| December 31, 2005 |
Pascal in a Cyclic Quadrilateral |
| December 30, 2005 |
Orthologic Triangles in a Quadrilateral |
| December 29, 2005 |
All Triangles Are Isosceles |
| December 28, 2005 |
Pedal Triangle and Isogonal Conjugacy |
| December 26, 2005 |
Complex Numbers: A Dynamic Tool |
| December 25, 2005 |
Carpets in a Parallelogram |
| December 24, 2005 |
Two Rectangles in a Rectangle |
| December 24, 2005 |
More Bottles in a Wine Rack |
| December 23, 2005 |
A Property of Rhombi |
| December 23, 2005 |
Circle-Stacking Theorem |
| December 22, 2005 |
Gergonne and Medial Triangles Are Orthologic |
| December 21, 2005 |
Cartesian Coordinate System |
| December 18, 2005 |
Common Tangents to Two Circles II |
| December 17, 2005 |
Bottles in a Wine Rack |
| December 16, 2005 |
Isosceles on the Sides of a Triangle |
| December 15, 2005 |
Self-descriptive Strings |
| December 14, 2005 |
3-Term Arithmetic Progression |
| December 12, 2005 |
Variations on the Theme of Tremas II |
| December 10, 2005 |
Listing All Permutations: Johnson-Trotter Method |
| December 9, 2005 |
Dominoes on a Chessboard |
| December 7, 2005 |
Party Acquaintances |
| December 5, 2005 |
Common Tangents to Two Circles I |
| November 27, 2005 |
Straight Tromino on a Chessboard |
| November 22, 2005 |
Eight Digits Puzzle |
| November 20, 2005 |
Square From Nowhere |
| November 18, 2005 |
Parallel Chords |
| November 17, 2005 |
Variations on the Theme of Tremas |
| November 15, 2005 |
Counting Triangles II |
| November 14, 2005 |
Carpet With a Hole |
| November 13, 2005 |
Carpets Theorem With Parallelograms |
| November 12, 2005 |
Six Incircles in an Equilateral Triangle |
| November 11, 2005 |
Equidecomposition of Two Rectangles |
| November 10, 2005 |
Perigal's Proof of the Pythagorean Proposition |
| November 4, 2005 |
Equidecomposition of Two Parallelograms |
| November 3, 2005 |
100 Prisoners and a Light Bulb by Stuart Anderson |
| November 3, 2005 |
The Carpets Theorem |
| November 2, 2005 |
Wallace-Bolyai-Gerwien Theorem |
| November 1, 2005 |
Equidecomposition of a Rectangle and a Square |
| October 31, 2005 |
Equidecomposition of a Triangle and a Rectangle |
| October 31, 2005 |
The Chaos Game: Address Space vs IFS |
| October 30, 2005 |
Sierpinski Gasket By Common Trema Removal |
| October 29, 2005 |
Inequality (1 + 1-3)(1 + 2-3)(1 + 3-3)...(1 + n-3) < 3 |
| October 28, 2005 |
A Property of Equiangular Polygons |
| October 27, 2005 |
Sierpinski Gasket Via Chaos Game |
| October 15, 2005 |
Who Needs Monty? |
| October 10, 2005 |
Upgraded the Y Can't End in a Draw page |
| October 5, 2005 |
The Lepidoptera of the Quadrilateral |
| October 4, 2005 |
Y Can't End in a Draw |
| September 28, 2005 |
Haruki's Theorem |
| September 27, 2005 |
Fixed Point of Circles Orthogonal to the Given One |
| September 26, 2005 |
Mirror property of the altitudes |
| September 25, 2005 |
Hiroshi Haruki's Lemma |
| September 22, 2005 |
The Two Men of Tibet |
| September 19, 2005 |
Mathematicians Doze Off |
| September 19, 2005 |
The Affirmative Action Problem |
| September 18, 2005 |
A Circle With Two Centers |
| September 16, 2005 |
Two Perpendiculars From a Point to a Line |
| September 16, 2005 |
Desargues in the Bride's Chair (with Pythagoras) |
| September 15, 2005 |
