| Dec 29 |
Vector proof of Monge's Theorem of three circles |
| Dec 28 |
Concyclicity in Rectangle |
| Dec 25 |
In Pursuit of the Traveling Salesman |
| Dec 24 |
Sample Probability Problems from AMC |
| Dec 24 |
Property of Semicircles |
| Dec 22 |
The Contest Problem Book I-IV |
| Dec 21 |
Star of David Theorems in Pascal Triangle |
| Dec 20 |
Two Cevians and Proportions in a Triangle |
| Dec 16 |
Mathematics and Physics in the car market |
| Dec 16 |
Fermat's Like Equation |
| Dec 16 |
Viviani by Vectors |
| Dec 15 |
Review of How To Fold It by J. O'Rourke |
| Dec 13 |
Pantograph |
| Dec 13 |
What Is Linkage? |
| Dec 8 |
Probabilistic Method |
| Dec 7 |
A problem for the innocent minds |
| Dec 4 |
What Is Random? |
| Dec 3 |
Gauss' theorem on constructibility of regular polygons |
| Dec 2 |
Review of Leonardo's Mirror and The Monty Hall Probalem by Ivan Moscovich |
| Dec 1 |
Review of An Invitation to Mathematics by Dierk Schleicher and Malte Lackmann |
| Nov 28 |
Serendipitous Proofs Of The Pythagorean Theorem |
| Nov 27 |
Solve the equation cos^n(x) - sin^n(x) = 1 |
| Nov 27 |
cos(pi/7)-cos(2pi/7)+cos(3pi/7) = 1/2 |
| Nov 22 |
Collinearity via Concyclicity |
| Nov 20 |
Collinearity with the Orthocenter |
| Nov 17 |
Orbital Resonance and the Existence of Irrational Numbers |
| Nov 15 |
A Newly Born Pair of Siblings to Archimedes' Twins |
| Nov 11 |
On the Perimeters of Embedded Polygons |
| Nov 11 |
The Extreme Principle |
| Nov 9 |
A Proof of the Pythagorean Theorem with Orthocenter and Right Isosceles Triangles |
| Nov 9 |
Enchanted by Fascinating Mathematical People |
| Nov 7 |
Thought provokers to start a class with, II |
| Nov 7 |
Golden Section in Two Equilateral Triangles, II |
| Nov 6 |
Golden Section in Two Equilateral Triangles |
| Nov 5 |
A Characteristic Property Of Right Triangles |
| Nov 2 |
Solve cos2x + cos22x + cos23x = 1 |
| Oct 31 |
Finicky Diophantine Equations |
| Oct 31 |
Given the Probability, Find the Sample Space |
| Oct 31 |
Review of Magical Mathematics |
| Oct 28 |
Constructive Existence of the de Bruijn Cycles |
| Oct 27 |
Existence of the de Bruijn Cycles via Graphs |
| Oct 27 |
Euler Cycles in Digraph |
| Oct 26 |
Infinitude of Primes Via Lower Bounds |
| Oct 22 |
Order and Chaos in Multiple Pendulums |
| Oct 22 |
The Parabolic Sieve of Prime Numbers |
| Oct 22 |
Tiling a Rectangle with L-tetrominoes |
| Oct 22 |
Tiling a Square with T-, L-, and a Square Tetrominoes |
| Oct 21 |
Tiling a Square with Tetrominoes Fault-Free |
| Oct 20 |
1961 IMO, Problem 4. An exercise in barycentric coordinates |
| Oct 18 |
1961 IMO. Problem 1. A system of three equations with two parameters |
| Oct 18 |
Curvy Dissection |
| Oct 16 |
Dissection of a Vase |
| Oct 13 |
A Decomposition of Isosceles Triangles into 4 Isosecles Triangles |
| Oct 13 |
1960 IMO, Problem 5: Loci of points in a cube |
| Oct 11 |
1959 IMO, Problem 3 |
| Oct 9 |
Flipping Items Simultaneously III |
| Oct 7 |
Geometric Application of Ramsey's Theory |
| Oct 7 |
Viete's Formulas |
| Oct 7 |
Ramsey Number R(5, 3) |
| Oct 6 |
Derivative in Heron's Formula |
| Oct 5 |
A Proof by Game for a Sum of a Convergent Series |
| Oct 4 |
Tiling a Chessboard with Dominoes |
| Oct 3 |
Round Carpets |
| Oct 3 |
Review of The IMO Compendium |
| Oct 3 |
Angle Trisection |
| Oct 2 |
Ramsey Number R(4, 4) |
| Oct 2 |
Ramsey Number R(4, 3) |
| Oct 1 |
Ramsey Number R(3, 3, 3) |
| Sep 29 |
Sylvester's Problem |
| Sep 27 |
1962 IMO, Problem 2: an inequality with a twist |
| Sep 26 |
1=2 via Continued Fractions |
| Sep 26 |
Another proof of the Pythagorean theorem |
| Sep 23 |
Viviani in Isosceles Triangle |
| Sep 20 |
Majority Judgement: Measuring, Ranking and Electing by Michel Balinski and Rida Laraki |
| Sep 19 |
Review of Number-Crunching by Paul H. Nahin |
| Sep 19 |
The leapfrog problem - who is right? |
| Sep 16 |
Rectilinear Paradox |
| Sep 13 |
