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 Roads, 3 Travelers [Java]
  4. 3 Utilities Puzzle
  5. 3D Concurrency Of Altitudes
  6. 3D Quadrilateral - a Coffin Problem
  7. 3-4-5 Triangle by a Kid
  8. 4 Travelers problem
  9. 5x5 Square Grid and 5 Circes [Java, GeoGebra]
  10. 6 to 9 Point Circle [Java]
  11. 60o Breeds 90o [Java]
  12. 7 = 2 + 5 Sangaku
  13. 9-point Circle as a Locus of Concurrency [Java]
  14. A better solution to a difficult sangaku problem
  15. A Case of Similarity [Java]
  16. A Chain of Touching Circles in a Polygon (a la Bui Quang Tuan) [Java]
  17. A Chain of Touching Circles in a Polygon (à la Evelyn) [Java]
  18. A Characterization of the Euler Line [Java]
  19. A Circle in an Isosceles triangle from the 2006 Itish MO
  20. A Circle Related to Incenter and Circumcenter [Java]
  21. A Circle Rolling in an Equilateral Triangle [Java]
  22. A Circle With Two Centers [Java]
  23. A Conic in a Triangle [JavaScript, GeoGebra]
  24. A Combinaton Locus
  25. A Corrected Version of the Calculus Proof of the Pythagorean Theorem
  26. A Curious Identity in Triangle
  27. A Degenerate Case of Bottema's Configuration [Java, GeoGebra]
  28. A Diameter As a Diagonal of Inscribed Quadrilateral [Java, GeoGebra]
  29. A dissection puzzle. Proof #99 of the Pythagorean theorem
  30. A Double Meaning of an Arc's Midpoint [Java, GeoGebra]
  31. A Family of Cyclic Quadrilaterals [JavaScript, GeoGebra]
  32. A Generalization of Simson Line [JavaScript, GeoGebra]
  33. A Generalization of the Pythagorean Theorem
  34. A Generalized Cavalieri-Zu Principle
  35. A Geometric Limit
  36. A Geometry Problem from 2012 IMO - Problem 5
  37. A Hard but Important Sangaku
  38. A Hinged Realization of a Plane Tessellation [Java]
  39. A Lemma of Equal Areas [Java]
  40. A Lemma on the Road to Sawayama
  41. A Line in a Square Grid [Java]
  42. A Line in Triangle Through the Circumcenter [Java]
  43. A Matter of Collinearity: Metamorphosis of a Problem
  44. A Multiplicative Identity of Areas in a Triangle [Java]
  45. A Note on Cavalieri's Indivisibles
  46. A Parallelogram in Triangle [Java]
  47. A Possibly First Proof of the Concurrence of Altitudes
  48. A Problem In an Isosceles Right Triangle [Java]
  49. A Problem in Three Pentagons [JavaScript, GeoGebra]
  50. A Problem of Acute Triangle
  51. A Problem on an Icy Cone
  52. A problem with equilateral triangles [Java]
  53. A Problem with Right Isosceles Triangles [JavaScript]
  54. A Problem with Two Isosceles Triangles [JavaScript]
  55. A Proof Perigal and All Others After Him Missed
  56. A Property of Circle Through the Incenter [JavaScript]
  57. A Property of Cyclic Quadrilateral
  58. A Property of Equiangular Polygons [Java]
  59. A Property of Isogonal Lines [JavaScript, GeoGebra]
  60. A Property of Orthic Triangle [JavaScript, GeoGebra]
  61. A Property of Pascal's Hexagon Pascal May Have Overlooked
  62. A Property of Perspective Triangles [JavaScript, GeoGebra]
  63. A Property of Points on Excircle
  64. A Property of Points on Incircle
  65. A Property of Rhombi [Java]
  66. A Property of the Line IO [Java]
  67. A Property of the Line IO: A Bundled Statement and Proof [Java]
  68. A Property of the Line IO: a proof from the Book [Java]
  69. A Relation in Triangle
  70. A Restored Sangaku
  71. A Sangaku Follow-Up on an Archimedes' Lemma [Java]
  72. A Sangaku: Two Unrelated Circles [Java]
  73. A Sangaku with an Egyptian Attachment [Java]
  74. A Sangaku with Many Circles and Some [Java]
  75. A square in parallel lines
  76. A Stronger Triangle Inequality [Java]
  77. A Sushi Morsel
  78. A Three Pegs Question [Java]
  79. A Triangle of Antreas Hatzipolakis [Java]
  80. A Trigonometric Identity in a Right Triangle from the 1960 IMO
  81. A Trigonometric Solution to a Difficult Sangaku Problem
  82. A View on the Circle of Apollonius [JavaScript,GeoGebra]
  83. About a Line and a Triangle [Java]
  84. Abul Wafa al-Buzjani's Proof of the Pythagorean Theorem [Java]
  85. Abutting Equilateral Triangles on a Line I [JavaScript, GeoGebra]
  86. Acute Angle Bisectors in a Right Triangle [Java]
  87. Adams' Circle [Java]
  88. Addition and Subtraction Formulas for Sine and Cosine
  89. Addition and Subtraction Formulas for Sine and Cosine II
  90. Algebraic proof of the theorem of butterflies in quadrilaterals
  91. Algebraic-Geometric Equation All about altitudes
  92. All Triangles Are Isosceles [Java]
  93. Altitudes and the Euler Line [GeoGebra]
  94. Altitudes and the Power of a Point [Java]
  95. Altitudes Concur at a Point: a Second Look
  96. Altitudes have ears, foot, stem, and root
  97. An Affine Property of Barycenter
  98. An Algebraic Lemma with Geometric Consequences [JavaScript]
  99. An Angle Inequality in Simple Polygons
  100. An Area Inequality
  101. An Euclidean Construction with Inversion [Java, GeoGebra]
  102. An Extension of van Schooten's Theorem
  103. An Extra Triple of Equilateral Triangles for Napoleon/a> [JavaScript, GeoGebra]
  104. An Identity for Regular Tetrahedra
  105. An Identity in a Regular Heptagon
  106. An Identity in (Cyclic) Quadrilaterals [JavaScript, GeoGebra]
  107. An Identity in Triangle
  108. An Identity in Triangle II
  109. An Inequality from the 2015 Romanian TST
  110. An Inequality in Triangle
  111. An Inequality Involving Fermat Point
  112. An Isoperimetric Theorem [Java]
  113. An Old Japanese Theorem
  114. An Unexpected Pair of Similar Triangles Which Are Equal [JavaScript, GeoGebra]
  115. An Unexpected Rhombus [JavaScript, GeoGebra]
  116. An Universal Inequality for Cevians
  117. An Unusual Generalization of the Pythagorean Theorem
  118. An Unusual Generalization of the Pythagorean Theorem, a Variant
  119. Angle: An Illustrated Classification [Java]
  120. Angle Bisectors Cross Circumcircle
  121. Angle Bisector in Equilateral Trapezoid
  122. Angle Bisector in Parallelogram [Java]
  123. Angle Bisectors In Rectangle [Java]
  124. Angle Bisector in Touching Circles [Java]
  125. Angle Bisectors [Java]
  126. Angle Bisectors and Perpendiculars in a Quadrilateral [Java]
  127. Angle Bisectors in Ellipse [Java]
  128. Angle Bisectors in Ellipse II [Java]
  129. Angle Bisectors in a Quadrilateral [Java]
  130. Angle Bisectors in a Quadrilateral - Cyclic and Otherwise [Java]
  131. Angle Bisectors On Circumcircle [Java]
  132. Angle Chasing on Radical Axis [JacaScritp, GeoGebra]
  133. Angle in Square
  134. Angle in Right Triangle
  135. Angle Preservation Property [Java]
  136. Angle Subtended by a Diameter [Java]
  137. Angle Trisection, the Impossibility of Thereof
  138. Angle Trisection by Archimedes [Java]
  139. Angle Trisection by Hippocrates [Java]
  140. Angle Trisection by Paul Vjecsner [Java]
  141. Angle Trisectors on Circumcircle [Java]
  142. Angle Trisection by Paper Folding
  143. Angles in 4-5-6 Triangle [JavaScript]
  144. Angles in a Cube I [Java]
  145. Angles in a Cube II [Java]
  146. Angles in a Cube III [Java]
  147. Angles in Triangle Add to 180o
  148. Angles in a Triangle: an Exercise
  149. Angles Inscribed in an Absent Circle [Java]
  150. Another Concurrence on the 9-Point Circle [JavaScript, GeoGebra]
  151. Another Geometry Problem from 2012 IMO - Problem 1
  152. Another Golden Ratio in Semicircle
  153. Golden Ratio in Isosceles Right Triangle, Square, and Semicircle
  154. Another Identity in Triangle
  155. Another Pair of Archimedean Twins - a Redux [JavaScript, GeoGebra]
  156. Another Property of the 9-Point Circle [JavaScript, GeoGebra]
  157. Another Sangaku in Square
  158. Another Seven Circles Theorem [JavaScript, GeoGebra]
  159. Anticenter and Orthocenters [JavaScript, GeoGebra]
  160. Anticomplementary Triangle Surprise [Java]
  161. Antiparallel [Java]
  162. Antiparallel via Three Reflections [Java]
  163. APMO 1995 Problem 3
  164. APMO 1998, Problem 4
  165. APMO 2002, Problem 3
  166. APMO 2003, Problem 2
  167. APMO 2004, Problem 2
  168. The Problem of Apollonius
  169. Approximate Construction of Regular Pentagon by A. Dürer
  170. Arbelos -- the Shoemaker's Knife [Java]
  171. Archimedean Siblings out of Wedlock, i.e., Arbelos (JavaScript, GeoGebra)
  172. Archimedes' Book of Lemmas
  173. Archimedes' Law of the Lever [Java]
  174. Archimedes' Method
  175. Archimedes' Twins in the Edo Period
  176. Area and Perimeter Splitters in a Triangle
  177. Area Inequality in Triangle
  178. Area Inequality in Triangle II
  179. Area of a Bicentric Quadrilateral