Dividing a Segment by Paper Folding |
| September 15, 2005 |
Integers and Rectangles: Two Simple Proofs |
| September 14, 2005 |
Three Tangents, Three Secants |
| September 13, 2005 |
Area of Median Triangle |
| September 12, 2005 |
Solitaire in Two Colors |
| September 10, 2005 |
Loop or Halt |
| September 9, 2005 |
A Maimed Cake |
| September 8, 2005 |
Euclid I.43 |
| September 7, 2005 |
Fractions on a Binary Tree II |
| September 4, 2005 |
Archimedes' Quadruplets |
| August 17, 2005 |
The Symmedians |
| August 15, 2005 |
Bisectal Circle |
| August 11, 2005 |
Three Tangent Circles |
| August 10, 2005 |
Ceva and Menelaus Meet on the Roads |
| August 9, 2005 |
Fermat's Point |
| August 3, 2005 |
Malfatti's Problem, Hart's Solution |
| July 29, 2005 |
Properties of the Circle of Similitude |
| July 27, 2005 |
Circle of Similitude |
| July 26, 2005 |
Malfatti's Problem |
| July 25, 2005 |
Internal Tangents to Three Circles |
| July 24, 2005 |
Inscriptible and Exscriptible Quadrilaterals |
| July 22, 2005 |
Four Pegs That Form a Square |
| July 20, 2005 |
A solution to the four travelers problem |
| July 16, 2005 |
Two Colors in Two Rows II |
| July 16, 2005 |
Two Colors in Two Rows |
| July 15, 2005 |
Inequality 1/2·3/4·5/6· ... ·99/100 < 1/10 |
| July 14, 2005 |
Life-like Automaton With Definable Rules |
| July 14, 2005 |
The Game of Life |
| July 13, 2005 |
On Bottema's Shoulders II |
| July 12, 2005 |
On Bottema's Shoulders |
| July 10, 2005 |
Simple Cellular Automaton |
| July 9, 2005 |
Weighing 12 coins |
| July 8, 2005 |
Integer Rectangle on a Chessboard by N. Bowler |
| July 7, 2005 |
Pole and Polar with respect to a Triangle |
| July 6, 2005 |
Pythagorean Theorem By Plane Tessellation |
| July 5, 2005 |
Three Tangents II |
| July 4, 2005 |
See-Saw Lemma |
| July 3, 2005 |
Birds on a Wire by S. Anderson |
| July 2, 2005 |
Concurrency in the Intouch Triangle |
| July 1, 2005 |
Dissection of a Rectangle into Two Chessboards |
| June 25, 2005 |
Proof #54 of the Pythagorean theorem |
| June 24, 2005 |
A Neglected Pythagorean-Like Formula |
| June 19, 2005 |
Minimax Theorem |
| June 18, 2005 |
A Versatile Theorem |
| June 14, 2005 |
Cube Counting Ambiguity |
| June 12, 2005 |
Shifting Cube Illusion |
| June 11, 2005 |
Viviani's theorem II |
| June 10, 2005 |
Integers and Rectangles: a Proof by Induction |
| June 8, 2005 |
Integers and Rectangles |
| June 7, 2005 |
Proof #51 of the Pythagorean theorem |
| June 5, 2005 |
Hart's Inversor |
| June 2, 2005 |
Hart Circle |
| June 1, 2005 |
Polar Circle |
| June 1, 2005 |
Four Triangles, One Circle |
| May 30, 2005 |
Feuerbach's Theorem: A Proof |
| May 29, 2005 |
Incidence in Feuerbach's Theorem |
| May 28, 2005 |
Rectangle on a Chessboard |
| May 26, 2005 |
Proofs #49 and #50 of the Pythagorean theorem |
| May 25, 2005 |
Proofs #46, #47 and #48 of the Pythagorean theorem |
| May 24, 2005 |
3-Colors Tower of Hanoi |
| May 23, 2005 |
Hanoing |
| May 22, 2005 |
Shepard's Parallelogram Illusion |
| May 21, 2005 |
Parallelogram Illusion |
| May 20, 2005 |
Plane Isometries |
| May 19, 2005 |
Simple Quadrilaterals Tessellate the Plane |
| May 18, 2005 |
Glide Reflection |
| May 17, 2005 |
Rotation Transform |
| May 16, 2005 |
Homothety |
| May 15, 2005 |
Nagel Line |
| May 12, 2005 |
Coaxal Circles Theorem |
