| Dec 28 |
Semi-regular Tessellation on Hinges C |
| Dec 26 |
Semi-regular Tessellation on Hinges B |
| Dec 26 |
Semi-regular Tessellation on Hinges A |
| Dec 24 |
A Hinged Realization of a Plane Tessellation |
| Dec 23 |
A Corrected Version of the Calculus Proof of the Pythagorean Theorem |
| Dec 23 |
Proof #89 of the Pythagorean Theorem |
| Dec 22 |
Dancing Squares or a Hinged Plane Tessellation |
| Dec 21 |
Filling a Grid with Good Neighbors |
| Dec 20 |
Review of A Decade of the Berkley Math Circle |
| Dec 20 |
No Flipping without End |
| Dec 18 |
Viviani by Inversion |
| Dec 17 |
Absolute Value and 1998 integers |
| Dec 17 |
Word Ladders |
| Dec 16 |
Phantom Circle and Recaptured Symmetry |
| Dec 15 |
Eight Selections in Six Sectors |
| Dec 14 |
A Game of Candy Squares |
| Dec 13 |
Angles Inscribed in an Absent Circle |
| Dec 12 |
A Three Pegs Question |
| Dec 12 |
Escape of the Clones |
| Dec 11 |
Guests at a Round Table |
| Dec 11 |
Ptolemy by Inversion |
| Dec 9 |
Treasure Hunt from Outside the Grid |
| Dec 9 |
Treasure Hunt in a Square Grid |
| Dec 7 |
12 Coins in Verse |
| Nov 30 |
Menelaus from 3D |
| Nov 30 |
Chromatic Number of the Plane |
| Nov 29 |
The Rascal Triangle |
| Nov 29 |
Coloring Points in the Plane |
| Nov 28 |
Szilassi Polyhedron |
| Nov 28 |
Csaszar Polyhedron 4 |
| Nov 28 |
Csaszar Polyhedron 1 |
| Nov 27 |
Acute Angle Bisectors in a Right Triangle |
| Nov 27 |
1995 British Mathematical Olympiad, Problem 3 |
| Nov 27 |
Circle through the Circumcenter |
| Nov 26 |
Skyscrapers Puzzle |
| Nov 25 |
Cevian Cradle |
| Nov 24 |
Diophantine Equations |
| Nov 24 |
Curious Identities Involving Integer Squares |
| Nov 24 |
AM-GM Inequality |
| Nov 23 |
VMO 1992 Problem 1 |
| Nov 23 |
A Quickie Limit |
| Nov 23 |
Any Integer with Three 2s |
| Nov 21 |
Two-Parameter Solutions to Three Almost Fermat Equations |
| Nov 21 |
A Review of Geometric Etudes in Combinatorial Mathematics |
| Nov 20 |
Coloring Plane with Three Colors |
| Nov 17 |
Tiling Rectangles with L-Trominoes |
| Nov 15 |
Subtraction in a Rectangular Array |
| Nov 13 |
Not Exceeding 24 |
| Nov 13 |
Knots on a Torus |
| Nov 12 |
Averaging Raindrops, Part 2 |
| Nov 11 |
Averaging Raindrops - an exercise in geometric probability |
| Nov 10 |
Solution #4 to a three circles problem |
| Nov 7 |
100 Grasshoppers on a Triangular Board |
| Oct 31 |
Polygon in a Rectangle |
| Oct 31 |
Three Jugs - Equal Amounts |
| Oct 30 |
Many Jugs to One II |
| Oct 30 |
Many Jugs to One I |
| Oct 30 |
3 Jugs Problem - A Water Doubling Variant |
| Oct 29 |
Riemann Rearrangement Theorem |
| Oct 28 |
1/2 = 1 |
| Oct 27 |
Review of An Introdcution to Diophantine Equations by T. Andreescu et al |
| Oct 27 |
A Short Equation in Reciprocals |
| Oct 25 |
An Equation in Reciprocals |
| Oct 25 |
Segment Trisection Induced by Parallels to Medians |
| Oct 23 |
Angle Bisectors In Rectangle |
| Oct 20 |
First Applications of Helly's Theorem |
| Oct 20 |
Helly's Theorem |
| Oct 19 |
Diophantine Quadratic Equation in Three Variables |
| Oct 18 |
Dissection of Triangle into Rhombus by Hubert Shutrick |
| Oct 18 |
Minus One But What a Difference |
| Oct 14 |
Homothety between In- and Excircles |
| Oct 13 |
Filling Pool with Fluids |
| Oct 12 |
Calculus Proof of the Pythagorean Theorem |
| Oct 11 |
Review of Mathematical Plums by R. Honsberger |
| Oct 9 |
Dissection of Triangle into Rhombus |
| Oct 8 |
Pentagon in a Semicircle |
| Oct 7 |