  180. Area of a Circle by Leonardo da Vinci [Java]
  181. Area of a Circle by Rabbi Abraham bar Hiyya Hanasi [Java]
  182. Area of Median Triangle [Java]
  183. Area of Parallelogram [Java]
  184. Area of Parallelogram Formula by Shearing
  185. Area of the Union of Two Squares [Java]
  186. Area of Triangle [Java]
  187. Areas and Centroid in a Triangle [Java]
  188. Areas In Circle
  189. Areas in Square by Dissection [Java]
  190. Areas in Two Parallelograms and a Translation [JavaScript, GeoGebra]
  191. Arithmetic-Geometric Mean Inequality
  192. Arithmetic Mean Sangaku [Java]
  193. Arithmetic Mean Sangaku II [Java]
  194. Around the Incircle [Java]
  195. Around the Incircle in a Polygon [Java]
  196. Artisans vs Mathematicians
  197. Asian Pacific Kite [Java]
  198. Assigning Numbers to Points in the Plane
  199. Assimilation Illusion [Java]
  200. Axis of Similitude of Three Circles
  201. Barbier, The Theorem of [Java]
  202. Barycentric coordinates
  203. Bender: A Visual Illusion [Java]
  204. Bespectacled Eyeballs Extension [JavaSCript, GeoGebra]
  205. Between a Cross and a Square (lies a Golden Ratio)
  206. Between Major and Minor Circles [Java]
  207. Bevan's Point and Theorem [Java]
  208. Beyond Pythagoras
  209. Beyond Viviani [JavaScript]
  210. Bimedians and Diagonals in a Quadrilateral
  211. Bimedians in a Regular Tetrahedron [Java]
  212. Bisectal Circle [Java]
  213. Bisecting arcs
  214. Bisecting a shape
  216. Bisection of Yin and Yang
  217. Bisector of an imaginary angle may be real
  218. Bisectors and Proportions [JavaScript]
  219. BMO 2014, Problem 3 [JavaScript, GeoGebra]
  220. Bottema Shatters Japan's Seclusion [Java]
  221. Bottema's theorem [Java]
  222. Bottles in a Wine Rack [Java]
  223. Bounded Distance
  224. Bounds for the Sum of Distances to the Vertices [JavaScript]
  225. Brahmagupta's Formula and Theorem
  226. Brahmagupta's Theorem [Java]
  227. Brahmagupta-Mahavira Identities
  228. Brianchon in Ellipse [Java]
  229. Brianchon's theorem [Java]
  230. Brick Wall Illusion [Java]
  231. Bride's Chair [Java]
  232. Brief introduction to Rational Trigonometry
  233. Broken Chord Theorem [Java]
  234. Broken Line in Triangle
  235. Building a Bridge [Java]
  236. Building Bridges [Java]
  237. Bulging lines illusion [Java]
  238. Butterfly Theorem
  239. Cabart's Collinearity
  240. Cantor Set and Function
  241. Cantor's Theorem [Java]
  242. Carnot's Theorem
  243. Carnot's Theorem
  244. Carnot's Theorem from Ptolemy's Theorem
  245. Carnot's Theorem (Generalization of Wallace's theorem) [Java]
  246. Carnot's Theorem for Conics
  247. Carpet With a Hole [Java]
  248. Carpets Theorem [Java]
  249. Casey's Theorem [Java]
  250. Cassini's Ovals and Geometric Optimization [JavaScript, GeoGebra]
  251. centers of similitude
  252. Centroid, a Characteristic Property Of
  253. Centroids and Circumcenters
  254. Centroids in a Polygon [Java]
  255. Cevian Parallelogram [JavScript, GeoGebra]
  256. Chasing Angles Among Angle Bisectors [JavaScript]
  257. Chasing Angles in Pascal's Hexagon [Java]
  258. Circle, Isosceles Triangle and Fixed Point [Java]
  259. Circle Centers on Radical Axes [Java]
  260. Circle Chains on Napoleon Triangles [Java]
  261. Circle Concurrence on Circumcircle/a> [JavaScript, GeoGebra]
  262. Circle in a Square Inscribed in a Circle [Java]
  263. Circle Rotations and Fixed Points
  264. Circles on the sides of a triangle from the 2005 Austrian MO
  265. Circles Tangent to Circumcircle [Java]
  266. Circles Tangent to Medians at the Centroid [JavaScript, GeoGebra]
  267. Circles with Tangent Diameters [Java]
  268. Ceva and Menelaus Meet on the Roads
  269. Ceva in Circumscribed Quadrilateral
  270. Ceva's Theorem
  271. Ceva's Theorem and Fibonacci Bamboozlement [Java]
  272. Cevian Cradle [Java]
  273. Cevian Cradle II [JavaScript, GeoGebra]
  274. Cevian Nest [Java]
  275. Cevian Triangle [Java]
  276. Cevians And Semicircles [JavaScript]
  277. Chain of Inscribed Circles [Java]
  278. Chaos, Emergence of [Java]
  279. Characteristic Property Of Right Triangles
  280. Chasles' Theorem
  281. Cherchez le quadrilatère cyclique [Java]
  282. Cherchez le quadrilatère cyclique II [Java]
  283. Chords, Concurrency and Orthic Triangle [Java]
  284. Chromatic Number of the Plane
  285. Chvatal's Art Gallery Theorem [Java]
  286. Circle and Hyperbola as Lighthouse Curves
  287. Circle and Hyperbola as Lighthouse Curves II
  288. Circle Crosses Triangle [Java]
  289. Circle Concurrency and Spiral Similarity [Java]
  290. Circle Division by Euclid and Leonardo [Java]
  291. Circle of Apollonius in Equilateral Triangle
  292. Circle of Similitude [Java]
  293. Circle Rotations and Fixed Points [JavaScript, GeoGebra]
  294. Circle through the Circumcenter [Java]
  295. Circle through the Incenter [Java]
  296. Circle through the Incenter And Antiparallels [Java]
  297. Circle-Stacking Theorem [Java]
  298. Circles And Parallels [Java]
  299. Circles and Semicircles in Rectangle [Java]
  300. Circles Cover a Quadrilateral [Java]
  301. Circles in a Circular Segment
  302. Circles in a Regular Polygon [Java]
  303. Circles in Morley's Triangles [Java]
  304. Circles Lined on the Legs of a Right Triangle [Java]
  305. Circles On Cevians [Java]
  306. Circles through the Orthocenter [Java]
  307. Circles with Equal Collinear Chords [Java]
  308. Circular Poggendorff Illusion [Java]
  309. Circle Inscribed in a Circular Segment [Java]
  310. Circumcenter on Angle Bisector [Java]
  311. Circumcevian Triangle [Java]
  312. Classification of Quadrilaterals [Java]
  313. Cleavance Center [Java]
  314. Cleaver [Java]
  315. Clifford Algebras
  316. Clifford's Chain [Java]
  317. Climbing Pyramidal Slopes
  318. Clough's theorem: the simplest proof [JavaScript, GeoGebra]
  319. Coaxal Circles on Perpendicular Bisector [Java]
  320. Coaxal Circles Theorem [Java]
  321. Collage Theorem [Java]
  322. Collinear Intersections and Products of Ratios [JavaScript, GeoGebra]
  323. Collinearity from the IMO 2013 (Problem 4) [Javacript, GeoGebra]
  324. Collinearity in Bicentric Quadrilaterals [Java]
  325. Collinearity via Concyclicity [Java]
  326. Collinearity with the Orthocenter [Java]
  327. Color Cycling on the Mandelbrot Set [Java]
  328. Coloring Plane with Three Colors
  329. Coloring Points in the Plane
  330. Common Chord and a Tangent [Java]
  331. Common Tangents to Two Circles I [Java]
  332. Common Tangents to Two Circles II [Java]
  333. Compass Only Construction - A Chord Tangent to an Inner circle [Java, GeoGebra]
  334. Complete Quadrilateral [Java]
  335. Complex Numbers and Geometry
  336. Concurrence on a Circle [JavaScript, GeoGebra]
  337. Concurrence Not from School Geometry [Java, GeoGebra]
  338. Concurrency of Medians and Medial Triangles
  339. Concurrency of the Altitudes in a Triangle - Trigonometric Proof
  340. Concyclic Points at the IMO 2014 [JavaScript, GeoGebra[
  341. Concyclicity in Rectangle [Java]
  342. Concurrence in Equilateral Triangle [JavaScript,GeoGebra]
  343. Concurrence of Ten Nine-Point Circles [JavScript, GeoGebra]
  344. Concurrency in the Intouch Triangle [Java]
  345. Concurrent and Parallel Lines in Parallelogram [JavaScript, GeoGebra]
  346. Concurrent Cevians and a Conic through Their Feet [JavaScript, GeoGebra]
  347. Concyclic Points from Midpoint of an Arc [GeoGebra, JavaScript]
  348. Concyclic Incenters in Bicentric Quadrilateral [JavaScript, GeoGebra]
  349. Concyclic Points in Inscriptible Quadrilateral [JavaScript, GeoGebra]
  350. Concyclicity from Collinearity [JavaScript,GeoGebra]
  351. Concyclicity in Two Semicircles [JavaScript, GeoGebra]
  352. Concyclic Points of Two Ellipses with Orthogonal Axes [JavaScript, GeoGebra]
  353. Concyclic Circumcenters: A Dynamic View [Java]
  354. Concyclic Points in a Triangle
  355. Concyclic Points in Bride's Chair [Java]
  356. Concyclic Points in Equilateral Bumps [Java]
  357. Conic from Parallel Chords [JavaScript, GeoGebra]
  358. Conic in Hexagon [Javascript, GeoGebra]
  359. Conic in Mixtilinear Incircles [JavaScript, GeoGebra]
  360. Conic Sections
  361. Conic Sections as Loci of Points [Java]
  362. Conics Intersecting Sides Of A Triangle [JavaScript, GeoGebra]
  363. Conics in Triangle [JavaScript, GeoGebra]
  364. Conics Related To In- and Excircles [JavaScript, GeoGebra]
  365. Conjugate Diameters in Ellipse [Java]
  366. Consecutive Isosceles Decomposition [Java]
  367. Constant Chord
  368. Constrained Area in Triangle
