1725. Urquhart's Theorem
  1726. USA 1975 Problem 4
  1727. Use of Homogeneous Coordinates for Geometrical Calculations
  1728. Van Aubel's Theorem for Quadrilaterals and Generalization
  1729. Van Khea's Fourth Identity in Triangle
  1730. Van Khea's Quickie
  1731. Van Obel Theorem, Determinants, and Barycentric Coordinates
  1732. Van Schooten's and Pompeiu's Theorems [Java]
  1733. Van Schooten's Locus Problem [Java]
  1734. Variations on the Theme of Tremas [Java]
  1735. Variations on the Theme of Tremas II [Java]
  1736. Varignon's Theorem, Proof Without Words
  1737. Varignon Parallelogram [Java]
  1738. Various Geometries
  1739. Vecten-Nikolin Hexagon [Java]
  1740. Vecten's Collinearity [Java]
  1741. Vecten's Mesh [Java]
  1742. Vector Addition and Subtraction [Flash]
  1743. Vector Algebra in Tetrahedron
  1744. Vector product
  1745. Versatile Theorem [Java]
  1746. Vertical and Horizontal Dominoes on a Chessboard
  1747. Vietnamese Extension of a Japanese Theorem [JavaScript]
  1748. Vietnamese Lemma towards an Extension of a Japanese Theorem [JavaScript, GeoGebra]
  1749. Viewing a Statue
  1750. Viviani's Theorem [Java]
  1751. Viviani's Theorem II [Java]
  1752. Viviani in Isosceles Triangle [Java]
  1753. Viviani by Inversion
  1754. Viviani by Vectors
  1755. Viviani's 3D Analogue
  1756. Sanchez's Viviani's Area Analogue [JavaScript, GeoGebra]
  1757. Volume and Area of Torricelli's Trumpet [JavaScript]

    Volume Inequality in Tetrahedron

  1758. Volume of Fibonacci Tetrahedron
  1759. Volume of Sphere and Volume of an Ellipsoid
  1760. Volumes of Two Pyramids
  1761. Wallace-Bolyai-Gerwien Theorem
  1762. Wallace's Theorem [Java]
  1763. Watt's and Chebyshev's Linkage [Java]
  1764. Weird curves bound normal areas
  1765. Weitzenbock by Sanchez
  1766. Weitzenböck Inequality [Java]
  1767. What does one see inside a spherical mirror? [Java]
  1768. What Is Analytic Geometry?
  1769. What Is Angle?
  1770. What Is Angle Chasing?
  1771. What Is Area?
  1772. What Is Ellipse?
  1773. What Is Indirect Proof?
  1774. What Is Line?
  1775. What Is Point?
  1776. When a Triangle is A-cute
  1777. When a Triangle is Equilateral [Java]
  1778. When Is Triangle Equilateral: Marian Dinca's Criterion
  1779. When Is Triangle Isosceles: Miguel Ochoa Sanchez's Criterion
  1780. When Two Segments Intersect? [JavaScript]
  1781. When index equals content [Java]
  1782. Wonderful Trigonometry In Equilateral Triangle
  1783. Why a Diameter Is the Longest Chord?
  1784. William Wallace's Proof of the Butterfly Theorem
  1785. William Wallace's 1803 Statement of the Butterfly Theorem [JavaScript, GeoGebra]
  1786. Wittenbauer's Parallelogram [Java]
  1787. Wundt Illusion [Java]
  1788. Wundt Block Illusion [Java]
  1789. Y. Sawayama's Lemma [Java]
  1790. Y. Sawayama's Theorem
  1791. YATPOPT, Yet Another Trigonometric Proof of the Pythagorean Theorem
  1792. Yet Another Appearance of the Golden Ratio [JavaScript, GeoGebra]
  1793. Yet Another Concurrence on the 9-Point Circle [JavaScript, GeoGebra]
  1794. Yet Another Seven Circles Theorem [JavaScript, GeoGebra]
  1795. Zaslavsky's theorem [Java]
  1796. Zöllner's Illusion [Java]

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