Memory and Matching Arithmetic Algebra
Logic Fractals Probability
Visual Illusions Calculus Math Magic
Combinatorics Combinatorial Games Puzzles & Games
Geometric Fallacies Social Sciences Elementary Geometry
Stereometry Outline Mathematics Miscellaneous Demonstrations

Interactive Mathematics Activities

    Memory and Matching

  1. Match answers
  2. Memory - Easy
  3. Memory - Medium
  4. Memory - Hard

    Arithmetic

  5. 1089 and a Property of 3-digit Numbers
  6. 2 Pails Puzzle
  7. 3 Jugs Puzzle
  8. 3 Jugs Puzzle in Barycentric Coordinates
  9. 3-Term Arithmetic Progression
  10. Abacus in Various Number Systems
  11. Algorithm for Computing LCM
  12. Aliquot Game
  13. Arithmetic Operations in Various Bases
  14. Broken Calculator
  15. Coin Game
  16. Collatz Conjecture
  17. Common Multiples and the Least Common Multiple
  18. Compare Fractions: Interactive Practice
  19. Counting and Grouping
  20. Distributive Law
  21. EAN-13 Encoding
  22. Equivalent Fractions
  23. Euclid's Algorithm: An Interactive Illustration
  24. Euclid's Game
  25. Euclid's Game on a Square Grid
  26. Even, Odd and Total Number of Digits
  27. Factoring with the Factor Tree
  28. Farey Fractions
  29. Fibonacci Numbers in Equilateral Triangle
  30. Flipping Items Simultaneously
  31. Fraction Comparison
  32. Fraction Comparison Sped up
  33. GCD and LCM via Factor Tree
  34. GCD and LCM by Plain Factorization
  35. GCD(M, N) × LCM(M, N) = M × N
  36. Geometric view of the Sieve of Eratosthenes
  37. ISBN Encoding
  38. Kaprekar's Iterations and Numbers
  39. Lattice Multiplication
  40. Long Multiplication
  41. Less, Equal, More
  42. Listing All the Composite Numbers
  43. Lucky Numbers
  44. Make An Identity
  45. Make It All Zeros
  46. Moving Chips in Pairs Down a Checkerboard
  47. Napier Bones
  48. Plain Multiplication table up to 20×20
  49. Product of Simple Fractions
  50. Rule of Change of Addends
  51. Sieve of Eratosthenes
  52. Sieve of Squares
  53. Soroban in Various Number Systems
  54. Suan Pan in Various Number Systems
  55. Subtraction in a Rectangular Array
  56. Sums and Products
  57. Sums of Powers of Digits
  58. Treasure Hunt in a Square Grid
  59. Treasure Hunt from Outside the Grid
  60. Two Simple Equations
  61. Universal Product Code
  62. Zeros and Nines

    Algebra

  63. A Line in a Square Grid
  64. Ambassadors at a Round Table
  65. Averages, Arithmetic and Harmonic Means
  66. Base (Binary, Decimal, etc.) Converter
  67. Binary Color Device
  68. Breaking Chocolate Bars
  69. Candy Game: Integer Iterations on a Circle
  70. Chebyshev polynomials
  71. Complex Numbers: A Dynamic Tool
  72. Constructible Numbers
  73. Counting Chips On a Circle
  74. Counting Squares in a Square
  75. Counting Triangles
  76. Counting Triangles II
  77. Divisibility Problem
  78. Dots and Fractions
  79. Ducci Sequences
  80. Egyptian Multiplication
  81. Filling an Array with 0s and 1s - and Counting
  82. First Geometric Interpretation of Complex Numbers
  83. Four Pegs That Form a Square
  84. Frieze Patterns
  85. Geometric Construction of Roots of Quadratic Equation
  86. Graph and Roots of a Third Degree Polynomial
  87. Graph and Roots of Quadratic Polynomial
  88. Heads and Tails (counting, invariance)
  89. Identities in the Multiplication Table
  90. Integer Iterations on a Circle II (superposition principle)
  91. Integer Iterations on a Circle III
  92. Integers and Rectangles
  93. Integers and Rectangles: a Proof by Induction
  94. Integers and Rectangles: Two Simple Proofs
  95. Interest Calculations
  96. Josephus Flavius Game
  97. Langford and Skolem Sequences
  98. Letter Count in a Sentence
  99. Lights Out
  100. Logistic Model
  101. Loop or Halt
  102. Mean Values
  103. Merlin's Magic Squares (modular arithmetic, boolean and linear algebra)
  104. Mini Lights Out
  105. Minimax Principle
  106. Minimax Theorem
  107. Modular Arithmetic
  108. Nine Squares
  109. Parrondo Paradox Via Simpson Paradox
  110. Peasant Multiplication
  111. Pennies in Boxes
  112. Plus or Minus (parity, invariance)
  113. PolygonalNumbers
  114. Proizvolov's Identity
  115. Pythagorean Triples
  116. Pythagorean Triples Calculator
  117. Quasigroup on a Triangular Grid
  118. Rectangle on a Chessboard
  119. Right Replacement
  120. Self-descriptive Strings
  121. Self-documenting Sentences
  122. Sierpinski's Gasket and Dihedral Symmetry
  123. Signs and Sums in a Sequence
  124. Signs in a Matrix
  125. Simple Cellular Automaton
  126. Simple Somos Sequence Calculator
  127. Simpson Paradox
  128. Sine of a Sum Formula
  129. Solitaire in Two Colors
  130. Squares and Circles (parity, invariance)
  131. Squares, Circles, and Triangles (modular arithmetic, invariance)
  132. Steinhaus' Problem
  133. Sum of Consecutive Integers is Triangular
  134. Sum of Consecutive Odd Numbers is Square
  135. Sum of Consecutive Triangular Numbers is Square
  136. Sums of Geometric Series - Proofs Without Words
  137. Swapping Rows and Columns
  138. Toads And Frogs Puzzle (counting, logic, problem solving)
  139. Two Colors in Two Rows
  140. Two Colors in Two Rows II
  141. What's next?
  142. Word Problems

    Logic

  143. Lewis Carroll's Bilateral Diagrams
  144. Lewis Carroll's Trilateral Diagrams
  145. Lewis Carroll's Logic Game
  146. Venn Diagrams I
  147. Venn Diagrams II
  148. Formal Systems - an Example

    Fractals

  149. All Peano Curves
  150. Apollonian Gasket
  151. Color Cycling on the Mandelbrot Set
  152. Cantor sets
  153. Dot Patterns, Pascal Triangle and Lucas Theorem
  154. Emergence of Chaos
  155. Following the Hilbert Curve
  156. Fractal Curves and Dimension
  157. Iterated Function Systems
  158. Iterations in the Mandelbrot Set
  159. Koch's Snowflake
  160. Mandelbrot Set and Indexing of Julia Sets
  161. Plane Filling Curves: Hilbert's and Moore's
  162. Plane Filling Curves: One of Sierpinski's Curves
  163. Plane Filling Curves: the Lebesgue Curve
  164. Plane Filling Curves: Peano's and Wunderlich's
  165. Sierpinski Gasket By Common Trema Removal
  166. Sierpinski Gasket Via Chaos Game
  167. Sierpinski Gasket by Trema Removal
  168. The Chaos Game: Address Space vs IFS
  169. Variations on the Theme of Tremas
  170. Variations on the Theme of Tremas II