  369. Construct Triangle from Angle, Inradius, and Altitude [JavaScript, GeoGebra]
  370. Construct Triangle by Angle, Median, and Circumradius [JavaScript, GeoGebra]
  371. Construct Triangle by Angle Bisector, Altitude, and Side [JavaScript, GeoGebra]
  372. Construct Triangle by Angle, Altitude and Median [JavaScript, GeoGebra]
  373. Construct Triangle from Altitude, Median and Inradius [JavaScript, GeoGebra]
  374. Constructing a triangle from its angle bisectors is in general impossible
  375. Construction and Properties of Mixtilinear Incircles [JavaScript, GeoGebra]
  376. Construction and Properties of Mixtilinear Incircles 2 [JavaScript, GeoGebra]
  377. Construction of a Cyclic Quadrilateral
  378. Construction of a Square from the 2008 Austrian MO
  379. Construction of a Triangle from the Circumcenter, Orthocenter and Incenter
  380. Construction of a Triangle from Two Vertices and the Centroid
  381. Construction of an Oval - the Roman Way [Java, GeoGebra]
  382. Construction of Conics from Pascal's Theorem [Java]
  383. Construction of Regular Pentagon by H. W. Richmond
  384. Construction of Thebault Circles [JavaScript, GeoGebra]
  385. Construction of the Angle Bisector [Java]
  386. Construction of the Perpendicular Bisector [Java]
  387. Construction of Triangle from Side, Angle, and that Angle's Bisector
  388. Construction problem [Java]
  389. Constructions Related To An Inaccessible Point
  390. Construction with the Compass Only
  391. Continuous Line Illusion [Java]
  392. Convex Polygon Is the Intersection of Half Planes [Java]
  393. Copernicus' Theorem [Java]
  394. Construction with Optimization in Angle - Problem the 1979 USA Mathematical Olympiad
  395. cos(36°) = (1 + √5)/4
  396. Cosine Law
  397. Counting Triangles and Segments in a Polygon [Java]
  398. Cross Points in a Polygon [Java]
  399. Cross-Ratio
  400. Crossed-Lines Construction of Shapes of Constant Width [Java]
  401. Crossing Number of a Graph
  402. Cube Counting Ambiguity [Java]
  403. Curry's Paradox [Java]
  404. Cut the Cone [Java]
  405. Cut the Cube [Java]
  406. Cutting a Hole in Half [JavaScript, GeoGebra]
  407. Cut the Cylinder [Java]
  408. Cutting Circle to Rearrange Two Dots [JavaScript]
  409. Cutting Squares
  410. Cutting Triangle in Two by a Line through a Point [Java, GeoGebra]
  411. Cutting Triangles off Regular Hexagon
  412. Cyclic Hexagon [Java]
  413. Cyclic Quadrilateral, Concurrent Circles and Collinear Points [Java]
  414. Cycloids [Java]
  415. Dancing Rectangles Model Auxetic Behavior [Java]
  416. Dancing Squares or a Hinged Plane Tessellation [Java]
  417. Dao's Archimedean Twins [JavaScript, GeoGebra]
  418. Dao's Archimedean Twins - Second Pair [JavaScript]
  419. Dao's Archimedean Twins - Third Pair [JavaScript]
  420. Dao Thanh Oai's Invariant
  421. David Richeson's Extention of an Old Japanses Theorem [Java]
  422. Day's Sine Illusion [Java]
  423. Decompose Cyclic Quadrilaterals into k≥4 Cyclic Quadrilaterals
  424. A Decomposition of Isosceles Triangles into 4 Isosecles Triangles
  425. Delboeuf Illusion [Java]
  426. Delian Problem Solved [Java]
  427. Desargues' Hexagon [Java, GeoGebra]
  428. Desargues in the Bride's Chair (with Pythagoras)
  429. Desargues' Theorem [Java]
  430. Determination of π
  431. Diagonal Count [Java]
  432. Diagonals in a Cyclic Quadrilateral
  433. Diameters and Chords [Java]
  434. Directly Similar Figures [Java]
  435. Disappearing Lines puzzle [Java]
  436. Discovery of Duane DeTemple [Java]
  437. Dissection of a 10×13 Rectangle into Two Chessboards
  438. Dissection of a Vase [Java]
  439. Dissection of Cyclic Quadrilateral [Java]
  440. Dissection of Triangle into Rhombus [Java]
  441. Dissection of Triangle into Rhombus by Hubert Shutrick [Java]
  442. Distance
  443. Distance Between Projections
  444. Distance between the Orthocenter and Circumcenter
  445. Distance Formula
  446. Distorted Lines Illusion [Java]
  447. Divergent Spirals Illusion [Java]
  448. Divide a Circle into N Parts of Equal Area
  449. Divide a segment into n equal parts
  450. Divide Triangle by Lines Parallel to Base [JavaScript, GeoGebra]
  451. Dividing Evenly a Quadrilateral [Java]
  452. Dividing Evenly a Quadrilateral II [Java]
  453. Double Generation Theorem [Java]
  454. Drawing circles [Java]
  455. Droz-Farny Circles [Java]
  456. Droz-Farny Line Theorem [Java]
  457. Droz-Farny Theorem - an Analytic Solution [JavaScript, GeoGebra]
  458. Dual of Maxwell's Theorem
  459. Duplication of the Cube
  460. Dynamic Construction of Ellipse and Other Curves [Java]
  461. Dynamic Software as Serendipity Enhancement [Java, GeoGebra]
  462. A. G. Samosvat's Proof by Dissection of the Pythagorean Theorem (#104) [GeoGebra]
  463. E. W. Dijkstra's Proof of the Pythagorean Theorem [Java]
  464. Easy Construction of Bicentric Quadrilateral [Java]
  465. Easy Construction of Bicentric Quadrilateral II [Java]
  466. Egyptian Triangle By Paper Folding
  467. Egyptian Triangle By Paper Folding II
  468. Egyptian Triangle By Paper Folding III
  469. Eight Equal Tangents [Java]
  470. Eight Point Circle [Java]
  471. Elementary Introduction into the Concept of Area
  472. Ellipse Between Two Circles [Java]
  473. Ellipse in Arbelos [Java]
  474. Ellipse Touching Sides of Triangle at Midpoints [Java, GeoGebra]
  475. Equal Angles in Two Circles [Java]
  476. Equal Angles in Two Circles II [Java]
  477. Equal areas In Circle [JavaScript]
  478. Equal Areas in Equilateral Triangle [Java]
  479. Equal Areas In Parallelogram à la Pythagoras [Java]
  480. Equal Areas in Regular 2n-gons [Java]
  481. Equal Chords in Crossing Circles [Java]
  482. Equal Circles, Medial Triangle and Orthocenter [Java]
  483. Equal Incircles Theorem [Java]
  484. Equichordal points: Just Do It [Java]
  485. Equidecomposition of a Rectangle and a Square [Java]
  486. Equidecomposition of Two Rectangles [Java]
  487. Equidecomposition of a Triangle and a Rectangle [Java]
  488. Equidecomposition of a Triangle and a Rectangle II [Java]
  489. Equidecomposition of Two Parallelograms [Java]
  490. Equilateral and 3-4-5 Triangles [Java]
  491. Equilateral Triangle in Equilateral Triangle [JavaScript, GeoGebra]
  492. Equilateral Triangle on a Closed Curve [JavaScript, GeoGebra]
  493. Equilateral Triangle on Angle Bisectors
  494. Equilateral Triangle on Parallel Lines [Java]
  495. Equilateral Triangle on Three Lines [JavaScript, GeoGebra]
  496. Equilateral Triangle, Straight Line and Tangent Circles [Java]
  497. Equilateral Triangles and Incircles in a Square
  498. Equilateral Triangles formed by Circumcenters [JavaScript, GeoGebra]
  499. Equilateral Triangles on Diagonals of Antiequilic Quadrilateral [Java]
  500. Equilateral Triangles On Sides of a Parallelogram [Java]
  501. Equilateral Triangles On Sides of a Parallelogram II [Java]
  502. Equilateral Triangles on Sides of a Quadrilateral [Java]
  503. Equilic Quadrilateral I, a Flawed Proof [Java]
  504. Equilic Quadrilateral I, A Variation [Java]
  505. Equilic Quadrilateral II [Java]
  506. Erdös-Mordell Inequality
  507. Escher's Theorem [Java]
  508. Euclid's Fifth Postulate
  509. Euclid's Elements Reference Page
  510. Euclid I.43 [Java]
  511. Euclid I.43 Extended [Java]
  512. Euclidean Construction of Center of Ellipse [Java]
  513. Euclidean Construction of Tangent to Ellipse
  514. Euler Line Cuts Off Equilateral Triangle [Java]
  515. Euler Line and 9-Point Circle [Java]
  516. Euler's Formula and Poncelet Porism
  517. Every Parallelogram Is a Rectangle
  518. Exeter Point [Java, GeoGebra]
  519. Existence of the Circumcenter [Java]
  520. Existence of the Orthocenter [GeoGebra]
  521. Existence of the Euler Line: An Elementary Proof [Java]
  522. Existence of the Incenter: a Second Look
  523. Experimentation with Dynamic Geometry Software: An Example [Java]
  524. Expressions Invariant under Projecive Mappings
  525. Exterior Angle Theorem - an appreciation
  526. External Angle Bisector [Java]
  527. Extouch Triangle in Poncelet Porism [Java]
  528. Extra Feature of Van Aubel Configuration [JavaScript,GeoGebra]
  529. Extras in Bottema's Configuration [JavaScritpt, GeoGebra]
  530. Extremal Problem in a Quadrilateral
  531. Extremal Distance Ratio [GeoGebra]
  532. Extremal Problem in a Circular Segment
  533. The Extreme Principle
  534. Eye-to-Eye Theorem I [JavaScript, GeoGebra]
  535. Eye-to-Eye Theorem II [JavaScript, GeoGebra]
  536. Eyeball Theorem [JavaScript, GeoGebra]
