December 30 |
Horner's Method |

December 29 |
Calculation of the Digits of pi (Faster Version) |

December 28 |
Calculation of the Digits of pi by the Spigot Algorithm |

December 24 |
It's All About Powers of 10 |

December 24 |
Four Pedal Circles |

December 23 |
Griffiths Points in Cyclic Quadrilateral |

December 22 |
Added a proof of Griffiths' Theorem |

December 17 |
Nine Point Circle II |

December 16 |
Ducci Sequences |

December 13 |
The Basic Rules of Counting |

December 13 |
The Deadly Parallel |

December 12 |
From Foci to a Tangent in Ellipse |

December 11 |
Harmonic Serires And Its Parts |

December 11 |
Infinitude of Primes Via Harmonic Series |

December 6 |
La Hire's Theorem in Ellipse |

December 6 |
Σ2^{-n} = Σn·2^{-n} |

December 5 |
Poncelet's Porism in Ellipses |

December 3 |
Euclid I.43 Extended |

November 28 |
Golden Ratio in an Irregular Pentagon |

November 28 |
Golden Ratio in an Irregular Pentagon, Construction I |

November 28 |
Golden Ratio in an Irregular Pentagon, Construction II |

November 26 |
Sample Spaces and Random Variables |

November 24 |
Lattice Multiplication |

November 22 |
Long Multiplication |

November 21 |
Egyptian Multiplication |

November 19 |
Unfolding Spirals Illusion |

November 18 |
What Is Probability? |

November 13 |
Added a Gaelic word for *centipede* |

November 12 |
Added a few variants to the 80-80-20 problem |

November 11 |
A Sangaku with Many Circles and Some |

November 1 |
Carpets in a Quadrilateral II |

November 1 |
Two Arbelos, Two Chains |

October 30 |
Archimedes' Twins in the Edo Period |

October 30 |
Sangaku with 8 Circles |

October 30 |
Reflections in Ellipse |

October 29 |
Property of 6-Parpolygon |

October 27 |
Conic Sections as Loci of Points |

October 25 |
Optical Property of Ellipse |

October 24 |
Al-Nayrizi's Construction |

October 24 |
Euclid's Segment Division |

October 24 |
Similar Right Triangles |

October 23 |
7 = 2 + 5 Sangaku |

October 23 |
Steiner's Sangaku |

October 22 |
Twin Segments in Arbelos |

October 22 |
Ellipse in Arbelos |

October 21 |
Consecutive Isosceles Decomposition |

October 20 |
Squares in Arbelos |

October 19 |
6 Solutions to a derivative problem in the 80-80-20 triangle |

October 17 |
2 Solutions to a modified problem in the 80-80-20 triangle |

October 16 |
Pascal's Theorem, Homogeneous Coordinates |

October 15 |
Three Incircles In a Right Triangle |

October 12 |
Octagon in Parallelogram: Overlapping Regions |

October 12 |
Octagon in Parallelogram |

October 10 |
10 Solutions to the classical problem in the 80-80-20 triangle |

October 9 |
Brianchon in Ellipse |

October 9 |
Arithmetic Mean Sangaku II |

October 8 |
What is so natural about “natural logarithms”? |

October 8 |
The 80-80-20 Triangle |

October 7 |
Euler’s formula for *e*^{iθ} |

October 3 |
The 80-80-20 Triangle Problem, A Variant |

October 3 |
√2 is irrational, proof #14 |

October 2 |
Three Squares and Two Ellipses |

October 1 |
√N is irrational, proof #13 |

October 1 |
Chasles' Theorem, a Proof |

September 30 |
Projective Proof of Pascal's Theorem |

September 29 |
Illustration of Pascal's Theorem |

September 25 |
Hjelmslev Theorem |

September 24 |
Generalizing a Romanian Olympiad Problem |

September 23 |
Four Incircles in Equilateral Triangle |

September 21 |
Maximal Properties of the Pythagorean Relation |

September 20 |
Pythagorean Condition in An Isosceles Right Triangle |

September 18 |
Artisans vs Mathematicians |

September 17 |
Approximate Construction of Regular Pentagon by A. Dürer |

September 16 |
Construction of Regular Pentagon by H. W. Richmond |

September 14 |
Regular Pentagon Construction by Y. Hirano |

September 14 |
Pentagon Proportions Sangaku |

September 13 |
Equilateral Triangle, Straight Line and Tangent Circles |

September 11 |
Proof 75 of the Pythagorean Theorem |

September 4 |
Circles in a Circular Segment |

September 1 |
Steinhaus' Problem |

August 30 |
Isotomy and Isogonality Hand-in-Hand |

August 29 |
Lean Napoleon's Triangles |

August 25 |
Reverse Spoke Illusion |

August 25 |
Importance of Occluders: Motion Binding |

August 25 |
Brick Wall Illusion |

August 24 |
Occluded Wheel Illusion |

August 22 |
Divergent Spirals Illusion |

August 21 |
Rotating Top Illusion |

August 20 |
White's Illusion, V-Variant |

August 20 |
White's Illusion |

August 19 |
Koffka's Illusion |

August 14 |
Two Circles Inscribed in a Parallelogram |