    Probability

  171. Bertrand's Paradox
  172. Binomial Distribution
  173. Birds On a Wire
  174. Buffon's Noodle
  175. Chess Players Truel
  176. Conditional Probability and Independent Events
  177. Eight Selections in Six Sectors
  178. Family Statistics
  179. Lewis Carroll's pillow problem
  180. Monty Hall Dilemma's Simulation
  181. Parrondo Paradox
  182. Random Clock Hands
  183. Stick Broken Into Three Pieces (Cartesian Coordinates)
  184. Stick Broken Into Three Pieces (Trilinear Coordinates)
  185. Who Needs Monty?

    Visual Illusions

  186. Assimilation Illusion
  187. Balls and Shadows Illusion
  188. Brick Wall Illusion
  189. Bulging Lines illusion
  190. Circular Poggendorff Illusion
  191. Continuous Line Illusion
  192. Cube Counting Ambiguity
  193. Day's Sine Illusion
  194. Delboeuf Illusion
  195. Distorted Lines Illusion
  196. Divergent Spirals Illusion
  197. Gerbino's Illusion
  198. Heaver: A Visual Illusion
  199. Height/Width Interplay Illusion
  200. Hering Illusion
  201. Hermann Grid Illusion
  202. Importance of Occluders: Motion Binding
  203. Judd Illusion
  204. Kanizsa Triangle
  205. Müller-Lyer Illusion
  206. Necker Cube
  207. Occluded Wheel Illusion
  208. Orbison Illusion
  209. Parallelogram Illusion
  210. Perspective Illusion
  211. Poggendorff Illusion
  212. Poggendorff Illusion II
  213. Ponzo Illusion
  214. Ponzo Illusion II
  215. Reverse Spoke Illusion
  216. Revolving Circles Illusion
  217. Rotating Top Illusion
  218. Scintillating Grid Illusion
  219. Shepard's Parallelogram Illusion
  220. Shifting Cube Illusion
  221. Shimmer Illusion
  222. Simultaneous Contrast Illusion
  223. Simultaneous Contrast Illusion II
  224. Simultaneous Contrast: Koffka's Illusion
  225. Simultaneous Contrast: White's Illusion
  226. Simultaneous Contrast: White's Illusion, V-Variant
  227. Staircase Illusion
  228. Twisted Cord Illusion
  229. Unfolding Spirals Illusion
  230. Wundt Illusion
  231. Wundt Block Illusion
  232. Zöllner's Illusion

    Calculus

  233. Addition and Subtraction of Functions
  234. Area of a Circle by Leonardo da Vinci
  235. Area of a Circle by Rabbi Abraham bar Hiyya Hanasi
  236. Cartesian Coordinate System
  237. Cavalieri's Principle
  238. Derivative of Sine and Cosine
  239. Distance From a Point to a Straight Line
  240. Equations of a Straight Line
  241. Estimating Circumference of a Circle
  242. Function, Derivative and Integral
  243. Graph of a Polynomial
  244. Graph of a Polynomial Defined by Its Roots
  245. Horner's Method
  246. Inflection Points of Fourth Degree Polynomials
  247. Lagrange Interpolation
  248. Maximum Volume of a Cut Off Box
  249. Mistrust Intuition of the Infinite
  250. Naturally Discontinuous Functions
  251. Newton's Method
  252. Riemann Sums - Function Integration
  253. Rolle's and Mean Value Theorems
  254. Schwarz Lantern
  255. Taylor Series Approximation to Cosine
  256. Two Circles and a Limit

    Math Magic

  257. An Arithmetic Magic Trick
  258. Arithmetic magic matrix
  259. Bachet's Magic Trick
  260. Barcode Magic
  261. Calendar Magic
  262. Gergonne's Magic Trick
  263. Hummer's Mind Reader
  264. Magic in Square
  265. Math Telepathy
  266. Number Guessing Game
  267. Two Numbers Guessing Game

    Combinatorics

  268. 3-Colors Tower of Hanoi
  269. Affirmative Action Problem
  270. Balanced Incomplete Block Design on a Triangular Grid
  271. Ballot Lemma
  272. Bicolor Tower of Hanoi
  273. Blithe 12
  274. Cheapest Link & Kruskal's Algorithms - skill practice
  275. Chvatal's Art Gallery Theorem
  276. Coin change
  277. Coloring a Graph
  278. Construction of Pascal's Triangle
  279. Critical Path in a Weighted Digraph
  280. Scheduling and Critical Path Algorithm
  281. de Bruijn Cycle
  282. Dominoes on a Chessboard
  283. Euler & Hamilton Paths - skill practice
  284. Filling a Grid with Good Neighbors
  285. Five Lattice Points
  286. Fleury's Algorithm and Euler's Paths and Cycles
  287. Flipping Items Simultaneously II
  288. Flipping Items Simultaneously III
  289. Flipping pancakes
  290. Futurama Theorem and Puzzle
  291. Gray Codes
  292. Group multiplication of permutations
  293. Finding Hamilton Paths and Circuits
  294. Hanoing
  295. Happy 8
  296. Hex Can't End in a Draw
  297. How to define a permutation
  298. Infinite Latin Square
  299. Jumping Isn't Everything
  300. Latin Squares
  301. Leibniz and Pascal Triangles
  302. Life-like Automaton With Definable Rules
  303. Light Bulbs in a Circle
  304. Listing All Combinations
  305. Listing All Permutations
  306. Listing All Permutations: Johnson-Trotter Method
  307. Lucky 7
  308. Make Your Move, Kid!
  309. Marriage Problem, simulation
  310. Mazes
  311. Minumum Spanning Trees and Kruskal's Algorithm
  312. Monotone Number Sequences
  313. No Flipping without End
  314. Number sequences and Pigeonhole
  315. Party Acquaintances
  316. Permutations as a Product of Transpositions
  317. Product of Permutations
  318. Project Scheduling
  319. Property of the Powers of 2
  320. Random Walks
  321. Recombining Permutations
  322. Reflection Lemma
  323. Sam Loyd's Fifteen
  324. Scrub Tile Puzzle
  325. Shuttle Puzzle
  326. Simple Graphs
  327. Simple Graph Practice
  328. Sliders (slider games on torus, Moebius strip, projective plane, permutations, cycles)
  329. Straight Tromino on a Chessboard
  330. The Game of Life
  331. Tiling Rectangles with L-Trominoes
  332. Tool for Constructing Orthogonal Latin Squares
  333. Tower of Hanoi
  334. Tower of Hanoi, the Hard Way
  335. Traveling Salesman Problem
  336. Two Men of Tibet
  337. Universal Coloring
  338. Y Can't End in a Draw