  537. Eyeball Theorem Rectified [JavaScript]
  538. Eyeballing a Ball [JavaScript, GeoGebra]
  539. Eyeballs Projected [JavaScript, GeoGebra]
  540. Fagnano's problem [Java]
  541. Faulty Symmetry
  542. Fermat's Hexagon [JavaScript, GeoGebra]
  543. Fermat point and 9-point Centers [Java]
  544. Fermat Point Several Times Over
  545. Feuerbach's Theorem: A Proof [Java]
  546. Find a Common Chord of Given Length [Java]
  547. Find the Angle! [Java]
  548. Finding a Parallelogram in 3D
  549. Finding Circle Center By Ruler Alone [Java]
  550. Five Concyclic Points [Java]
  551. Five Incircles in a Square [Java]
  552. Five Incircles Theorem [Java]
  553. Five Squares in Complex Numbers [Java, GeoGebra]
  554. Fixed Point in a Kite - Problem from the 1993 Asian Pacific MO
  555. Fixed Point in Isosceles and Equilateral Triangles
  556. Fixed Point on Perpendicular Bisector [GeoGebra, JavaScript]
  557. Fixed Point of Circles Orthogonal to the Given One [Java]
  558. Fixed points from 2007 Irish Mathematical Olympiad
  559. Fleury's Algorithm and Euler's Paths and Cycles [Java]
  560. Focal Definition of Ellipse [Java]
  561. Focal Definition of Parabola [Java, GeoGebra]
  562. Focus and Directrix of Ellipse [Java]
  563. Focus on the Eyeball Theorem [JavaScript, GeoGebra]
  564. Folding Square in a Line through the Center [Java, GeoGebra]
  565. Fold Square into Equilateral Triangle [JavaScript]
  566. Following the Hilbert Curve [Java]
  567. Foot of Altitude and Minimum Distance [Java]
  568. For every object there is a distance at which it looks its best.
  569. Ford's touching circles
  570. Four Centroids and Parallels [Java]
  571. Four Circles In a Triangle [Java]
  572. Four Concurrent Lines in a Cyclic Quadrilateral [Java]
  573. Four Construction Problems [Java]
  574. Four Crossing Circles [Java]
  575. Four Geometric Problems of Antiquity
  576. Four Golden Circles
  577. Four Hinged Squares [Java]
  578. Four Incident Circles [Java]
  579. Four Incircles in Equilateral Triangle [Java]
  580. Four Isosceles Triangles Hinged at Vertices [JavaScript, GeoGebra]
  581. Four 9-Point Circles in a Quadrilateral [Java]
  582. Four Pedal Circles [Java]
  583. Four Touching Circles [Java]
  584. Four Touching Circles II [Java]
  585. Four Touching Circles III [Java]
  586. The Four Touching Circles Problem IV [Java, GeoGebra]
  587. Four Triangles, One Circle [Java]
  588. Four Turtles (or Bugs, or Dogs, etc.) [Java]
  589. Fractal curves and dimension [Java]
  590. François Viète's Reduction of CCC to PCC [Java, GeoGebra]
  591. Friendly Kiepert's Perspectors [Java]
  592. From 3 to Golden Ratio in Semicircle
  593. From Arbitrary Hexagon to Regular One [JavaScript, GeoGebra]
  594. From Arbitrary Pentagon to Regular One [JavaScript, GeoGebra]
  595. From Equilateral Triangle and Square to Golden Ratio
  596. From Foci to a Tangent in Ellipse [Java]
  597. From One Collinearity to Another
  598. From Straight Line to Regular Hexagon [JavaScript, GeoGebra]
  599. From Triangle Inequality to Inequality in Triangle
  600. Fundamental Theorem of 3-Bar Motion [Java]
  601. Further Properties of Peculiar Circles
  602. Further properties of Van Aubel Configuration [JavaScript, GeoGebra]
  603. Fuss' Theorem [Java]
  604. Garcia's Archimedean Quadruplets [JavaScript, GeoGebra]
  605. Garcia's Two Circles Lemmas [JavaScript, GeoGebra]
  606. Garcia-Feuerbach Collinearity [JvaScript, GeoGebra]
  607. Garfield's Ghost Revisited - by Tony Foster
  608. Generalizing a Romanian Olympiad Problem [Java]
  609. Geometric Illustration of a Convergent Series
  610. Geometric Mean Sangaku
  611. Geometric Meaning of the Geometric Mean
  612. Geometric Optimization from the Asian Pacific Mathematical Olympiad [Java]
  613. Geometric Proofs Of the Irrationality of Square Roots
  614. Geometry, Algebra, and Illustrations
  615. Gergonne and Medial Triangles Are Orthologic [Java]
  616. Gergonne and Soddy Lines Are Perpendicular [Java]
  617. Gergonne in Ellipse [Java]
  618. Gergonne and Van Obel Theorems
  619. Getting the first digits of Pi by counting collisions
  620. Gion Shrine Problem
  621. Given Parabola, Find Axis
  622. Glide Reflection [Java]
  623. Golden Ratio in Geometry
  624. Golomb's inductive proof of a tromino theorem [Java]
  625. Gothic Arc [Java]
  626. Graph Theory [Java]
  627. Grebe: from Ladies' Diary to Carroll's Pillow [Java]
  628. Grebe's Theorem
  629. Greg Markowsky's Problem for Parabola [Java]
  630. Griffiths Points in Cyclic Quadrilateral [Java]
  631. Griffiths' Theorem
  632. Half Turn, Reflection in Point [Java]
  633. Halving a square
  634. Harmonic Mean in Geometry
  635. Harmonic Mean Sangaku [Java]
  636. Harmonic Ratio
  637. Harmonic Ratio in Complex Domain
  638. Hart Circle [Java]
  639. Hart's Inversor [Java]
  640. Haruki's Lemma [Java]
  641. Haruki's Theorem
  642. Hausdorff Distance
  643. Hearty Munching on Cardioids [Java]
  644. Height/Width Interplay Illusion [Java]
  645. Helly's Theorem
  646. Hering Illusion [Java]
  647. Hermann Grid Illusion [Java]
  648. Heron's formula
  649. Heron's Formula: a Proof [Java]
  650. Heron's Problem [Java]
  651. Hexagon Parallel to Medial Triangle [Java]
  652. Hexagon Parallel to Orthic Triangle [Java]
  653. Hexagons in a Square
  654. Hidden Orthogonality [JavaScript, GeoGebra]
  655. Hinged Greek Cross Tessellation [Java]
  656. Hinged Squares [Java]
  657. Hinged Squares II [JavaScript, GeoGebra]
  658. Hippocrates' Squaring of a Lune [Java]
  659. Hippocrates' Squaring of Lunes
  660. Hjelmslev Theorem [Java]
  661. Homologous Lines under Three Spiral Similarities [Java]
  662. Homothety [Java]
  663. Homothety between In- and Excircles [Java]
  664. Homothety in Equilateral Triangles [JavaScript, GeoGebra]
  665. Hooper's Paradox [Java]
  666. How Fast Does One's Shadow Grow?
  667. How to Construct a Radical Axis [Java, GeoGebra]
  668. How to Construct Tangents from a Point to a Circle [Java, GeoGebra]
  669. Hunting Right Angles [Java]
  670. Huygens' Problem
  671. Ian McGee's Observation [Java]
  672. IMO 1998 Problem 1
  673. IMO 2004, Problem 5
  674. IMO 2006, Problem 1
  675. Impossible Fork [Java]
  676. Impossible Frame [Java]
  677. Importance of Having an Angle of 60 Degrees
  678. Importance of Occluders: Motion Binding [Java]
  679. In the Spirit of Thebault I [Java, GeoGebra]
  680. In the Wasan Spirit
  681. Incenters in Cyclic Quadrilateral [Java]
  682. Incidence in Feuerbach's Theorem [Java]
  683. Inequality in Rectangle
  684. Inequalities in Triangle
  685. Infinitude of Primes - A Topological Proof
  686. Inscribed and Central Angles in a Circle [Java]
  687. Inscribed Angles [Java]
  688. Inscriptible and Exscriptible Quadrilaterals [Java]
  689. Inscriptible Quadrilateral: An Illustration [Java]
  690. Inscriptible Quadrilateral of Triangle Incenters [JavaScript, GeoGebra]
  691. Integer Triangles with Two Angles in the Ratio 1 : 2 [JavaScript, GeoGebra]
  692. Internal Tangents to Three Circles [Java]
  693. Intersecting Chords Theorem
  694. Intersections of a Circle with the Four Quadrants [Java]
  695. Intouch Triangle in Poncelet Porism [Java]
  696. Invariance in Orthodiagonal Quadrilaterals [Java]
  697. Invariant Area Sweep Implies Pythagorean Theorem [Java]
  698. Inverse Similarity through Reflections
  699. Inversion: Reflection in a Circle [Java]
  700. Involution on the Projective Line
  701. Is Every Trapezoid Parallelogram? [Java]
  702. Isogonal Concurrencies [JavaScript, GeoGebra]
  703. Isogonal Lemma [JavaSCript, GeoGebra]
  704. Isosceles Configuration in Triangle [JavaScript, GeoGebra]
  705. Isosceles Tetrahedron
  706. Isosceles Trapezoid In Cyclic Quadrilateral [JavaScript, GeoGebra]
  707. Isogonal and Isotomic Conjugalities [Java]
  708. Isogonal Concurrency [Java]
  709. Isogonal image of the circumcircle [Java]
  710. Isoperimetric Theorem and Inequality
  711. Isosceles on the Sides of a Triangle [Java]
  712. Isotomic Reciprocity [JavaScript, GeoGebra]
  713. Isotomy and Isogonality Hand-in-Hand [Java]
  714. Iterations and the Mandelbrot Set [Java]
  715. Iterations on a Circle Through Three Points [Java]
  716. Iterations on Euler Lines [Java]
  717. J. Casey's Additions to Euclid I.47
  718. Jan Stevens' proof of E. W. Dijkstra's Generalization of the Pythagorean theorem
  719. Joachimsthal's Notations
  720. John Sharp's Paradox [Java]
  721. Johnson Circles [Java]
  722. Join Circles by Given Segment [Java]
