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 |