    Combinatorial Games

  339. Date Game
  340. Dawson's Chess
  341. Dawson's Kayles
  342. Fraction Game
  343. Grundy's Game
  344. Hex 7
  345. Kayles
  346. Nim
  347. Nimble
  348. Northcott's game
  349. Odd Scoring
  350. One Pile
  351. Plainim
  352. Plainim Misère
  353. Scoring
  354. Scoring Misère
  355. Scoring Misère: Two Heaps Perfect Strategy
  356. Silver Dollar Game
  357. Silver Dollar Game With No Silver Dollar
  358. Sticks, Jess realization of Scoring Misère
  359. Sticky Problem
  360. Sticky Problem II
  361. Subtraction Game
  362. TacTix
  363. Take-Away Games
  364. Turning Turtles
  365. Wythoff's Nim
  366. Wythoff's Nim II

    Puzzles & Games

  367. 3-Chain
  368. 4×4×4 Tic Tac Toe (spacial visualization)
  369. A Game of Candy Squares
  370. Achieve the Equilibrium
  371. Bulls and Cows
  372. Caterpillar
  373. Changing Colors (combinatorics, invariance)
  374. Changing Colors II (invariance)
  375. Color Balls
  376. Computer Mastermind (logic and problem solving)
  377. Covering a Chessboard with a Hole with L-Trominoes
  378. Eight Digits Puzzle
  379. Escape of the Clones
  380. Farmer and Wife To Catch Rooster and Hen (invariance, city block distance)
  381. Fif (multiple representations)
  382. Fill a Hexagonal Grid (space visualization)
  383. Fish Soup Game (multiple representations)
  384. Four Knights (multiple representations)
  385. Full House
  386. Getting a Scout out of Desert
  387. Goat, Cabbage and Wolf to move across a river (multiple representations)
  388. Hare and Hounds
  389. Jam (multiple representations)
  390. Looping Chips (multiple representations)
  391. Mastermind (logic and problem solving)
  392. Mastermind Variants (logic and problem solving)
  393. Mirror Maze
  394. Peg Solitaire (logic, problem solving, subproblems)
  395. Pick A Label (logic, problem solving)
  396. Reverse Solitaire (logic, problem solving, subproblems)
  397. Sending scouts into the desert (algebra, geometric series, problem solving)
  398. Seven Coins Puzzle (multiple representations)
  399. Shuttle Puzzle Practice I
  400. Shuttle Puzzle Practice II
  401. Skyscrapers Puzzle
  402. Solitaire on a Circle (iterations, invariance)
  403. Stones in Cups
  404. Super Nim
  405. Thugs and Bowmen
  406. Tiling a Triangulated Hexagon (a proof without words)
  407. Toads And Frogs in 2 dimensions (repeated application of same idea)
  408. Tromino Puzzle: Golomb's Theorem
  409. Tromino Puzzle: Deficient Squares
  410. Vector Addition and Subtraction
  411. Vowel Movement
  412. Wolf and Rabbit

    Geometric Fallacies

  413. A Circle With Two Centers
  414. All Triangles Are Isosceles
  415. Curry's Paradox
  416. Delian Problem Solved
  417. A Faulty Dissection
  418. Hooper's Paradox
  419. Is Every Trapezoid Parallelogram?
  420. John Sharp's Paradox
  421. Langman's Paradox
  422. Popping A Square
  423. Rouse Ball's Fallacy
  424. Sam Loyd's Son's Dissection
  425. Two Perpendiculars From a Point to a Line

    Social Science

  426. Adams' Apportionment Method
  427. Banzhaf Power Index Calculator
  428. Fair Division: Method of Lone Divider
  429. Fair Division: Method of Markers
  430. Fair Division: Method of Sealed Bids
  431. Fair Division: Method of Sealed Bids II
  432. Fast Power Indices
  433. Five Methods of Apportionment
  434. Four Voting Methods
  435. Hamilton's Apportionment Method
  436. Huntington-Hill Apportionment Method
  437. Jefferson's Apportionment Method
  438. Method of Markers II
  439. Shapley-Shubik Power Index Calculator
  440. Social Choice
  441. Webster's Apportionment Method
  442. Weighted Voting and Power Indices