  723. Joined Common Chords of Napoleon's Circumcircles [JavaScript, GeoGebra]
  724. Joseph Keech in Bride's Chair [Java]
  725. Judd Illusion [Java]
  726. Julia sets indexing [Java]
  727. Kanizsa Triangle [Java]
  728. Kiepert's Centroid [JavaScript, GeoGebra]
  729. Kiepert's Theorem [Java]
  730. Kiepert's Triangles Graduate to Ears of Arbitrary Shape [JavaScript, GeoGebra]
  731. Knots [avi movie]
  732. Knots on a Torus [Java]
  733. Kürschak's Tile and Theorem [Java]
  734. La Hire's Theorem [Java]
  735. Langman's Paradox [Java]
  736. LCC: Apollonius' Problem with Two Circles and a Line [Java, GeoGebra]
  737. Lean Napoleon's Triangles [Java]
  738. Length of a Median
  739. Length of the diagonal of the unit square equals the square root of 2
  740. Lennes' Polyhedron [Java]
  741. Leo's Lemma, Second Application
  742. Leo Giugiuc's Trigonometric Lemma
  743. Leonardo's Petals
  744. Lepidoptera of the Circles [Java]
  745. Lighthouse at Fermat Points [JavaScript, GeoGebra]
  746. Line IO in Bicentric Quadrilaterals
  747. Line Not Through a Center of Similarity [JavaScript, GeoGebra]
  748. Line Through a Center of Similarity [JavaScript, GeoGebra]
  749. Line through a Point in an Angle
  750. Line, Circle, and Fixed Points [Java]
  751. Linear Function with Coefficients in Arithmetic Progression [Java, GeoGebra]
  752. Lines Crossing Circles at Vertices of Equilateral Triangle
  753. Lines through Circles at Vertices of Equilateral Triangle [JavaScript]
  754. LLC: Apollonius' Problem with Two Lines and a Circle [Java, GeoGebra]
  755. Lipogrammatic Proof of the Pythagorean Theorem
  756. Loci of points in a cube
  757. Locus of Points in a Given Ratio to Two Points [Java]
  758. Longest segment
  759. Longitude, Latitude and Distance to the Equator
  760. Looking Back at Bottema [JavaScript, GeoGebra]
  761. Mach's Conservation of Area and the Pythagorean Theorem
  762. MacLaurin's Construction of Conics [Java]
  763. Maimed Cake [Java]
  764. Malfatti's Problem [Java]
  765. Malfatti's Problem, Hart's Solution [Java]
  766. Mascheroni Construction of a Regular Pentagon
  767. Mathematical Droodles [Java]
  768. Mathematics in Pizzeria [Java]
  769. MathPro Logo [Java]
  770. Maximal Properties of the Pythagorean Relation
  771. Maximum Area Property of Equilateral Triangles
  772. Maximum Area Property of the Medial Triangle
  773. Maximum Perimeter Property of the Incircle [Java]
  774. Maximum Ratio of Similarity - Belarus Olympiad Problem
  775. Maxwell's Theorem [Java]
  776. May the Product of Planes Be a Sphere?
  777. McDougall's Generalization of Ptolemy's Theorem
  778. Mechanical Proofs of the Pythagorean Theorem
  779. Median in Touching Circles [Java]
  780. Medians
  781. Medians in a Quadrilateral [Java]
  782. Medians in a Triangle Meet at the Center: a Second Look
  783. Meisters' Two Ears Theorem
  784. Menelaus Theorem [Java]
  785. Metric Relations in a Triangle
  786. Midline in Quadrilateral [Java, GeoGebra]
  787. Midline in Similar Triangles [Java]
  788. Midline in Trapezoid [Java, GeoGebra]
  789. Midline in Triangle [Java, GeoGebra]
  790. Midpoint Reciprocity in Napoleon's Configuration [JavaScript,GeoGebra]
  791. Midpoints and Orthogonality in Isosceles Triangles [Java]
  792. Midpoints from Gergonne Triangle [Java]
  793. Midpoints of the Lines Joining In- and Excenters [Java]
  794. Miguel Ochoa's van Schooten Is a Slanted Viviani [JavScript, GeoGebra]
  795. Miguel Ochoa's van Schooten Like Theorem [JavaScript, GeoGebra]
  796. Miguel Ochoa's van Schooten Like Theorem II [JavaScript, GeoGebra]
  797. Miguel Ochoa's van Schooten Like Theorem III [JavaScript, GeoGebra]
  798. Mikhalev's Octahedrons
  799. Minesweeper Theorem
  800. Miquel's Point [Java]
  801. Miquel's Point of a 4-line Via Spiral Similarity [Java]
  802. Miquel's Theorem for Circles [Java]
  803. Miquel Circumcenters [JavaScrirpt, GeoGebra]
  804. Mirror on the Wall [Java]
  805. Mirror property of the altitudes [Java]
  806. Mirror Property of Altitudes via Pascal's Hexagram [Java]
  807. Mixtilinear Circles and Concurrence [Java]
  808. Modern Day Sangaku
  809. Moebius Strip [avi movie]
  810. Möbius' Strip [Java]
  811. Models and Metamathematics
  812. Moment of Inertia of a Regular Polygon [JavaScript]
  813. Monge via Desargues [Java]
  814. Monge via Desargues II [Java]
  815. Morley Constellation [Java]
  816. Morley's Miracle [Java]
  817. Morphing [Java]
  818. Müller-Lyer Illusion [Java]
  819. Multifaceted Cork [Java]
  820. Multiplication of Points on a Circle [JavaScript,GeoGebra]
  821. Multiplication of Points on an Ellipse [JavaScript, GeoGebra]
  822. Munching on Circles
  823. Munching on Inscribed Angles
  824. My logo
  825. Nagel Line [Java]
  826. Nagel point [Java]
  827. Nagel Point of the Medial Triangle [Java]
  828. Nagel's Theorem [Java]
  829. Napoleon's Hexagon [JavaScript, GeoGebra]
  830. Napoleon's Theorem
  831. Necker Cube [Java]
  832. Neuberg Cubic [Java, GeoGebra]
  833. Neuberg Sangaku [Java]
  834. Newly Born Pair of Siblings to Archimedes' Twins [Java]
  835. Newton's Construction of Conics [Java]
  836. Newton's Theorem [Java]
  837. Nine Point Circle [Java]
  838. Nine Point Circle: an Elementary Proof [Java]
  839. No Equilateral Triangles, Please [Java]
  840. Nobbs' Points, Gergonne Line [Java]
  841. Non-Eclidean Geometries
  842. No-Pedal Collinearity [Java]
  843. Not So Hidden Homotheties [JavaScript, GeoGebra]
  844. Novel Concurrency of Perpendicular Bisectors [JavaScript, GeoGebra]
  845. Number of Regions N Lines Divide Plane
  846. Occluded Wheel Illusion [Java]
  847. Olof Hanner's Jigsaw Puzzle [Java]
  848. Circumcenter and Orthocenter Are Isogonal Conjugate/a> [JavaScript, GeoGebra]
  849. On the Difference of Areas
  850. One More Seven Circles Theorem [JavaScript, GeoGebra]
  851. One Sheet Hyperboloid [Java]
  852. Optimal Quadrilateral Inscribed in a Square
  853. Optimization in a Crooked Trapezoid
  854. Optimization Problem in Acute Angle [Java]
  855. Octagon in Parallelogram: Overlapping Regions [Java]
  856. Octagon in Parallelogram [Java]
  857. Optical Property of Ellipse [Java]
  858. Orbison illusion [Java]
  859. Orthic Semiperimeter [Java, GeoGebra]
  860. Orthogonal Lines, Midpoints, and Collinearity [Java, GeoGebra]
  861. Orthocenter and Three Equal Circles [Java]
  862. Orthocenters
  863. Orthocenters of Two Triangles Sharing Circumcenter and Base [Java]
  864. Orthocentric System From Rectangle [Java]
  865. Orthodiagonal and Cyclic Quadrilaterals [Java]
  866. Orthogonality in Isosceles Triangles [Java]
  867. Orthogonality in Two Squares [JavaScript, GeoGebra]
  868. Orthologic Triangles in a Quadrilateral [Java]
  869. Orthopole [Java]
  870. Out of Pentagon Sangaku
  871. Packing shapes in a plane
  872. Pairs of Areas in Equilateral Triangle
  873. Pairs of Homologous Lines under Spiral Similarities [Java]
  874. Pairs of Incircles in a Quadrilateral [Java]
  875. Pantograph [Java]
  876. Paper Folding & Cutting Sangaku
  877. Paper Folding Geometry
  878. Paper strip activities [avi movies]
  879. Paper strip activities, two strips
  880. Pappus' Generalization of Euclid I.47 [Java]
  881. Pappus' Theorem [Java]
  882. Parabola [Java]
  883. Parabola and Abutting Equilateral Triangles
  884. Parabolas Related to the Orthic Triangle [JavaScript, GeoGebra]
  885. Parabolic Mirror, Illustration [Java]
  886. Parabolic Mirror, Theory [Java]
  887. Parabolic Reciprocity [JavaScript, GeoGebra]
  888. Parabolic Sieve of Prime Numbers
  889. Paragon [Java]
  890. Parahexagon [Java]
  891. Parallel Chords [Java]
  892. Parallel Chords II [Java]
  893. Parallel Chords in Conics [Java, GeoGebra]
  894. Parallel Chords in Ellipse [Java]
  895. Parallel Chords in Crossing Circles [Java]
  896. Parallel Lines in a Cyclic Quadrilateral [Java]
  897. Parallel Lines in a Quadrilateral [Java]
  898. Parallel Lines in a Triangle [Java, GeoGebra]
  899. Parallelogram and Ellipses [Java, GeoGebra]
  900. Parallelogram and Four Equilateral Triangles [JavaScript, GeoGebra]
  901. Parallelogram and Similar Triangles [Java]
  902. Parallelogram Illusion [Java]
  903. Parallelogram in Four Circles [JavaScript, GeoGebra]
  904. Parallelogram in Parallelogram And in Projection [JavaScript, GeoGebra]
  905. Parallelogram Iterations [Java]
  906. Parallelogram Law [Java]
  907. Parallelogram Law: A PWW [Java]
  908. Parallelogram Law: A Tessellation [Java]
  909. Parallelogram with Side Lines through Fixed Points [JavaScript, GeoGebra]