August 13 |
Eight Equal Tangents |

August 12 |
Why 1/3 + 1/4 = 7/12? |

August 12 |
Counting Chips On a Circle |

August 11 |
Infinitude of Primes Via Coprime Pairs |

August 10 |
Pythagorean Triples Calculator |

August 9 |
Committee Chairs |

August 8 |
Infinitude of Primes Via *-Sets |

August 8 |
Infinitude of Primes Via Fermat Numbers |

August 7 |
Langford and Skolem Sequences |

August 4 |
Pythagorean Theorem by Hinged Dissection I |

August 3 |
Proof #16 of the Butterfly Theorem |

August 3 |
Two Triangles With Common Base and Altitude |

August 2 |
Mirror Property of Altitudes via Pascal's Hexagram |

July 24 |
Chameleons of Three Colors |

July 19 |
Sangakus with a Mixtilinear Circle |

July 18 |
cos(36°) = (1 + √5)/4 |

July 17 |
Area of Triangle |

July 13 |
Pythagorean Theorem by Hinged Dissection II |

July 12 |
Pythagorean Theorem by Hinged Dissection |

July 11 |
Out of Pentagon Sangaku |

July 10 |
Angle Trisection by Paul Vjecsner |

July 9 |
Circles Lined on the Legs of a Right Triangle |

July 9 |
Sequences of Touching Circles |

July 8 |
Similar Triangles And More |

July 8 |
Angle Bisectors On Circumcircle |

July 8 |
Two Circles in a Square II |

June 23 |
An Extension of van Schooten's Theorem |

June 22 |
Relations in a Cyclic Polygon |

June 22 |
Chasles' Theorem |

June 21 |
Nine Squares |

June 20 |
A Sangaku with an Egyptian Attachment |

June 20 |
Sangaku with Versines |

June 19 |
Harmonic Mean Sangaku |

June 18 |
Abul Wafa al-Buzjani's Proof of the Pythagorean Theorem |

June 17 |
Three Tangent Circles Sangaku |

June 13 |
Arithmetic Mean Sangaku |

June 12 |
Cyclic Hexagon |

June 10 |
Make An Identity |

June 6 |
Proof 5 of the Eyeball Theorem |

June 1 |
Mirror Maze |

May 28 |
Equilateral Triangles on Diagonals of Antiequilic Quadrilateral |

May 26 |
Equilic Quadrilateral II |

May 26 |
Equilic Quadrilateral I, A Variation |

May 26 |
Equilic Quadrilateral I (a Flawed Proof) |

May 25 |
Equilateral Triangles on Segments of Equilic Quadrilateral |

May 24 |
Similar Triangles on Sides and Diagonals of a Quadrilateral |

May 22 |
Full House |

May 20 |
Circle Division by Euclid and Leonardo |

May 19 |
Color Balls: a Game of Logic |

May 18 |
Ways To Count |

May 15 |
Signs and Sums in a Sequence |

May 14 |
Product of Diagonals in Regular N-gon |

May 13 |
A Relation in Triangle |

May 11 |
Proof 12 of the irrationality of the square root of 2 |

May 10 |
Three Points on a Parabola |

May 9 |
Greg Markowsky's Problem for Parabola |

May 8 |
Proof #73 of the Pythagorean Theorem |

May 7 |
Amoeba's Survival |

May 6 |
Shortest Fence in a Quarter-Circle Pasture |

May 5 |
Jumping Isn't Everything |

May 4 |
3-Chain |

May 4 |
Super Nim |

May 4 |
Achieve the Equilibrium |

May 4 |
Vector Addition and Subtraction |

May 4 |
Caterpillar |

May 4 |
Wolf and Rabbit |

May 2 |
4 Travelers' Problem, Michel Cabart's Solution. |

May 1 |
Sangaku Iterations, Is it Wasan? |

April 30 |
The Erdös-Mordell Inequality |

April 30 |
An Elementary Proof of Urquhart's Theorem |

April 29 |
Lights Out |

April 28 |
Mini Lights Out |

April 27 |
Midline in Similar Triangles |

April 17 |
Proof #15 of the Butterfly Theorem |

April 13 |
Two Envelopes Paradox |

April 12 |
Added a dynamic illustration to Archimedes' Lemma 9 |

April 10 |
Tower of Hanoi, the Hard Way |

April 9 |
Thébault's Problem III, Proof |

April 8 |
Y. Sawayama's Lemma |

April 6 |
Parallel Chords II |

March 29 |
Olof Hanner's Jigsaw Puzzle |

March 20 |
Pythagorean Triples and Perfect Numbers |

March 18 |
Butterflies in Quadrilaterals and Elsewhere |

March 16 |
Napoleon's Theorem by Transformation |

March 13 |
A brief introduction to Rational Trigonometry |

March 12 |
Inaugurated the system for purchasing of individual applets |

February 24 |
Hooper's Paradox |

February 22 |
Square and Circle in a Gothic Cupola |

February 20 |
Quadrilateral With Equal Opposite Sides And Angles |

February 12 |
Started the No-ads Subscription |

February 4 |
Update for the page of January 31 |

February 2 |
A Stronger Triangle Inequality |

January 31 |
Equilateral Triangles and Incircles in a Square |

January 29 |
Sangaku in a Square |

January 28 |
Twenty five boys and twenty five girls around a table. |

January 27 |
Six Balls, Two Weighings |

January 18 |
Remarkable Line in a Quadrilateral |

January 17 |
Two Circles in an Angle |

January 6 |
Crossing Number of a Graph |