| 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 eiθ |
| 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 |