  910. Partition of point sets in a plane
  911. Partitioning 3-Space with Circles
  912. Partitioning a Circle
  913. Pascal: Necessary and Sufficient [Java]
  914. Pascal in a Cyclic Quadrilateral [Java]
  915. Pascal Lines: Steiner and Kirkman Theorems [Java]
  916. Pascal Lines: Steiner and Kirkman Theorems II [Java]
  917. Pascal's theorem [Java]
  918. Peacock's Tail Sangaku
  919. Peaucellier Linkage [Java]
  920. Pedal Collinearities [Java]
  921. Pedal Parallelogram [JavScript, GeoGebra]
  922. Pedal Polygons [Java]
  923. Pedal Property in Equilateral Triangle
  924. Pedal SimilarityPedal Triangle and Isogonal Conjugacy [Java]
  925. Pedal Triangles of Inverse Points [JavaScript, GeoGebra]
  926. Pedoe's Theorem [Java]
  927. Pencils of Cubics
  928. Pentagon, construction of
  929. Pentagon in a Semicircle [Java]
  930. Pentagon Proportions Sangaku
  931. Perimeters of Convex Polygons, One within the Other
  932. Periodic patterns in sin(N) [Java]
  933. Perpendicular Bisectors in an Inscriptible Quadrilateral [Java]
  934. Perpendicular Bisectors in an Inscriptible Quadrilateral II [Java]
  935. Perpendicular lines in a cyclic quadrilateral from 1975 Canadian Mathematical Olympiad
  936. Perspective Triangles in Circle
  937. Pick's Theorem [Java]
  938. Phantom Circle and Recaptured Symmetry
  939. Plane Filling Curves [Java]
  940. Plane Isometries
  941. Plane Isometries As Complex Functions
  942. Plato's Geometric Numbers: can you better Sam Loyd?
  943. Pleasant Proportions in Triangle
  944. Poggendorff's Illusion
  945. Point common to two similar rectangles [Java]
  946. Point in a Square
  947. Point on Bisector in Right Angle
  948. Points Generated by the Nine Points
  949. Polar Circle [Java]
  950. Poles and Polars [Java]
  951. Polygon in a Rectangle
  952. Polygons: formality and intuition [Java]
  953. Polygons Formed by Perpendicular Bisectors [Java]
  954. Pompeiu's Theorem [Java]
  955. Poncelet's Porism [Java]
  956. Poncelet's Porism in Ellipses [Java]
  957. Poncelet's Theorem [Java]
  958. Ponzo Illusion [Java]
  959. Ponzo Illusion II [Java]
  960. Possible or Impossible? [Java]
  961. Power of a point with respect to a circle
  962. PCC: Apollonius' Problem with Two Circles and a Point [Java, GeoGebra]
  963. PLC: Apollonius Problem with a point, a line, and a circle [Java, GeoGebra]
  964. PLL: Apollonius' Problem with Two Lines and a Point [Java, GeoGebra]
  965. PPC: Apollonius' Problem with Two Points and a Circle [Java, GeoGebra]
  966. PPL: An Elementary Solution [Java, GeoGebra]
  967. PPL: Apollonius' Problem with Two Points and a Line [Java, GeoGebra]
  968. Praying Eyes Theorem [JavaScript, GeoGebra]
  969. Problem 4 from the 1959 IMO: Construction of a Right Triangle [Java, GeoGebra]
  970. Problem 4, 1975 USA Math Olympiad and the Radical Axis [Java]
  971. Problem 4, 1975 USA Math Olympiad and Isosceles Triangles [Java]
  972. Problem 4, 1975 USA Math Olympiad: Normals and Tangents [Java]
  973. Problem 4, 1975 USA Math Olympiad: Problem 4, 1975 USA Math Olympiad: The Final Touch [Java]
  974. Problem 4 from the IMO 2009
  975. Problem in an Equilateral Triangle [Java]
  976. Problem 4 from the IMO 2013 - Synthetic Solution [Javacript, GeoGebra]
  977. Problem in an Equilateral Triangle II [Java]
  978. Problem in Direct Similarity [JavaScript, GeoGebra]
  979. Problem in Three Squares [Java]
  980. Problem of Equal Steps [Java]
  981. Problem of Equal Steps II [Java]
  982. Problem on a Pentagonal Star
  983. Problem with angle bisector from 1975 Canadian Mathematical Olympiad
  984. Problem with equal angles from 1987 IberoAmerican Mathematical Olympiad
  985. Proclivity of Conjoint Archimedean Twins for Proliferation [JabvaScript, GeoGebra]
  986. Projections of Convex Quadrilateral [JavaScript, GeoGebra]
  987. Projections of Isogonal Conjugate are Concyclic [JavaScript, GeoGebra]
  988. Projections on Internal and External Angle Bisectors [Java]
  989. Projective Collinearity in a Quadrilateral [Java]
  990. Projective infinity
  991. Projective Invariants for Pascal And Desargues
  992. Properties of Flank Triangles
  993. Properties of the Circle of Similitude [Java]
  994. Properties of Circle Through the Incenter
  995. Properties of the Figures in Euclid I.47
  996. Properties of the Harmonic Ratio
  997. Property of 6-Parpolygon [Java]
  998. Property of Angle Bisectors [Java]
  999. Property of Circumscribed Quadrilaterals [Java]
  1000. Property of Points Where In- and Excircles Touch a Triangle [Java]
  1001. Property of Right Isosceles Triangle [Java, GeoGebra]
  1002. Property of Right Trapezoids [GeoGrebra]
  1003. Property of Semicircles [Java]
  1004. Property of Thébault Circles [JavaScript, GeoGebra]
  1005. Property of Two Pencils of Parallel Lines
  1006. Proportions in Square
  1007. Ptolemy's Theorem
  1008. Pure Angle Chasing [JavaScript, GeoGebra]
  1009. Pure Angle Chasing II [JavaScript, GeoGebra]
  1010. Pure Angle Chasing III [JavScript, GeoGebra]
  1011. Puzzles on graphs.
  1012. Pythagoras' Theorem (111 proofs)
  1013. Pythagoras and Vecten Break Japan's Isolation [Java]
  1014. Pythagorean Triples [Java]
  1015. Quadrature: A Child's Play
  1016. Quadrilateral from a Segment
  1017. Quadrilateral With Equal Opposite Sides And Angles [Java]
  1018. Quadrilateral with 3 Equal Sides [Java]
  1019. Quadrilaterals Formed by Perpendicular Bisectors [Java]
  1020. Quest for Paragon [Java]
  1021. Radical Axis and Center, an Application [Java]
  1022. Radical Axis of Circles Inscribed in a Circular Segment [Java]
  1023. Radical Center [Java]
  1024. Radius and Construction of a Mixtilinear Circle [Java]
  1025. Radius of a Circle by Paper Folding [Java]
  1026. Random Dot Stereograms [Java]
  1027. Ratios and Orthogonality in a Triangle - Problem from the 2006 Romania MO
  1028. Rational Points On a Circle
  1029. Rectified, Halved, Sheared, Eyeballs Still Surprise [JavaScript, GeoGebra]
  1030. Reflection in a Triangle Tangent to Parabola [JavaScript, GeoGebra]
  1031. Reflection In Line [Java]
  1032. Reflection in the Circumcenter
  1033. Reflections in Ellipse [Java]
  1034. Reflections of a Line Through the Orthocenter [Java]
  1035. Reflections of a Point on the Circumcircle [Java]
  1036. Reflections of the Orthocenter
  1037. Reflections of the Orthocenter [Java]
  1038. Reflections of the Orthocenter II Regular Hexagon and Triangle Joined at Vertex [JavaScript, GeoGebra]
  1039. Regular Hexagon from Arbitrary Triangle [JavaScript, GeoGebra]
  1040. Regular Octagon by Paper Folding
  1041. Regular Polygons in a Triangular Grid [Java]
  1042. Regular Polyhedra - Platonic Solids
  1043. Other Solids
  1044. Regular Pentagon Inscribed in Circle by Paper Folding
  1045. Regular polyhedra and Euler's Theorem
  1046. Reim's Similar Coins I
  1047. Reim's Similar Coins II
  1048. Reim's Similar Coins III
  1049. Reim's Similar Coins IV
  1050. Relation Engendered By Altitudes
  1051. Relation Engendered By Medians
  1052. Relations in a Cyclic Polygon
  1053. Remarkable Line in a Quadrilateral [Java]
  1054. Remarkable Line in Cyclic Quadrilateral [Java]
  1055. Rendezvous [Java]
  1056. Reverse Spoke Illusion [Java]
  1057. Revolving Circles Illusion [Java]
  1058. Rhombus in a Cyclic Quadrilateral [Java]
  1059. Rhombus in Circles [Java, GeoGebra]
  1060. Riemann Sphere and Möbius Transformation
  1061. Right Triangles on Sides of a Square [Java]
  1062. Rotating Top Illusion [Java]
  1063. Rotating Gears [Java]
  1064. Rotation Transform [Java]
  1065. Rouse Ball's Fallacy [Java]
  1066. Rusty Compass Construction of Equilateral Triangle [Java]
  1067. Salinon: From Archimedes' Book of Lemmas [Java]
  1068. Sam Loyd's Geometric Puzzle
  1069. Sam Loyd's Son's Dissection [Java]
  1070. Sangaku: Reflections and the Phenomenon
  1071. Sangaku: Critique of My View and a Response
  1072. Sangaku and The Egyptian Triangle
  1073. Sangaku in a Square
  1074. Sangaku Iterations, Is it Wasan? [Java]
  1075. Sangaku with 8 Circles
  1076. Sangaku with Angle between a Tangent and a Chord [Java]
  1077. Sangaku with Quadratic Optimization
  1078. Sangaku with Three Mixtilinear Circles [Java]
  1079. Sangaku with Versines [Java]
  1080. Sangakus with a Mixtilinear Circle [Java]
  1081. Scintillating Grid Illusion [Java]
  1082. Schwarz Lantern [Java]
  1083. Secant Angles [Java]
  1084. Secant Angles II [Java]
  1085. Secant, Normal, Tangent [Java]
  1086. Secant, Tangents and Orthogonality [Java]
