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 cos^{2}x + cos^{2}2x + cos^{2}3x = 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 x^{y} = y^{x} |

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 |