    Elementary Geometry

  443. A Characterization of the Euler Line
  444. A Hinged Realization of a Plane Tessellation
  445. A Lemma of Equal Areas
  446. A Multiplicative Identity of Areas in a Triangle
  447. A Property of Equiangular Polygons
  448. A Three Pegs Question
  449. Acute Angle Bisectors in a Right Triangle
  450. Al-Nayrizi's Construction
  451. An Extra Illustration of J. E. Bottcher's Proof of the Pythagorean Theorem
  452. Angle: An Illustrated Classification
  453. Angle Bisector
  454. Angle Bisectors in a Quadrilateral - Cyclic and Otherwise
  455. Angle Bisectors in Ellipse
  456. Angle Bisectors in Ellipse II
  457. Angle Bisectors On Circumcircle
  458. Angle Subtended by a Diameter
  459. Angles Inscribed in an Absent Circle
  460. Antiparallel
  461. Antiparallel via Three Reflections
  462. Archimedes' Law of the Lever
  463. Area of Median Triangle
  464. Area of Parallelogram
  465. Area of the Union of Two Squares
  466. Area of Triangle
  467. Equal Areas in Regular 2n-gons
  468. Areas in Square by Dissection
  469. Arithmetic in Disguise
  470. Between Major and Minor Circles
  471. Building a Bridge
  472. Building Bridges
  473. Carpet With a Hole
  474. Circle and Hyperbola as Lighthouse Curves II
  475. Circle Chains on Napoleon Triangles
  476. Circles and Semicircles in Rectangle
  477. Circle in a Square Inscribed in a Circle
  478. Circles with Equal Collinear Chords
  479. Circumcenter on Angle Bisector
  480. Classification of Quadrilaterals
  481. Common Chord and a Tangent
  482. Concyclicity in Rectangle
  483. Conic Sections as Loci of Points
  484. Construction of the Angle Bisector
  485. Construction of the Perpendicular Bisector
  486. Cross Points in a Polygon
  487. Dancing Rectangles Model Auxetic Behavior
  488. Dancing Squares or a Hinged Plane Tessellation
  489. A Decomposition of Isosceles Triangles into 4 Isosecles Triangles
  490. Diagonal Count
  491. Dissection of a Vase
  492. Dissection of Cyclic Quadrilateral
  493. Divide a Circle into N Parts of Equal Area
  494. E. W. Dijkstra's Proof of the Pythagorean Theorem
  495. Eight Equal Tangents
  496. Equal Areas in Equilateral Triangle
  497. Equal Chords in Crossing Circles
  498. Equal Circles, Medial Triangle and Orthocenter
  499. Equidecomposition of a Rectangle and a Square
  500. Equidecomposition of Two Rectangles
  501. Equidecomposition of a Triangle and a Rectangle
  502. Equidecomposition of a Triangle and a Rectangle II
  503. Equidecomposition of Two Parallelograms
  504. Equilateral Triangle on Parallel Lines
  505. Equilic Quadrilateral I
  506. Equilic Quadrilateral I, A Variation
  507. Equilic Quadrilateral II
  508. Euclid's Segment Division
  509. Existence of the Circumcenter
  510. Existence of the Euler Line: An Elementary Proof
  511. Fibonacci Bamboozlement
  512. Famous Theorem
  513. Finding Circle Center By Ruler Alone
  514. Fixed Point in Isosceles and Equilateral Triangles
  515. Focal Definition of Ellipse
  516. Focus and Directrix of Ellipse
  517. Four Hinged Squares
  518. Geoboard
  519. Half Turn, Reflection in Point
  520. Harmonic Mean Sangaku
  521. Hinged Greek Cross Tessellation
  522. Hippocrates' Squaring of a Lune
  523. Hunting Right Angles
  524. Huygens' proof of the Pythagorean Theorem
  525. Inscribed and Central Angles in a Circle
  526. Inscribed Angles
  527. Inscriptible Quadrilateral: An Illustration
  528. Intersections of a Circle with the Four Quadrants
  529. Invariance in Orthodiagonal Quadrilaterals
  530. Join Circles by Given Segment
  531. Lean Napoleon's Triangles
  532. Maimed Cake
  533. Mathematics in Pizzeria
  534. Napoleon's Theorem: A third proof with complex numbers
  535. Napoleon's Theorem via Two Rotations
  536. Napoleon on Hinges
  537. Nine Point Circle: an Elementary Proof
  538. Octagon in Parallelogram
  539. Octagon in Parallelogram: Overlapping Regions
  540. Olof Hanner's Jigsaw Puzzle
  541. Orthocenters of Two Triangles Sharing Circumcenter and Base
  542. Pappus' Generalization of Euclid I.47
  543. Orthodiagonal and Cyclic Quadrilaterals
  544. Parallel Chords II
  545. Parallel Chords in Crossing Circles
  546. Parallel Lines in a Quadrilateral
  547. Pascal: Necessary and Sufficient
  548. Polygon Metamorphosis
  549. Pompeiu's Theorem
  550. Property of Angle Bisectors
  551. Property of Rhombi
  552. Property of Semicircles
  553. Pythagorean Theorem By Dissection
  554. Pythagorean Theorem By Dissection II
  555. Pythagorean Theorem by Hinged Dissection
  556. Pythagorean Theorem by Hinged Dissection I
  557. Pythagorean Theorem by Hinged Dissection II
  558. Pythagorean Theorem: J. Adams' Proof by Dissection
  559. Pythagorean Theorem: Versluys' Proof by Dissection
  560. Pythagoras' Theorem By Sheer Shearing
  561. Pythagoras' Theorem By Similarity
  562. Pythagoras' Theorem Solely By Sliding
  563. Pythagorean Theorem via an Isosceles Triangle
  564. Pythagorean Segment Division
  565. Quadrilateral With Equal Opposite Sides And Angles
  566. Rhombus in a Cyclic Quadrilateral
  567. Right Triangles on Sides of a Square
  568. Sangaku with Angle between a Tangent and a Chord
  569. Secant Angles
  570. Secant Angles II
  571. Secant, Normal, Tangent
  572. Segment Trisection Induced by Parallels to Medians
  573. Semi-regular Tessellation on Hinges A
  574. Semi-regular Tessellation on Hinges B
  575. Semi-regular Tessellation on Hinges C
  576. Shearing a Polygon into a Triangle of Equal Area
  577. Simple Quadrilaterals Tessellate the Plane
  578. Shearing and Translation in Pythagorean Pants
  579. Square From Nowhere
  580. Square in a Circle Inscribed in a Square
  581. Square in Chair
  582. Squaring a Rectangle
  583. Three Touching Circles
  584. Translated Triangles
  585. Translation Transform
  586. Triangle Areas in a Parallelogram
  587. Triangle Areas in a Parallelogram II
  588. Triangle Classification
  589. Trigonometric Functions
  590. Two Altitudes, One Midpoint
  591. Two Color Coloring of the Plane
  592. Two Equilateral Triangles
  593. Two Intersecting Circles
  594. Two Parallels in a Triangle and One More
  595. Two Symmetric Triangles Are Directly Equidecomposable
  596. Two Symmetric Triangles Are Directly Equidecomposable II
  597. Two Symmetric Triangles Are Directly Equidecomposable III
  598. Two Symmetric Triangles Are Directly Equidecomposable IV
  599. Two Touching Circles
  600. Van Schooten's and Pompeiu's Theorems
  601. Viviani's Theorem
  602. Viviani's Theorem II
  603. Viviani in Isosceles Triangle

    Miscellaneous Demonstrations

  604. Calculation of the Digits of pi by the Spigot Algorithm
  605. Calculation of the Digits of pi (Faster Version)
  606. Convex Polygon Is the Intersection of Half Planes
  607. Disapperances à la Sam Loyd
  608. Disappearing Lines
  609. Disappearing Rectangles
  610. Distance Between Strings
  611. Experimentation with Dynamic Geometry Software: An Example
  612. Genetic Algorithm Solves the Toads and Frogs Puzzle
  613. Impossible Fork
  614. Impossible Frame
  615. Morphing
  616. Order and Chaos in Multiple Pendulums
  617. Projectile Trajectory
  618. Random Dot Stereograms
  619. Ratchet Effect
  620. Rotating Gears
  621. Sorting Algorithms
  622. Structural Constellation
  623. Watt's and Chebyshev's Linkage

    Outline (Fill-It-In) Mathematics

  624. A bunch of fill-it-in outline problems and solutions

 