  1087. See-Saw Lemma [Java]
  1088. Segment Projections in Equilateral Triangle
  1089. Segment Trisection [Java]
  1090. Segment Trisection Induced by Parallels to Medians [Java]
  1091. Semicircle on Square [JavaScript]
  1092. Semi-regular Tessellation on Hinges A [Java]
  1093. Semi-regular Tessellation on Hinges B [Java]
  1094. Separating point sets with a circle
  1095. Sequences of Concyclic Points on a Conic
  1096. Sequences of Touching Circles
  1097. Serendipitous Beauty [Java]
  1098. Serendipitous Proofs Of The Pythagorean Theorem
  1099. Seven and the Eighth Circle Theorem
  1100. Seven Circles Theorem [Java]
  1101. Seven Concyclic Points [Java, GeoGebra]
  1102. Seven Equal Circles [JavaScript, GeoGebra]
  1103. 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
  1104. Shaggy Dog Theorem
  1105. Shapes in a lattice
  1106. Shapes of constant width [Java]
  1107. Shearing and Translation in Pythagorean Pants [Java]
  1108. Shearing a Polygon into a Triangle of Equal Area [Java]
  1109. Shearing Butterflies in Quadrilaterals [Java]
  1110. Shedding Light on the Ball for Eyeballing
  1111. Shepard's Parallelogram Illusion [Java]
  1112. Shifted by the Inradius Tangent Collinearities [JavaScript, GeoGebra]
  1113. Shifting Cube Illusion [Java]
  1114. Shimmer Illusion [Java]
  1115. Short Construction of the Geometric Mean
  1116. Shortest Fence in a Quarter-Circle Pasture
  1117. Shredding the torus
  1118. Sides and Area of Pedal Triangle
  1119. Sierpinski Gasket By Common Trema Removal [Java]
  1120. Sierpinski Gasket Via Chaos Game [Java]
  1121. Sierpinski Gasket by Trema Removal [Java]
  1122. Similar Triangles And More
  1123. Similar Triangles in Crossing Circles [JavaScript, GeoGebra]
  1124. Similar Triangles on Sides of a Quadrilateral [Java]
  1125. Similar Triangles on Sides and Diagonals of a Quadrilateral [Java]
  1126. Similarity Is About Proportion - And Ways to Look at It
  1127. Simple dissection of an acute triangle
  1128. Simple Property of Circle Through the Incenter [JavaScript]
  1129. Simple Quadrilaterals Tessellate the Plane [Java]
  1130. Simson Line [Java]
  1131. Simsons and 9-Point Circles in Cyclic Quadrilateral [Java]
  1132. Simultaneous Contrast Illusion [Java]
  1133. Simultaneous Contrast Illusion II [Java]
  1134. Simultaneous Contrast: Koffka's Illusion [Java]
  1135. Simultaneous Contrast: White's Illusion [Java]
  1136. Simultaneous Contrast: White's Illusion, V-Variant [Java]
  1137. Simultaneous Diameters in Concurrent Circles [Java]
  1138. Simultaneous Generalization of the Theorems of Ceva and Menelaus
  1139. Sine and Cosine of 15 Degrees Angle
  1140. Sine, Cosine, and Ptolemy's Theorem
  1141. Six Circles with Concurrent Pairwise Radical Axes
  1142. Six Circles Theorem (Bui Quang Tuan) [Java]
  1143. Six Circles Theorem (Elkies) [Java]
  1144. Six Circles Theorem (Evelyn) [Java]
  1145. Six Concyclic Circumcenters in Fermat's Configuration [JavaScript, GeoGebra]
  1146. Six Concyclic Points [Java]
  1147. Six Concyclic Points on Sides of a Triangle
  1148. Six Concyclic Points II [Java]
  1149. Six Concyclic Points via Antipedal Triangle [JavaScript, GeoGebra]
  1150. Six Incircles in an Equilateral Triangle [Java]
  1151. Six Point Circle [Java]
  1152. SixPoints, ThreeLines [Java]
  1153. Soddy Circles and David Eppstein's Centers [Java]
  1154. Some Properties of Common Tangents [JavaScript, GeoGebra]
  1155. Some Properties of Napoleon's Configuration [Java]
  1156. Sperner's Lemma [Java]
  1157. Spiral Similarity [Java]
  1158. Spiral Similarity and CollinearitySpiral Similarity and Collinearity [Java, GeoGebra]
  1159. Spiral Similarity Leads to Equilateral Triangle [JavaScript, GeoGebra]
  1160. Square and Circle in a Gothic Cupola
  1161. Square from Four Points, One on Each Side
  1162. Square From Nowhere [Java]
  1163. Square in a Circle Inscribed in a Square [Java]
  1164. Square in a Right Triangle [Java]
  1165. Square in Chair [Java]
  1166. Square Inscribed in a Triangle [Java]
  1167. Square Inscribed in a Triangle II [Java]
  1168. Square, Similarity and Slopes [Java]
  1169. Squares and Straight Tetrominoes
  1170. Squares in Circles [Java]
  1171. Squares in Semicircle and Circle
  1172. Squares in Triangles
  1173. Squares Inscribed In a Triangle III [Java]
  1174. Squares on Sides of a Quadrilateral [Java]
  1175. Square out of a Quadrilateral
  1176. Squaring a circle
  1177. Squaring a Rectangle [Java]
  1178. Squinting Eyes Theorem [Java]
  1179. SSA
  1180. SSS
  1181. Staircase Illusion [Java]
  1182. Star of David [Java]
  1183. Steiner's Circumellipse in Barycentric Coordinates [GeoGebra]
  1184. Steiner's Inellipse
  1185. Steiner's Sangaku
  1186. Steiner's Theorem
  1187. Stereographic Projection [Java]
  1188. Stereographic Projection and Inversion
  1189. Stereographic Projection and Radical Axes
  1190. Stewart's theorem
  1191. Straight Edge Only Construction of Polar
  1192. Structural Constellation [Java]
  1193. Sum of Squares in Equilateral Triangle
  1194. Sum of Squares of Distances to Vertices
  1195. Sylvester's Problem
  1196. Symmedians
  1197. Symmetries in a Triangle
  1198. Symmetries in Triangle II [JavaScript, GeoGebra]
  1199. Symmetry in an Asymmetric Configuration [JavaScript, GeoGebra]
  1200. Tangency Point of Two Circles [Java]
  1201. Tangent and Secant [Java]
  1202. Tangent as a Radical Axis [Java]
  1203. Tangent Circles, Similarity and Equal Segments [JavaScript, GeoGebra]
  1204. Tangent Circles and an Isosceles Triangle [Java]
  1205. Tangent Circles in a Parallelogram [Java]
  1206. Tangent Curiosity in Equilateral Triangle [JavaScript, GeoGebra]
  1207. Tangent in Concurrency [Java]
  1208. Tangent Lines and Circles in Convex Quadrilateral [Java]
  1209. Tangent of 22.5° - Proof Wthout Words
  1210. Tangent to the Incircle [JavaScript]
  1211. Tangent to two circles
  1212. Tangents And Bisectors
  1213. Tangents and Diagonals in Cyclic Quadrilateral [Java]
  1214. Tangents, Perpendiculars and Geometric Mean [Java]
  1215. Tarski-Banach Decompositions
  1216. Taylor circle [Java]
  1217. Terquem's Theorem [Java]
  1218. Tesseract [Java]
  1219. Tetrahedron in Parallelepiped
  1220. Tetrahedron with Equiareal Faces
  1221. Tetrahedron with Equiareal Faces, II
  1222. Tetrahedron with Orthogonal Perpendiculars to Opposite Edges
  1223. Thales' Theorem [Java, GeoGebra]
  1224. Thales' Theorems
  1225. Thales on Angle Bisectors [JavaScript, GeoGebra]
  1226. The 80-80-20 Triangle
  1227. Center of Gravity and Motion of Material Points [JavaScript, GeoGebra]
  1228. The Chaos Game: Address Space vs IFS [Java]
  1229. The Eutrigon Theorem [Java, GeoGebra]
  1231. The Law of Cosines by Larry Hoehn
  1232. The only rational triangle
  1233. The Pythagorean Theorem from a Combinatorial Identity
  1234. The Schwarz Lantern Explained [JavaScript]
  1235. The Shape of the Colosseum [Java, GeoGebra]
  1236. The Shortest Crease [JavaScript, GeeoGebra]
  1237. Thébault's Problem I [Java]
  1238. Thébault's Problem II [Java]
  1239. Thébault's Problem III [Java]
  1240. Theorem of Complete Quadrilateral [Java]
  1241. Theorem of Three Tangents to a Conic [JavaScript, GeoGebra]
  1242. Theorems of Ceva and Menelaus, an Illustrated Generalization [Java]
  1243. There is no Difference Between Equilateral Triangles
  1244. Third Unusual Identity in Triangle
  1245. Three Circles and Common Tangents
  1246. Three Circles through the Incenter
  1247. Three Collinear and Four Concyclic Points [Java, GeoGebra]
  1248. Three Concurrent Circles [Java]
  1249. Three Common Chords in Three Concurrent Circles [Java, GeoGebra]
  1250. Three Congruent Circles by Reflection [Java]
  1251. Three Congruent Circles by Reflection II [Java]
  1252. Three Congruent Circles by Reflection III [Java]
  1253. Three Equal Circles in a Semicircle
  1254. Three Euler Lines That Are Four [JavaScript]
  1255. Three Incircles In a Right Triangle [Java]
  1256. Three Incircles in a Triangle [Java]
  1257. Three Isosceles Triangles [Java]
  1258. Three Orthogonal Circles Through Three Given Points [Java]
  1259. Three lines at 60 degres and Circumcenters [JavaScript, GeoGebra]
  1260. Three pairs of Parallel Lines and a Conic [JavaScript, GeoGebra]
  1261. Three Parabolas with Common Directrix [JavaScript,GeoGebra]
  1262. Three Parallels in a Triangle [Java]
  1263. Three Points on a Parabola [Java]
  1264. Three Pyramids are Better Than Two [Java]
  1265. Three regions sharing a common boundary
