December 30 |
Line IO in Bicentric Quadrilaterals |

December 29 |
Equal Angles in Two Circles II |

December 25 |
Hippocrates' Squaring of Lunes |

December 15 |
Quadrature: A Child's Play |

December 13 |
Hippocrates' Squaring of a Lune |

December 11 |
Squaring a Rectangle |

December 10 |
Shearing a Polygon into a Triangle of Equal Area |

November 24 |
Proof 72 of the Pythagorean Theorem |

November 22 |
Pythagorean Theorem: Subtle Dangers of Visual Proof |

November 20 |
Proof 71 of the Pythagorean Theorem |

November 19 |
Cherchez le quadrilatère cyclique II |

November 18 |
Altitudes and the Power of a Point |

November 17 |
Use of Homogeneous Coordinates for Geometrical Calculations, by R. F. Housholder |

November 15 |
Proof 70 of the Pythagorean Theorem |

November 9 |
Orthodiagonal and Cyclic Quadrilaterals |

November 8 |
Circumcenter on Angle Bisector |

November 7 |
Projections on Internal and External Angle Bisectors |

November 6 |
Dissection of Cyclic Quadrilateral |

November 5 |
Orthocentric System From Rectangle |

November 3 |
In the Wasan Spirit |

November 2 |
Equilateral Triangles On Sides of a Parallelogram II |

November 1 |
What Is Angle? |

October 27 |
An Arithmetic Magic Trick |

October 26 |
Finding Circle Center By Ruler Alone |

October 26 |
Cherchez le quadrilatère cyclique |

October 25 |
Equal Angles in Two Circles |

October 24 |
Tangents, Perpendiculars and Geometric Mean |

October 22 |
Why 17? |

October 19 |
Angle: An Illustrated Classification |

October 17 |
A Circle Related to Incenter and Circumcenter |

October 16 |
Ramsey's Theorem |

October 15 |
Property of the Line IO: a proof from the Book |

October 10 |
Inscriptible Quadrilateral: An Illustration |

October 10 |
When A Quadrilateral Is Inscriptible? |

October 9 |
Egyptian Triangle By Paper Folding |

October 9 |
A Problem on an Icy Cone |

October 8 |
Common Chord and a Tangent |

October 7 |
Sangaku and The Egyptian Triangle |

October 5 |
Orthocenters of Two Triangles Sharing Circumcenter and Base |

October 3 |
Combinatorial Proofs |

October 1 |
Dividing Evenly a Quadrilateral II |

September 29 |
Lucas' Theorem |

September 28 |
Area of the Union of Two Squares |

September 27 |
Dividing Evenly a Quadrilateral |

September 26 |
Golden Ratio in Geometry |

September 25 |
Classification of Quadrilaterals |

September 24 |
Parallel Lines in a Quadrilateral |

September 23 |
Impossible Frame |

September 22 |
Triangle Classification |

September 21 |
What Is Proof? |

September 18 |
The SSA |

September 17 |
The SSS |

September 16 |
Expanded the page on Irrationality of sqrt(2) with introduction and two more proofs |