    Geometry

  1. 120° Breeds 90°
  2. 2N-Wing Butterfly Theorem
  3. 3 Isosceles Trapezoids
  4. 5-Star and A Circle
  5. 6 to 9 Point Circle
  6. 60° Breeds 90°
  7. 9-point Circle as a Locus of Concurrency
  8. A Chain of Touching Circles in a Polygon (à la Quang Tuan)
  9. A Chain of Touching Circles in a Polygon (à la Evelyn)
  10. A Circle Related to Incenter and Circumcenter
  11. A Circle Rolling in an Equilateral Triangle
  12. A Line in Triangle Through the Circumcenter
  13. A Parallelogram in Triangle
  14. A Sangaku Follow-Up on an Archimedes' Lemma
  15. A Sangaku: Two Unrelated Circles
  16. A Sangaku with an Egyptian Attachment
  17. A Sangaku with Many Circles and Some
  18. A Stronger Triangle Inequality
  19. A Triangle of Antreas Hatzipolakis
  20. Adams' Circle
  21. Addition of Radius-Vectors
  22. Altitudes and the Power of a Point
  23. An Isoperimetric Theorem
  24. Angle Bisector in Equilateral Trapezoid
  25. Angle Bisector in Parallelogram
  26. Angle Bisector in Touching Circles
  27. Angle Bisectors and Perpendiculars in a Quadrilateral
  28. Angle Bisectors in a Quadrilateral
  29. Angle Preservation Property
  30. Angle Trisection by Archimedes
  31. Angle Trisection by Hippocrates
  32. Angle Trisection by Paul Vjecsner
  33. Angle Trisectors on Circumcircle
  34. Angles in Triangle Add to 180°
  35. Another Pair of Twins in an Arbelos
  36. Anticomplementary Triangle Surprise
  37. Apollonian Circles Theorem
  38. Apollonius Problem
  39. Application of Ceva's Theorem
  40. Archimedes' Quadruplets
  41. Archimedes Triangle and Squaring of Parabola
  42. Archimedes' Twin Circles and a Brother
  43. Area of an Arbelos
  44. Areas and Centroid in a Triangle
  45. Areas in Triangle
  46. Areas in Triangle II
  47. Arithmetic Mean Sangaku
  48. Arithmetic Mean Sangaku II
  49. Around the Incircle
  50. Around the Incircle in a Polygon
  51. Asian Pacific Kite
  52. Asymmetric Propeller I
  53. Asymmetric Propeller II
  54. Asymmetric Propeller III
  55. Asymmetric Propeller by Plane Tiling
  56. Barycentric Coordinates: a Tool
  57. Bevan's Point and Theorem
  58. Bisectal Circle
  59. Book of Lemmas: Proposition 1
  60. Book of Lemmas: Proposition 2
  61. Book of Lemmas: Proposition 3
  62. Book of Lemmas: Proposition 5
  63. Book of Lemmas: Proposition 6
  64. Book of Lemmas: Proposition 9
  65. Book of Lemmas: Proposition 10
  66. Book of Lemmas: Proposition 12
  67. Book of Lemmas: Proposition 13
  68. Böttcher's Proof of the Pythagorean Theorem
  69. Böttcher's Proof Variant
  70. Bottema Shatters Japan's Seclusion
  71. Bottema's Theorem
  72. Bottles in a Slanted Rack
  73. Bottles in a Wine Rack
  74. Bottles in a Wine Rack: Proofs and Generalizations
  75. Brahmagupta's Theorem
  76. Brianchon in Ellipse
  77. Brianchon's Theorem
  78. Bride's Chair
  79. Broken Chord Theorem
  80. Broken Chord Theorem by Paper Folding
  81. Broken Chord Theorem: G. Patruno's proof
  82. Broken Chord Theorem: S. Anderson's proof
  83. Butterfly in Ellipse
  84. Butterfly Problem
  85. Cabart's Collinearity
  86. Cantor's Theorem
  87. Cardioid As Envelope of Circles
  88. Cardioid As Epicycloid
  89. Carnot's Theorem
  90. Carpets in a Parallelogram
  91. Carpets in a Quadrilateral
  92. Carpets in a Quadrilateral II
  93. Carpets Theorem
  94. Carpets Theorem With Parallelograms
  95. Casey's Theorem
  96. Center Circles and Their Chains
  97. Centroids in a Polygon
  98. Ceva and Menelaus Theorems for Angle Bisectors
  99. Ceva's Theorem
  100. Ceva's Theorem (PWW)
  101. Cevian Cradle
  102. Cevian Nest
  103. Cevian Triangle
  104. Chain of Circles on a Chord
  105. Chain of Inscribed Circles
  106. Chasing Angles in Pascal's Hexagon
  107. Chasles' Theorem, a Proof
  108. Cherchez le quadrilatère cyclique
  109. Cherchez le quadrilatère cyclique II
  110. Chords, Concurrency and Orthic Triangle
  111. Chords in Cardioid
  112. Circle and Hyperbola as Lighthouse Curves
  113. Circle Centers on Radical Axes
  114. Circle Chains and Inscribed Angles
  115. Circle Concurrency and Spiral Similarity
  116. Circle Crosses Triangle
  117. Circle Division by Euclid and Leonardo
  118. Circle Inscribed in a Circular Segment
  119. Circle of Similitude
  120. Circle through the Circumcenter
  121. Circle through the Incenter
  122. Circle through the Incenter And Antiparallels
  123. Circle-Stacking Theorem
  124. Circle, Isosceles Triangle and Fixed Point
  125. Circles And Parallels
  126. Circles and Reflections in a Triangle
  127. Circles Cover a Quadrilateral
  128. Circles in a Regular Polygon
  129. Circles in Morley's Triangles
  130. Circles Lined on the Legs of a Right Triangle
  131. Circles On Cevians
  132. Circles Tangent to Circumcircle
  133. Circles through the Orthocenter
  134. Circles with Tangent Diameters
  135. Circumcevian Triangle
  136. Cleavance Center
  137. Cleaver
  138. Clifford Chain
  139. Clifford's Lemma
  140. Coaxal Circles on Perpendicular Bisector
  141. Coaxal Circles Theorem
  142. Colburn's Proof of the Pythagorean Theorem
  143. Collinearity via Concyclicity
  144. Collinearity with the Orthocenter
  145. Common Tangents to Two Circles I
  146. Common Tangents to Two Circles II
  147. Complete Quadrilateral
  148. Concyclic Points in Equilateral Bumps
  149. Concurrency in Analytic Geometry
  150. Concurrency in Arbelos
  151. Concurrency in the Intouch Triangle
  152. Concyclic Circumcenters: A Dynamic View
  153. Concyclic Points in a Triangle
  154. Concyclic Points in Bride's Chair