Finite Sums of Terms 2^(n-i) i^2 |
| Sep 12 |
Countability of Rational Numbers via Conitnued Fractions |
| Sep 12 |
Ptolemy via Cross-Ratio |
| Sep 11 |
Countability Principle |
| Sep 11 |
Negative on the left, positive on the right: how come? |
| Sep 11 |
Physics Minus Mathematics: The Week of Creation |
| Sep 9 |
Pythagorean Guess |
| Sep 8 |
Asymmetric Propeller |
| Sep 8 |
All Integers Are Even |
| Sep 8 |
All Powers of 2 Are Equal to 1 |
| Aug 15 |
One Sheet Hyperboloid |
| Aug 12 |
Pairs of Areas in Equilateral Triangle |
| Aug 11 |
Review of The Man of Numbers: Fibonacci's Arithmetic Revolution by Keith Devlin |
| Aug 11 |
Pompeiu's Theorem |
| Aug 10 |
Proof #20 of the Butterfly Theorem |
| Aug 10 |
Identities with Triangular Numbers |
| Aug 10 |
Involution on the Projective Line |
| Aug 9 |
Quadrilateral with 3 Equal Sides |
| Aug 8 |
Biblical pi and Gematria |
| Aug 7 |
Fixed Point in Isosceles and Equilateral Triangles |
| Aug 7 |
Proportions in Square |
| Aug 7 |
Review of Viewpoints: Mathematical Perspective and Fractal Geometry in Art by Marc Frantz and Annalisa Crannell |
| Aug 5 |
Regular Polygons in a Triangular Grid |
| July 31 |
Disapperances a la Sam Loyd |
| July 29 |
Fibonacci Numbers in Equilateral Triangle |
| July 26 |
Fleas on a Chessboard |
| July 23 |
Wisdom of Kozma Prutkov |
| July 23 |
Solving an Equation with Inverse Functions |
| July 21 |
What Is Finite? |
| July 17 |
Cross Points in a Polygon |
| July 17 |
White and Black Balls in Urn. 1 in, 2 out. What Color Remains? |
| July 15 |
Inverse to a Curious Partition Problem, Correct Solution |
| July 15 |
The 80-80-20 Triangle. Inverse to a Curious Partition Problem (Solution with a flaw) |
| July 11 |
Three Colors on a Chessboard |
| July 11 |
Rooks on a Chessboard |
| July 8 |
Coloring a Cube with Subdivided Faces |
| July 7 |
Angle Bisectors in a Quadrilateral - Cyclic and Otherwise |
| July 2 |
Harmonic Mean in Geometry |
| June 25 |
Angle Bisector Theorem |
| June 25 |
Filling an Array with 0s and 1s - and Counting |
| June 24 |
Shuttle Puzzle Practice II |
| June 23 |
David Richeson's Extention of an Old Japanese Theorem |
| June 19 |
Three Points Casey's Theorem |
| June 18 |
Sum of two Cantor sets |
| June 18 |
Casey's Theorem |
| June 12 |
Moving Chips in Pairs Down a Checkerboard |
| June 12 |
An Olympiad Problem for a Kindergarten Investigation |
| June 10 |
Parallel Lines in a Cyclic Quadrilateral |
| June 9 |
Butterfly theorem, a Projective Proof |
| June 9 |
A Property of the fusc() Function |
| June 7 |
Brahmagupta-Mahavira Identities |
| June 5 |
Construction of a Cyclic Quadrilateral |
| June 5 |
Circle Centers on Radical Axes |
| June 5 |
Three Concurrent Circles and Simultaneous Diameters |
| June 4 |
PWW: How Geometry Helps Algebra |
| June 4 |
Simultaneous Diameters in Concurrent Circles |
| June 3 |
Jack D'Aurizio Proof of Sawayama's Lemma |
| June 2 |
Area of a Bicentric Quadrilateral |
| June 1 |
An Area Inequality |
| June 1 |
Brahmagupta's Formula and Theorem |
| May 31 |
Simson Line in Disguise |
| May 30 |
Terquem's Theorem |
| May 27 |
Tromino Puzzle: Deficient Squares |
| May 25 |
Vandermonde Determinant |
| May 24 |
Divisibility Of Prod-Dif And The Vandermonde Determinant |
| May 23 |
Countability of Rational Numbers: PWW |
| May 23 |
Covering a Chessboard with a Hole with L-Trominoes |
| May 21 |
In Calculus too 1 = 0 |
| May 21 |
Cyclic Quadrilateral, Concurrent Circles and Collinear Points |
| May 20 |
Equal Areas in Regular 2n-gons |
| May 19 |
Problems with Many Solutions |
| May 19 |
Inclusion-Exclusion Principle: an Example |
| May 17 |
Sums of Geometric Series - Proofs Without Words |
| May 16 |
Solution #11 to a Classical Problem in the 80-80-20 Triangle |
| May 15 |
Two Circles and a Limit - Trigonometric Solution |
| May 15 |
The 80-80-20 Triangle Problem, A Derivative, Solution #7 |