September 15 |
Geometric Meaning of the Geometric Mean |

September 14 |
Geometric Mean Sangaku |

September 11 |
Morley's Theorem, G. Zsolt Kiss' proof |

September 10 |
Circle Concurrency and Spiral Similarity |

September 9 |
Two Quadruplets of Tangent Circles |

September 8 |
Review of *Kiselev's Geometry* |

September 6 |
Two Circumcircles And Two Pairs of Parallels |

September 4 |
Pythagoras' Theorem Solely By Sliding |

August 22 |
Orthogonality in Isosceles Triangles |

August 21 |
Foot of Altitude and Minimum Distance |

August 20 |
An inequality: 1 + 2^{-2} + 3^{-2} + 4^{-2} + ... + n^{-2} < 2. |

August 19 |
Ian McGee's Observation |

August 18 |
A Median in Touching Circles |

August 16 |
Midpoints from Gergonne Triangle |

August 15 |
Five Incircles in a Square |

August 14 |
A Sangaku: Two Unrelated Circles |

August 12 |
Chords, Concurrency and Orthic Triangle |

August 10 |
Van Schooten's and Pompeiu's Theorems |

August 9 |
Harmonic Ratio in Complex Domain |

August 6 |
A Sangaku Follow-Up on an Archimedes' Lemma |

August 5 |
A Property of the Line IO: A Bundled Statement and Proof |

August 4 |
A Property of the Line IO |

August 3 |
Three Parallels in a Triangle |

August 1 |
Angle Bisector in Touching Circles |

July 31 |
Discovery of Duane DeTemple |

July 30 |
Two Circumcircles in Triangle |

July 27 |
Right Isosceles Triangles on Sides of a Quadrilateral |

July 26 |
Rotations in Disguise |

July 25 |
Toothpick Construction of a Square |

July 22 |
Fagnano's Problem, Izvolsky's Solution |

July 21 |
Antiparallel |

July 21 |
Nagel's Theorem |

July 20 |
Two Circles on a Side of a Triangle |

July 18 |
Shuttle Puzzle Practice |

July 16 |
Permutations as a Product of Transpositions |

July 14 |
Radius and Construction of a Mixtilinear Circle |

July 13 |
Tromino as a Rep-tile |

July 12 |
Mixtilinear Circles and Concurrence |

July 7 |
Secant, Tangents and Orthogonality |

July 6 |
60° Breeds 90° |

July 5 |
Triangle Areas in a Parallelogram II |

June 26 |
Triangle Areas in a Parallelogram |

June 25 |
Parallelogram and Similar Triangles |

June 22 |
Joachimsthal's Notations |

June 21 |
Urquhart's Theorem |

June 21 |
Reviewed the outstanding The 15 Puzzle |

June 20 |
Kürschak's Tile and Theorem |

June 18 |
Started the Book Reviews section |

June 17 |
MathPro Logo |

June 16 |
Stones in Cups |

June 14 |
Product of permutations |

June 13 |
Recombining Permutations |

June 11 |
Shearing and Translation in Pythagorean Pants |

June 10 |
Pythagoras' Theorem By Sheer Shearing |

June 9 |
Proof 69 of the Pythagorean theorem |

June 7 |
Integer roots of integers are irrational by S. Brodie |

June 6 |
Coloring a Graph |

June 5 |
Parallelogram Law: A PWW |

June 5 |
Parallelogram Law: A Tessellation |

June 3 |
The Law of Cosines: An Unfolded Variant |

June 2 |
The Law of Cosines: a proof without words |

May 14 |
Proof 68 of the Pythagorean theorem |

May 14 |
Parallelogram Law |

May 13 |
Proof 67 of the Pythagorean theorem |

May 12 |
Secant Angles II |

May 11 |
Broken Chord Theorem: S. Anderson's proof |

May 10 |
The Cleavance Center |

May 10 |
The Cleaver |

May 9 |
Broken Chord Theorem by Paper Folding |

May 8 |
Broken Chord Theorem: Patruno's proof |

May 7 |
Broken Chord Theorem |

May 6 |
Angle Subtended by a Diameter |

April 29 |
Graph of a Polynomial Defined by Its Roots |

April 28 |
Graph of a Polynomial |

April 27 |
The ass and the mule |

April 26 |
Midpoints of the Lines Joining In- and Excenters |

April 25 |
Pedoe's Theorem |

April 24 |
Proof 14 of the Butterfly theorem |

April 24 |
ISBN Encoding |

April 23 |
Barcode and EAN-13 Encodings |

April 22 |
Barcode Magic |

April 21 |
Universal Product Code |

April 12 |
Construction of the Angle Bisector |

April 11 |
Existence of the Circumcenter |

April 10 |
Perpendicular Bisector |

April 7 |
Three Touching Circles |

April 6 |
Two Touching Circles |

April 3 |
Proofs 65 and 66 of the Pythagorean theorem |

March 29 |
Pythagoras' Theorem By Similarity |

March 29 |
Proof #4 of the Eyeball Theorem |

March 29 |
Proof #8 of Irrationality of sqrt(2) |

March 28 |
Equidecomposition of a Triangle and a Rectangle II |

March 27 |
Square in a Right Triangle and its fill-it-in outline solution |

March 23 |
Billy is twice as old as Sally and other Outline Mathematics |

March 21 |
Areas and Centroid in a Triangle |

March 18 |
Proof 64 of the Pythagorean theorem |

March 18 |
Proof 63 of the Pythagorean theorem |

March 17 |
Symmedian in a Right Triangle |

March 16 |
Proof 62 of the Pythagorean theorem |

March 16 |
Pennies in Boxes |

March 11 |
Mirror on the Wall |

March 10 |
Math Telepathy |

March 9 |
Rhind Papyrus |

March 8 |
Peasant Multiplication |

March 3 |
Proofs 59, 60, 61 of the Pythagorean theorem |

February 28 |
Started a page on False Proofs of the Pythagorean Theorem |

February 28 |
Proofs 56, 57, 58 of the Pythagorean theorem |

February 27 |
A Problem In an Isosceles Right Triangle |

February 26 |
Equal Areas In Parallelogram à la Pythagoras |

February 25 |
Two Homotheties in a Parallelogram |

February 22 |
3-Color Tower of Hanoi (Algorithm) |

February 21 |
Another Sticky Problem II |

February 19 |
Four Turtles (or Bugs, or Dogs, etc.) |

February 17 |
Bottles in a Wine Rack: Proofs and Generalizations |

February 15 |
Angles in Triangle Add to 180° |

February 15 |
Rendezvous |

February 12 |
Two Symmetric Triangles Are Directly Equidecomposable IV |

February 9 |
Solution to the Four Travelers Problem by Rob Fatland |

February 8 |
Two Symmetric Triangles Are Directly Equidecomposable III |

February 7 |
Two Symmetric Triangles Are Directly Equidecomposable II |

February 7 |
Two Symmetric Triangles Are Directly Equidecomposable |

February 6 |
Angles in Triangle Add to 180° |

February 4 |
Distance From a Point to a Straight Line |

February 1 |
Tangent Circles and an Isosceles Triangle, a Solution |

January 31 |
Radius of a Circle by Paper Folding |

January 31 |
Bottema Shatters Japan's Seclusion |

January 30 |
Tangent Circles and an Isosceles Triangle |

January 29 |
Pythagoras and Vecten Break Japan's Isolation |

January 26 |
Evolution of a Solution |

January 25 |
Triangles, Squares and Areas from Temple Geometry |

January 24 |
Universal Coloring |

January 23 |
No Equilateral Triangles, Please |

January 22 |
Triangle Sliding on Two Straight Lines |

January 21 |
Bottles in a Slanted Rack |

January 18 |
First Geometric Interpretation of Complex Numbers |

January 12 |
Around the Incircle in a Polygon |

January 11 |
Crossed-Lines Construction of Shapes of Constant Width |

January 9 |
Around the Incircle |

January 8 |
Algebraic Structure of Complex Numbers |

January 4 |
Three Concurrent Circles |

January 3 |
Circles And Parallels |

January 3 |
Proof #13 of the Butterfly Theorem |

January 3 |
Carpets in a Quadrilateral |

January 2 |
Two Circles and a Limit |