  155. Conjugate Diameters in Ellipse
  156. Construction of Conics from Pascal's Theorem
  157. Consecutive Isosceles Decomposition
  158. Conway's Circle
  159. Copernicus' Theorem
  160. Crossed-Lines Construction of Shapes of Constant Width
  161. Cyclic Hexagon
  162. Cyclic Incenters
  163. Cyclic Quadrilateral, Concurrent Circles and Collinear Points
  164. Cycloids
  165. David Richeson's Extention of an Old Japanses Theorem
  166. Diameters and Chords
  167. Directly Similar Figures
  168. Desargues' Theorem
  169. Discovery of Duane DeTemple
  170. Dissection of Triangle into Rhombus
  171. Dissection of Triangle into Rhombus by Hubert Shutrick
  172. Dividing a Segment into N parts: Besteman's Construction
  173. Dividing a Segment into N parts: Besteman's Construction II
  174. Dividing a Segment into N parts: GLaD Construction
  175. Dividing a Segment into N parts: SaRD Construction
  176. Dividing Evenly a Quadrilateral
  177. Dividing Evenly a Quadrilateral II
  178. Double Generation Theorem
  179. Douglas' Theorem (complex variables, linear algebra)
  180. Droz-Farny Circles
  181. Droz-Farny Line Theorem
  182. Dual to Pappus' Theorem
  183. Dynamic Construction of Ellipse and Other Curves
  184. Easy Construction of Bicentric Quadrilateral
  185. Easy Construction of Bicentric Quadrilateral II
  186. Eight Point Circle
  187. Ellipse, how to draw
  188. Ellipse in Arbelos
  189. Ellipse Between Two Circles
  190. Equal Angles in Two Circles
  191. Equal Angles in Two Circles II
  192. Equal Areas In Parallelogram à la Pythagoras
  193. Equal Incircles Theorem
  194. Equichordal Curves
  195. Equilateral and 3-4-5 Triangles
  196. Equilateral Triangle, Straight Line and Tangent Circles
  197. Equilateral Triangles on Diagonals of Antiequilic Quadrilateral
  198. Equilateral Triangles on Segments of Equilic Quadrilateral
  199. Equilateral Triangles On Sides of a Parallelogram
  200. Equilateral Triangles On Sides of a Parallelogram II
  201. Equilateral Triangles on Sides of a Quadrilateral
  202. Escher's Theorem
  203. Euler Line Cuts Off Equilateral Triangle
  204. Euclid I.43
  205. Euclid I.43 Extended
  206. Euclidean Construction of Center of Ellipse
  207. Euclidean Construction of Tangent to Ellipse
  208. Extouch Triangle in Poncelet Porism
  209. Eyeball Theorem
  210. External Angle Bisector
  211. Fagnano's problem
  212. Fagnano's problem II
  213. Fagnano's Problem, Third Solution
  214. Fagnano's Problem, Fourth Solution
  215. Fagnano's Problem in Reverse
  216. Fermat point and 9-point Centers
  217. Fermat's Point
  218. Fermat Points and Concurrent Euler Lines I
  219. Fermat Points and Concurrent Euler Lines II
  220. Feuerbach's theorem
  221. Feuerbach's Theorem: A Proof
  222. Find a Common Chord of Given Length
  223. First Vecten Point
  224. Five Cardioids
  225. Five Concyclic Points
  226. Five Incircles in a Square
  227. Five Incircles Theorem
  228. Fixed Point of Circles Orthogonal to the Given One
  229. Fixed point on a rod rotating around a triangle
  230. Focal Properties of Parabola
  231. Foot of Altitude and Minimum Distance
  232. Four 9-Point Circles in a Quadrilateral
  233. Four Centroids and Parallels
  234. Four Circles In a Triangle
  235. Four Concurrent Lines in a Cyclic Quadrilateral
  236. Four Incident Circles
  237. Four Crossing Circles
  238. Four Incircles in Equilateral Triangle
  239. Four Pedal Circles
  240. Four Touching Circles
  241. Four Touching Circles II
  242. Four Touching Circles III
  243. Four Triangles, One Circle
  244. Four Turtles (or Bugs, or Dogs, etc.)
  245. Friendly Kiepert's Perspectors
  246. From Foci to a Tangent in Ellipse
  247. Fundamental Theorem of 3-Bar Motion
  248. Fuss' Theorem
  249. Generalizing a Romanian Olympiad Problem
  250. Geometric Optimization from the Asian Pacific Mathematical Olympiad
  251. Gergonne and Medial Triangles Are Orthologic
  252. Gergonne and Soddy Lines Are Perpendicular
  253. Gergonne in Ellipse
  254. Glide Reflection
  255. Golden Ratio in an Irregular Pentagon, Construction I
  256. Golden Ratio in an Irregular Pentagon, Construction II
  257. Golomb's inductive proof of a tromino theorem
  258. Gothic Arc
  259. Grebe: from Ladies' Diary to Carroll's Pillow
  260. Grebe's Theorem
  261. Greg Markowsky's Problem for Parabola
  262. Griffiths Points in Cyclic Quadrilateral
  263. Harmonic Ratio
  264. Hart Circle
  265. Hart's Inversor
  266. Haruki's Lemma
  267. Heron's Formula: a Proof
  268. Heron's Problem
  269. Hexagon Parallel to Medial Triangle
  270. Hexagon Parallel to Orthic Triangle
  271. Hinged Squares
  272. Hjelmslev Theorem
  273. Hofstadter Triangles and Points
  274. Homologous Lines under Three Spiral Similarities
  275. Homothety
  276. Homothety between In- and Excircles
  277. Hypocycloid Families
  278. Ian McGee's Observation
  279. Illustration of Pascal's Theorem
  280. Incenters in Cyclic Quadrilateral
  281. Incidence in Feuerbach's Theorem
  282. Incident Center Circles and Cardioid
  283. Incircles, Circumcircles and Inscribed Angles
  284. Inscriptible and Exscriptible Quadrilaterals
  285. Internal Tangents to Three Circles
  286. Intouch Triangle in Poncelet Porism
  287. Invariant Area Sweep Implies Pythagorean Theorem
  288. Inversion: Reflection in a Circle
  289. Inversion in the Incircle
  290. Inversion Tool
  291. Inversion with Negative Power
  292. Isogonal and Isotomic Conjugalities
  293. Isogonal Concurrency
  294. Isogonal image of the circumcircle