| May 11, 2005 |
Apollonian Circles Theorem |
| May 8, 2005 |
Hex Can't End in a Draw |
| May 5, 2005 |
Another Pair of Twins in an Arbelos |
| May 5, 2005 |
Divide a Circle into N Parts of Equal Area |
| May 4, 2005 |
Lost Boarding Pass |
| May 3, 2005 |
Area of Arbelos |
| May 3, 2005 |
Light Bulbs in a Circle |
| May 1, 2005 |
Translation Transform |
| April 30, 2005 |
Reflection In Line |
| April 29, 2005 |
Secant Angles |
| April 27, 2005 |
Sieve of Squares |
| April 26, 2005 |
Sieve of Eratosthenes |
| April 22, 2005 |
Nagel Point of Medial Triangle |
| April 21, 2005 |
An Interesting Number |
| April 21, 2005 |
Locus of Points in a Given Ratio to Two Points |
| April 20, 2005 |
External Angle Bisector |
| April 20, 2005 |
Tangency Point of Two Circles |
| April 19, 2005 |
Property of Angle Bisectors II |
| April 19, 2005 |
Property of Angle Bisectors |
| April 18, 2005 |
Adams' Circle |
| April 17, 2005 |
Inscribed Angles |
| April 16, 2005 |
Inscribed and Central Angles in a Circle |
| April 15, 2005 |
Divisibility by 7, 11, and 13 |
| April 14, 2005 |
Inflection Points of Fourth Degree Polynomials |
| April 12, 2005 |
Munching on Circles |
| April 10, 2005 |
Signs in a Matrix |
| April 8, 2005 |
Partitioning 3-Space with Circles |
| April 7, 2005 |
Maximum Volume of a Cut Off Box |
| April 2, 2005 |
A Sticky Problem |
| March 30, 2005 |
Angle Trisection by Hippocrates |
| March 30, 2005 |
Rotating Gears |
| March 30, 2005 |
Morphing |
| March 29, 2005 |
Concurrency in Arbelos |
| March 28, 2005 |
Structural Constellation |
| March 27, 2005 |
Archimedes' Twin Circles and a Brother |
| March 26, 2005 |
Concyclic Points in Arbelos |
| March 21, 2005 |
Problem of Equal Steps II |
| March 20, 2005 |
Problem of Equal Steps |
| March 19, 2005 |
Gothic Arc |
| March 18, 2005 |
Book of Lemmas: Proposition 15 |
| March 17, 2005 |
Book of Lemmas: Proposition 13 |
| March 17, 2005 |
Book of Lemmas: Proposition 12 |
| March 16, 2005 |
Book of Lemmas: Proposition 10 |
| March 16, 2005 |
Two Butterflies Theorem III |
| March 15, 2005 |
Two Butterflies Theorem II |
| March 15, 2005 |
Book of Lemmas: Proposition 6 |
| March 14, 2005 |
Book of Lemmas: Proposition 5 |
| March 13, 2005 |
Book of Lemmas: Proposition 3 |
| March 13, 2005 |
Book of Lemmas: Proposition 2 |
| March 12, 2005 |
Book of Lemmas: Proposition 1 |
| March 11, 2005 |
Rectangle in Arbelos |
| March 9, 2005 |
4×4×4 Tic Tac Toe |
| March 7, 2005 |
What Is Arithmetic? |
| March 5, 2005 |
Hummer's Mind Reader |
| March 3, 2005 |
Proof #45 of the Pythagorean theorem |
| March 2, 2005 |
Coin Game |
| February 22, 2005 |
What Is Geometry? |
| February 10, 2005 |
Staircase Illusion |
| February 9, 2005 |
Poggendorff's Illusion |
| February 9, 2005 |
Wundt Block Illusion |
| February 8, 2005 |
Wundt Illusion |
| January 31, 2005 |
Dividing a Segment into N parts: Besteman's Construction II |
| January 31, 2005 |
Dividing a Segment into N parts: Besteman's Construction |
| January 30, 2005 |
Dividing a Segment into N parts: GLaD Construction |
| January 29, 2005 |
Dividing a Segment into N parts: SaRD Construction |
| January 7, 2005 |
Problem in an Equilateral Triangle II |
| January 6, 2005 |
Property of the Powers of 2 |
| January 4, 2005 |
Problem in an Equilateral Triangle |