  1266. Three Similar Polygons [Java]
  1267. Three Similar Triangles [Java]
  1268. Three Similar Triangles II [Java]
  1269. Three Squares and Two Ellipses [Java]
  1270. Three Tangent Circles [Java]
  1271. Three Tangents, Three Chords in Ellipse [Java]
  1272. Three Tangent Circles Sangaku
  1273. Three Tangents Theorem [Java]
  1274. Three Tangents, Three Secants [Java]
  1275. Three Touching Circles [Java]
  1276. Three visions of a fact [GeoGebra]
  1277. Tiling a Chessboard with Dominoes
  1278. Tiling Sphere by Four Equal Triangles
  1279. Toothpick Construction of a Square [Java]
  1280. Topological preliminaries
  1281. Torque as a Mathematical Object
  1282. Touching Circles [Java]
  1283. Touching Circles and Concurrency [Java]
  1284. Touching Circles with Given Centers II [Java]
  1285. Train wheel quandary
  1286. Transitivity in Action [Java]
  1287. Translated Triangles [Java]
  1288. Translation Transform [Java]
  1289. Transversal Trigonometry [JavaScript, GeoGebra]
  1290. Triangle ABC is right iff sin²A + sin²B + sin²C = 2
  1291. Triangle Areas in a Parallelogram [Java]
  1292. Triangle Areas in a Parallelogram II [Java]
  1293. Triangle by HM segments [JavaScript, GeoGebra]
  1294. Triangle Classification [Java]
  1295. Triangle constructions and facts [Java]
  1296. Triangle Construction from Angle, Altitude and Median
  1297. Triangle from a, A, mc/mb
  1298. Triangle from Angle Bisector, Altitude and Circumradius
  1299. Triangle from Angle Bisector, Altitude and Inradius
  1300. Triangle from Inradius, Circumradius, Side or Angle
  1301. Triangle from Median, Altitude and Circumradius
  1302. Triangle from Side, Circumradius, and Median
  1303. Triangle from Angle, Inradius, and Difference of Sides
  1304. Triangle from Side, Inradius, and Altitude
  1305. Triangle from Side, Median, and Altitude
  1306. Triangle from Two Side Lines and the Euler Line
  1307. Triangle Sliding on Two Straight Lines [Java]
  1308. Triangle of Minimum Perimeter [JavaScript]
  1309. Triangles, Squares and Areas from Temple Geometry [Java]
  1310. Triangles with Equal Area [Java]
  1311. Triangles with Sides in Geometric Progression [JavaScript]
  1312. Triangular Areas in Circle [JavaScript, GeoGebra]
  1313. Triangular Billiard [Java]
  1314. Triangulating Squares
  1315. Triangle with a 60 degrees angle [JavaScript, GeoGebra]
  1316. Trigonometric Form of Ceva's Theorem [Java]
  1317. Trigonometric Functions [Java]
  1318. Trigonometric Identities with Arctangents
  1319. Trigonometric Proof of the Pythagorean Theorem
  1320. Trigonometry According to Ptolemy
  1321. Trigonometry by Paper Folding
  1322. Trisect Segment: 2 Circles, 4 Lines
  1323. Trisectable angle that is not constructible
  1324. Tucker Circles [Java]
  1325. Tucker Circles Through Homothety [Java]
  1326. Twelve Matchsticks Area Puzzle
  1327. Twin Segments in Four Semicircles
  1328. Twins Beget Twins
  1329. Twisted Cord Illusion [Java]
  1330. Two Altitudes, One Midpoint
  1331. Two Arbelos, Two Chains
  1332. Two Cevians and Proportions in a Triangle
  1333. Two Circles and a Limit - Analytic Proof
  1334. Two Circles and One More [Java]
  1335. Two Circles and Two More [Java]
  1336. Two Circles, Ellipse, and Parallel Lines
  1337. Two Circles in a Parallelogram [Java]
  1338. Two Circles Inscribed in a Parallelogram [Java]
  1339. Two Circles in a Square [Java]
  1340. Two Circles in a Square II [Java]
  1341. Two Circles in an Angle [Java]
  1342. Two Circles on Angle Bisector [Java]
  1343. Two Circles on a Side of a Triangle [Java]
  1344. Two Circles, Tangents and Two Collinearities [JavaScript, GeoGebra]
  1345. Two Circumcircles And Two Pairs of Parallels [Java]
  1346. Two Circumcircles in Triangle [Java]
  1347. Two coins puzzle
  1348. Two Congruent Circles by Reflection [Java]
  1349. Two Conics, Pascal, Chasles, and Cross-Ratio [JavaScript, GeoGebra]
  1350. Two Color Coloring of the Plane [Java]
  1351. Two Common Chords in Three Concurrent Circles [Java, GeoGebra]
  1352. Two Diameters and Longest Common Chord [Java, GeoGebra]
  1353. Two Equilateral Triangles [Java]
  1354. Two Homotheties in a Parallelogram [Java]
  1355. Two Intersecting Circles [Java]
  1356. Two Lines - Two Circles [Java]
  1357. Two Pencils of Parallel Lines [JavaScript, GeoGebra]
  1358. Two Pairs of Parallel Lines in a Triangle [Java, GeoGebra]
  1359. Two Parallels in a Triangle and One More [Java]
  1360. Two Pascals Merge into One [JavaScript, GeoGebra]
  1361. Two Perpendiculars From a Point to a Line [Java]
  1362. Two Planar Constructions Related to a 3D Problem
  1363. Two Perspective Triangles
  1364. Two Quadrilaterals [Java]
  1365. Two Quadruplets of Concyclic Points [JavaSCript,GeoGebra]
  1366. Two Quadruplets of Tangent Circles [Java]
  1367. Two Related Triangles of Equal Areas
  1368. Two Sangaku with Equal Incircles
  1369. Two Similar Triangles with Parallel Sides [JavaScript, GeoGebra]
  1370. Two Simsons in a Triangle [Java]
  1371. Two Squares and Another Square [Java]
  1372. Two Symmetric Triangles Are Directly Decomposable [Java]
  1373. Two Touching Circles [Java]
  1374. Two Triangles Inscribed in a Conic [Java, GeoGebra]
  1375. Two Triangles Inscribed in a Conic - with Elementary Solution [Java, GeoGebra]
  1376. Two Triangles Inscribed in a Conic - with Solution [Java, GeoGebra]
  1377. Two Triangles With Common Base and Altitude [Java]
  1378. Two Triangles Sharing the Circumcenter
  1379. Two Triples of Concurrent Cevians and a Conic [JavaScript, GeoGebra]
  1380. Two Triples of Concurrent Circles [Java]
  1381. Two Triples of Similar Triangles [Java]
  1382. Uncommon Triangle Constructions
  1383. Unfolding Spirals Illusion [Java]
  1384. Urquhart's Theorem
  1385. USA 1975 Problem 4
  1386. Use of Homogeneous Coordinates for Geometrical Calculations
  1387. Van Khea's Fourth Identity in Triangle
  1388. Van Obel Theorem, Determinants, and Barycentric Coordinates
  1389. Van Schooten's and Pompeiu's Theorems [Java]
  1390. Van Schooten's Locus Problem [Java]
  1391. Variations on the Theme of Tremas [Java]
  1392. Variations on the Theme of Tremas II [Java]
  1393. Varignon Parallelogram [Java]
  1394. Various Geometries
  1395. Vecten-Nikolin Hexagon [Java]
  1396. Vecten's Collinearity [Java]
  1397. Vecten's Mesh [Java]
  1398. Vector Addition and Subtraction [Flash]
  1399. Vector product
  1400. Versatile Theorem [Java]
  1401. Vertical and Horizontal Dominoes on a Chessboard
  1402. Vietnamese Extension of a Japanese Theorem [JavaScript]
  1403. Vietnamese Lemma towards an Extension of a Japanese Theorem [JavaScript, GeoGebra]
  1404. Viewing a Statue
  1405. Viviani's Theorem [Java]
  1406. Viviani's Theorem II [Java]
  1407. Viviani in Isosceles Triangle [Java]
  1408. Viviani by Inversion
  1409. Viviani by Vectors
  1410. Viviani's 3D Analogue
  1411. Sanchez's Viviani's Area Analogue [JavaScript, GeoGebra]
  1412. Volume and Area of Torricelli's Trumpet [JavaScript]
  1413. Volume of Sphere and Volume of an Ellipsoid
  1414. Volumes of Two Pyramids
  1415. Wallace-Bolyai-Gerwien Theorem
  1416. Wallace's Theorem [Java]
  1417. Watt's and Chebyshev's Linkage [Java]
  1418. Weird curves bound normal areas
  1419. Weitzenböck Inequality [Java]
  1420. What does one see inside a spherical mirror? [Java]
  1421. What Is Analytic Geometry?
  1422. What Is Angle?
  1423. What Is Angle Chasing?
  1424. What Is Area?
  1425. What Is Ellipse?
  1426. What Is Indirect Proof?
  1427. What Is Line?
  1428. What Is Point?
  1429. When a Triangle is A-cute
  1430. When a Triangle is Equilateral [Java]
  1431. When Two Segments Intersect? [JavaScript]
  1432. When index equals content [Java]
  1433. Why a Diameter Is the Longest Chord?
  1434. William Wallace's Proof of the Butterfly Theorem
  1435. William Wallace's 1803 Statement of the Butterfly Theorem [JavaScript, GeoGebra]
  1436. Wittenbauer's Parallelogram [Java]
  1437. Wundt Illusion [Java]
  1438. Wundt Block Illusion [Java]
  1439. Y. Sawayama's Lemma [Java]
  1440. Y. Sawayama's Theorem
  1441. YATPOPT, Yet Another Trigonometric Proof of the Pythagorean Theorem
  1442. Yet Another Appearance of the Golden Ratio [JavaScript, GeoGebra]
  1443. Yet Another Concurrence on the 9-Point Circle [JavaScript, GeoGebra]
  1444. Yet Another Seven Circles Theorem [JavaScript, GeoGebra]
  1445. Zaslavsky's theorem [Java]
  1446. Zöllner's Illusion [Java]

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