  295. Isosceles on the Sides of a Triangle
  296. Isotomy and Isogonality Hand-in-Hand
  297. Iterations in Geometry, an example
  298. Iterations in Geometry, Generalization
  299. Iterations on a Circle Through Three Points
  300. Iterations on Euler Lines
  301. Johnson Circles
  302. Joseph Keech in Bride's Chair
  303. Kiepert's Theorem
  304. Kürschak's Tile and Theorem
  305. Law of Cosines
  306. Law of Cosines: PWW
  307. Law of Cosines: An Unfolded Variant
  308. La Hire's Theorem
  309. La Hire's Theorem, a Variant
  310. La Hire's Theorem in Ellipse
  311. Lighthouse Curves
  312. Line, Circle, and Fixed Points
  313. Locus of Points in a Given Ratio to Two Points
  314. MacLaurin's Construction of Conics
  315. Malfatti's Problem
  316. Malfatti's Problem, Hart's Solution
  317. Maximum Perimeter Property of the Incircle
  318. Maxwell's Theorem
  319. Median in Touching Circles
  320. Medians in a Quadrilateral
  321. Menelaus and Ceva Theorems
  322. Menelaus From Ceva
  323. Midline in Similar Triangles
  324. Midpoints and Orthogonality in Isosceles Triangles
  325. Midpoints from Gergonne Triangle
  326. Midpoints of the Lines Joining In- and Excenters
  327. Minkowski's addition of convex shapes
  328. Miquel's Point
  329. Miquel's Point of a 4-line Via Spiral Similarity
  330. Miquel's Theorem for Circles
  331. Mirror on the Wall
  332. Mirror property of the altitudes
  333. Mirror Property of Altitudes via Pascal's Hexagram
  334. Mixtilinear Circles and Concurrence
  335. Monge via Desargues
  336. Monge via Desargues II
  337. More Bottles in a Wine Rack
  338. Morley Constellation
  339. Morley's Theorem
  340. Morley's Theorem, Cardioids and Such
  341. Morley's Theorem, G. Zsolt Kiss' proof
  342. Nagel Line
  343. Nagel point
  344. Nagel Point of Medial Triangle
  345. Nagel's Theorem
  346. Napoleon-Barlotti Theorem
  347. Napoleon Theorem by Plane Tessellation
  348. Napoleon's Relatives
  349. Napoleon's Theorem by Transformation
  350. Neuberg Sangaku
  351. Newly Born Pair of Siblings to Archimedes' Twins
  352. Newton's Construction of Conics
  353. Newton's Theorem
  354. Nine Point Circle
  355. No Equilateral Triangles, Please
  356. Nobbs' Points, Gergonne Line
  357. Non-classic Way To Draw Cardioid
  358. No-Pedal Collinearity
  359. On Bottema's Shoulders
  360. On Bottema's Shoulders II
  361. One Sided Surface in 4D
  362. Optical Property of Ellipse
  363. Optimization Problem in Acute Angle
  364. Orthocenter and Three Equal Circles
  365. Orthocentric System From Rectangle
  366. Orthogonality in Isosceles Triangles
  367. Orthologic Triangles in a Quadrilateral
  368. Orthopole
  369. Pairs of Homologous Lines under Spiral Similarities
  370. Pairs of Incircles in a Quadrilateral
  371. Pantograph
  372. Pappus' Theorem
  373. Parabola As Envelope of Straight Lines
  374. Parabola As Envelope II
  375. Parabolic Mirror, Illustration
  376. Parabolic Mirror, Theory
  377. Paragon
  378. Parahexagon
  379. Parallel Chords
  380. Parallel Chords in Ellipse
  381. Parallel Lines and Similar Triangles
  382. Parallel Lines in a Cyclic Quadrilateral
  383. Parallelogram and Similar Triangles
  384. Parallelogram Iterations
  385. Parallelogram Law
  386. Parallelogram Law: A PWW
  387. Parallelogram Law: A Tessellation
  388. Pascal in a Cyclic Quadrilateral
  389. Pascal Lines: Steiner and Kirkman Theorems
  390. Pascal Lines: Steiner and Kirkman Theorems II
  391. Pascal's Theorem
  392. Peaucellier Linkage
  393. Pedal Collinearities
  394. Pedal Polygons
  395. Pedal Triangle and Isogonal Conjugacy
  396. Pedoe's Theorem
  397. Pentagon in a Semicircle
  398. Perigal's Proof of the Pythagorean Proposition
  399. Perpendicular Bisectors in an Inscriptible Quadrilateral
  400. Perpendicular Bisectors in an Inscriptible Quadrilateral II
  401. Pinning Butterfly on Radical Axes
  402. Pivot Theorem
  403. Point common to two similar rectangles
  404. Polar Circle
  405. Pole and Polar with respect to a Triangle
  406. Poles and Polars
  407. Poles, Polars and Quadrilaterals
  408. Polygon from the midpoints of its sides
  409. Polygonal Ears and Triangulation Duals
  410. Polygons Formed by Perpendicular Bisectors
  411. Poncelet's Porism
  412. Poncelet's Porism in Ellipses
  413. Poncelet's Theorem
  414. Problem 4, 1975 USA Math Olympiad and the Radical Axis
  415. Problem 4, 1975 USA Math Olympiad and Isosceles Triangles
  416. Problem 4, 1975 USA Math Olympiad: Normals and Tangents
  417. Problem 4, 1975 USA Math Olympiad: Problem 4, 1975 USA Math Olympiad: The Final Touch
  418. Problem in an Equilateral Triangle
  419. Problem in an Equilateral Triangle II
  420. Problem In an Isosceles Right Triangle
  421. Problem in Three Squares
  422. Problem of Equal Steps
  423. Problem of Equal Steps II
  424. Problem of polygon construction
  425. Problem with Equilateral Triangles
  426. Product of Rotations
  427. Projections on Internal and External Angle Bisectors
  428. Projective Collinearity in a Quadrilateral
  429. Projective Generalization of Maxwell's Theorem
  430. Projective Proof of Pascal's Theorem
  431. Proof Without Words for the Pythagorean Theorem
  432. Properties of the Circle of Similitude
  433. Property of 6-Parpolygon
  434. Property of Angle Bisectors II
  435. Property of Circumscribed Quadrilaterals
  436. Property of Points Where In- and Excircles Touch a Triangle
  437. Property of the Line IO
  438. Property of the Line IO II
  439. Property of the Line IO: a proof from the Book