| May 15 |
Number of Factors of an Integer |
| May 14 |
Two Circles and a Limit - Analytic Proof |
| May 12 |
An Age Conundrum with Men of the Cloth |
| May 10 |
Two Problems from a Serbian 7 Grade Math Competition |
| May 10 |
Golden Ratio is Irrational |
| May 8 |
Cantor's First Uncountability Proof |
| May 7 |
Every Parallelogram Is a Rectangle |
| May 5 |
Mascheroni Construction of a Regular Pentagon |
| May 4 |
Let Them Count by My Boys |
| May 4 |
Math Behind Counting |
| May 1 |
A Proof Perigal and All Others After Him Missed |
| April 30 |
Is a Point a Part of a Line? |
| April 29 |
Areas on the Graphs of Power Functions |
| April 29 |
Rational Solutions to xy = yx |
| April 28 |
An Elementary Proof of Bottema's Theorem |
| April 22 |
Four Numbers, Six Differences, GCD of the Products |
| April 20 |
Dissection of a Square Pyramid |
| April 20 |
Octahedron In Tetrahedron |
| April 18 |
50th IMO - 50 Years of International Mathematical Olympiad |
| April 16 |
A Multiplicative Identity of Areas in a Triangle |
| April 15 |
Invariance in Orthodiagonal Quadrilaterals |
| April 14 |
Curious Identities Involving Integer Products |
| April 11 |
A Review of Rediscovering Mathematics by Shai Simonson |
| April 10 |
Adding a Long List of Numbers |
| April 6 |
William Wallace's Proof of the Butterfly Theorem |
| April 5 |
Golden Ratio and Midpoints |
| April 5 |
From Equilateral Triangle and Square to Golden Ratio |
| April 4 |
Sicherman Dice |
| April 2 |
Probability Generating Functions |
| April 2 |
Hexagons in a Square |
| April 1 |
A Review of The Cambridge Dictionary of Statistics |
| March 30 |
The Futurama Theorem and Puzzle |
| March 28 |
Bear Born on a Tuesday |
| March 21 |
Geometry, Algebra, and Illustrations |
| March 18 |
Five Digits Magic Prediction |
| March 18 |
Four Digits Magic Prediction |
| March 17 |
Inequality of a Series of Square Roots |
| March 16 |
1089 and a Property of 3-digit Numbers |
| March 14 |
Serendipitous Beauty |
| March 12 |
Schwarz Lantern |
| March 10 |
The Mean Property of the Mean |
| March 5 |
Circle Chains on Napoleon Triangles |
| March 2 |
The Law of Cosines (Independent of the Pythagorean Theorem) |
| Feb 28 |
Plane Filling Curves: One of Sierpinski's Curves |
| Feb 26 |
Following the Hilbert Curve |
| Feb 26 |
Six Misnamed Coins, Two Weighings |
| Feb 26 |
Plane Filling Curves: the Lebesgue Curve |
| Feb 24 |
What Is Area? |
| Feb 17 |
Mikhalev's Octahedrons |
| Feb 17 |
Psychology of 0.99999... |
| Feb 16 |
Area of a Circle by Leonardo da Vinci |
| Feb 13 |
Difference of two Cantor sets, II |
| Feb 11 |
Grandfather's Bill |
| Feb 10 |
A review of two combinatorics books |
| Feb 8 |
Intersections of a Circle with the Four Quadrants |
| Feb 6 |
Algebraic proof of the theorem of butterflies in quadrilaterals |
| Feb 4 |
Squares and Straight Tetrominoes |
| Feb 4 |
Areas In Circle |
| Feb 4 |
Determinant and Divisibility |
| Feb 3 |
What Is Determinant? |
| Feb 1 |
4 addtional proofs of the incidence of the altitudes |
| Feb 1 |
Midpoints and Orthogonality in Isosceles Triangles |
| Jan 31 |
Square, Similarity and Slopes |
| Jan 30 |
Bayesian Odds |
| Jan 25 |
Area of a Circle by Rabbi Abraham bar Hiyya Hanasi |
| Jan 24 |
Torque as a Mathematical Object |
| Jan 23 |
Pythagorean Theorem via an Isosceles Triangle |
| Jan 21 |
Dancing Rectangles Model Auxetic Behavior |
| Jan 19 |
Hinged Greek Cross Tessellation |
| Jan 18 |
Circles in a Regular Polygon |
| Jan 16 |
Subsets and Intersections |
| Jan 15 |
A Low Bound for 1/2 * 3/4 * 5/6 * ... * (2n-1)/2n |
| Jan 14 |
Pythagorean Theorem from the Shoelace Formula |
| Jan 13 |
Regular Pentagon Inscribed in Circle by Paper Folding |
| Jan 11 |
Odd Scoring |
| Jan 8 |
Right Triangles on Sides of a Square |
| Jan 7 |
Golden Window |
| Jan 5 |
Equal Incircles Theorem, Angela Drei's Proof |
| Jan 4 |
Circles Cover a Quadrilateral |