    Ptolemy on Hinges

  440. Pythagoras and Vecten Break Japan's Isolation
  441. Pythagoras' from Bottema's
  442. Pythagorean Condition in An Isosceles Right Triangle
  443. Pythagorean Theorem: Subtle Dangers of Visual Proof
  444. Pythagorean Theorem By Euclid
  445. Pythagorean Theorem By Plane Tessellation
  446. Pythagorean Theorem By Hexagonal Tessellation
  447. Pythagorean Theorem By Rearrangement
  448. Pythagorean Theorem By Shearing and Rotations I
  449. Pythagorean Theorem By Shearing and Rotations II
  450. Pythagorean Theorem in an Orthodiagonal Quadrilateral
  451. Quadrilaterals Formed by Perpendicular Bisectors
  452. Quadrilateral with 3 Equal Sides
  453. Quest for Paragon
  454. MathPro Logo
  455. Radical Axis and Center, an Application
  456. Radical Axis of Circles Inscribed in a Circular Segment
  457. Radical Center
  458. Radius and Construction of a Mixtilinear Circle
  459. Radius of a Circle by Paper Folding
  460. Rectangle in Arbelos
  461. Reflection In Line
  462. Reflections in Ellipse
  463. Reflections of a Line Through the Orthocenter
  464. Reflections of a Point on the Circumcircle
  465. Reflections of the Orthocenter
  466. Regular Polygons in a Triangular Grid
  467. Remarkable Line in a Quadrilateral
  468. Remarkable Line in Cyclic Quadrilateral
  469. Rendezvous
  470. Right Isosceles Triangles on Sides of a Quadrilateral
  471. Rotation Transform
  472. Rotations in Disguise
  473. Rusty Compass Construction of Equilateral Triangle
  474. Salinon: from Archimedes Book of Lemmas
  475. Sangaku Iterations, Is it Wasan?
  476. Sangakus with a Mixtilinear Circle
  477. Sangaku with Three Mixtilinear Circles
  478. Seven Circles Theorem
  479. Squares in Arbelos
  480. Secant, Tangents and Orthogonality
  481. See-Saw Lemma
  482. Segment Trisection
  483. Shape of Constant Width
  484. Shearing Butterflies in Quadrilaterals
  485. Siamese Triangles
  486. Siamese Triangles II
  487. Similar Triangles on Sides of a Quadrilateral
  488. Similar Triangles on Sides and Diagonals of a Quadrilateral
  489. Simson Line
  490. Simson Line From Isogonal Perspective
  491. Simson Line in Disguise
  492. Simson Lines Of Diametrically Opposite Points
  493. Simsons and 9-Point Circles in Cyclic Quadrilateral
  494. Simultaneous Diameters in Concurrent Circles
  495. sin(N)
  496. Six Circles Theorem (Bui Quang Tuan)
  497. Six Circles Theorem (Elkies)
  498. Six Circles Theorem (Evelyn)
  499. Six Concyclic Points
  500. Six Concyclic Points II
  501. Six Incircles in an Equilateral Triangle
  502. Six Point Circle
  503. SixPoints, ThreeLines
  504. Soddy Circles and David Eppstein's Centers
  505. Some Properties of Napoleon's Configuration
  506. Sperner's Lemma
  507. Spira Mirabilis - Wonderful Spiral
  508. Spiral Similarity
  509. Square in a Right Triangle
  510. Square Inscribed in a Triangle
  511. Square Inscribed in a Triangle II
  512. Square Inscribed In a Triangle III
  513. Square out of a Quadrilateral
  514. Square, Similarity and Slopes
  515. Squares in Circles
  516. Squares on Sides of a Quadrilateral
  517. Squinting Eyes Theorem
  518. Star Construction of Shapes of Constant Width
  519. Steiner's Chain
  520. Steiner's porism
  521. Straight Edge Construction of Polar
  522. Symmedian and Antiparallel
  523. Symmedian and 2 Antiparallels
  524. Symmedian and the Tangents
  525. Symmedian in a Right Triangle
  526. Tangency Point of Two Circles
  527. Tangent and Secant
  528. Tangent as a Radical Axis
  529. Tangent Circles and an Isosceles Triangle Tangent Circles and an Isosceles Triangle II
  530. Tangent Circles in a Parallelogram
  531. Tangent in Concurrency
  532. Tangent Lines and Circles in Convex Quadrilateral
  533. Tangents and Diagonals in Cyclic Quadrilateral
  534. Tangents, Perpendiculars and Geometric Mean
  535. Terquem's Theorem
  536. Tesseract
  537. The Plain Butterfly Theorem
  538. Thébault's Problem I
  539. Thébault's Problem II
  540. Thébault's Problem III
  541. Thébault's Problem IV
  542. Thébault's Problem III, Proof
  543. Theorem of Complete Quadrilateral
  544. Theorems of Ceva and Menelaus, an Illustrated Generalization
  545. Three Circles through the Incenter
  546. Three Concurrent Circles
  547. Three Congruent Circles by Reflection
  548. Three Congruent Circles by Reflection II
  549. Three Congruent Circles by Reflection III
  550. Three Incircles In a Right Triangle
  551. Three Incircles in a Triangle
  552. Three Isosceles Triangles
  553. Three Orthogonal Circles Through Three Given Points
  554. Three Parabola Tangents
  555. Three Parallels in a Triangle
  556. Three Points Casey's Theorem
  557. Three Points on a Parabola
  558. Three Roads, Three Travelers
  559. Three Similar Polygons
  560. Three Similar Triangles
  561. Three Similar Triangles (but differently oriented)
  562. Three Similar Triangles (but differently oriented) II
  563. Three Squares and Two Ellipses
  564. Three Tangent Circles
  565. Three Tangents Theorem
  566. Three Tangents Theorem II
  567. Three Tangents, Three Chords in Ellipse
  568. Three Tangents, Three Secants
  569. Toothpick Construction of a Square
  570. Touching Circles
  571. Touching Circles and Concurrency
  572. Touching Circles with Given Cnters II
  573. Triangle and Segment Count in a Polygon
  574. Triangle Geometry
  575. Triangle Sliding on Two Straight Lines
  576. Triangles, Squares and Areas from Temple Geometry
  577. Triangles with Equal Area
  578. Triangular Billiard
  579. Trigonometric Form of Ceva's Theorem (a tool for discovery of trigonometric identities and other problems)
  580. Tromino as a Rep-tile
  581. Tucker Circles
  582. Tucker Circles Through Homothety
  583. Twin Segments in Arbelos
  584. Two Butterflies Theorem
  585. Two Butterflies Theorem II
  586. Two Butterflies Theorem III
  587. Two Circles and One More
  588. Two Circles and Two More
  589. Two Circles in a Parallelogram
  590. Two Circles Inscribed in a Parallelogram
  591. Two Circles in a Square
  592. Two Circles in a Square II
  593. Two Circles in an Angle
  594. Two Circles on Angle Bisector
  595. Two Circles on a Side of a Triangle
  596. Two Circumcircles And Two Pairs of Parallels
  597. Two Circumcircles in Triangle
  598. Two Congruent Circles by Reflection
  599. Two Homotheties in a Parallelogram
  600. Two Lines - Two Circles
  601. Two Proofs of MenelausTheorem
  602. Two Quadrilaterals
  603. Two Quadruplets of Tangent Circles
  604. Two Rectangles in a Rectangle
  605. Two Simsons in a Triangle
  606. Two Squares and Another Square
  607. Two Triples of Similar Triangles
  608. Two Tangents to Parabola
  609. Two Triangles With Common Base and Altitude
  610. Two Triples of Concurrent Circles
  611. Van Schooten's Locus Problem
  612. Varignon Parallelogram
  613. Vecten's Collinearity
  614. Vecten's Mesh
  615. Vecten's Theorem
  616. Versatile Theorem
  617. Weitzenböck Inequality
  618. What does one see inside a spherical mirror?
  619. When a Triangle is Equilateral
  620. Wittenbauer's Parallelogram
  621. Y. Sawayama's Lemma
  622. Zaslavsky's theorem

    Stereometry

  623. Angles in a Cube I
  624. Angles in a Cube II
  625. Angles in a Cube III
  626. Bimedians in a Regular Tetrahedron
  627. Cut the Cone
  628. Cut the Cube
  629. Cut the Cylinder
  630. Knots on a Torus
  631. Möbius' Strip
  632. One Sheet Hyperboloid
  633. Platonic Solids - Regular Polyhedra
  634. Other Solids

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