Extremal Problem in a Circular Segment |
| Oct 6 |
Counting Ordered Pairs |
| Oct 4 |
Asymmetric Propeller by Plane Tiling |
| Oct 2 |
A Mathematical Rabbit out of an Algebraic Hat |
| Oct 1 |
Carpets in Hexagon |
| Sep 29 |
Distinct Multisets with the Same Pairwise Sum |
| Sep 28 |
A Characterization of the Euler Line |
| Sep 27 |
Lennes' Polyhedron |
| Sep 24 |
Review of Classical Topics in Discrete Geometry by K. Bezdek |
| Sep 24 |
Morley's Theorem: Proof by H. Shutrick |
| Sep 23 |
A Chain of Touching Circles in a Polygon (a la Bui Quang Tuan) |
| Sep 23 |
A Chain of Touching Circles in a Polygon (a la Evelyn) |
| Sep 21 |
Fraction Comparison Sped up |
| Sep 19 |
Pythagoras' from the Star of David |
| Sep 17 |
Areas in Square by Dissection |
| Sep 14 |
Review of Charming Proofs by C. Alsina and R. B. Nelsen |
| Sep 11 |
Antiparallel via Three Reflections |
| Sep 10 |
Johnson Circles |
| Sep 8 |
Assigning Numbers to Points in the Plane |
| Sep 6 |
Squares in Semicircle and Circle |
| Sep 5 |
Are Most Triangles Obtuse? |
| Sep 3 |
Volumes of Two Pyramids |
| Sep 3 |
Squares in Triangles |
| Sep 1 |
Pythagorean Theorem: An Algebraic Proof with Three Trapezoids |
| Aug 27 |
A Maximum Area Property of the Medial Triangle |
| Aug 26 |
The Broken Chord Theorem: proof by Mariano Perez de la Cruz |
| Aug 26 |
The Illustrated Law of Cosines |
| Aug 16 |
Pythagoras' from Bottema's |
| Aug 15 |
A Lemma of Equal Areas |
| August 4 |
Touching Circles with Given Centers II |
| August 4 |
Review of Numbers Rule by G. Szpiro |
| August 3 |
2001 Poland Mathematical Olympiad, Problem 2 |
| August 2 |
Are Australian Elections Fair As Claimed? |
| August 2 |
Nested Radicals |
| August 1 |
Pythagoras' from Broken Chords (proof #85) |
| August 1 |
The Broken Chord Theorem: proof by Bui Quang Tuan |
| August 1 |
Three Equal Circles in a Semicircle |
| July 31 |
Shuffling Probability |
| July 27 |
Two Triples of Concurrent Circles |
| July 23 |
Six Circles Theorem (Bui Quang Tuan) |
| July 23 |
Finger Counting |
| July 16 |
Circle in a Square Inscribed in a Circle |
| July 11 |
J. Casey's Additions to Euclid I.47 |
| July 6 |
A Circle Rolling in an Equilateral Triangle |
| June 27 |
Line, Circle, and Fixed Points |
| June 26 |
An inequality from 1971 Canadian Mathematical Olympiad |
| June 26 |
Problem with angle bisector from 1975 Canadian Mathematical Olympiad |
| June 26 |
Fixed points from 2007 Irish Mathematical Olympiad |
| June 25 |
Problem with equal angles from 1987 IberoAmerican Mathematical Olympiad |
| June 24 |
Perpendicular lines in a cyclic quadrilateral from 1975 Canadian Mathematical Olympiad |
| June 23 |
Review of What's Luck Has to Do with It? by Joseph Mazur |
| June 22 |
A Trigonometric Identity in a Right Triangle from the 1960 IMO |
| June 22 |
Ancient Problem = Ancient Solution |
| June 21 |
Euclid's Game on a Square Grid |
| June 18 |
Square in a Circle Inscribed in a Square |
| June 17 |
Parametric Problem in Quartic Polynomial from 1984 USAMO |
| June 16 |
Example: A Poker Hand |
| June 15 |
A Property of Centrally Symmetric Hexagons |
| June 14 |
Chain of Circles on a Chord |
| June 9 |
Circle, Isosceles Triangle and Fixed Point |
| June 9 |
A Circle in an Isosceles triangle from the 2006 Irish MO |
| June 8 |
Circles on the sides of a triangle from the 2005 Austrian MO |
| June 8 |
Problem of divisibility from the 1970 Canadian MO |
| June 8 |
Concurrency from the 2009 Austrian MO |
| June 8 |
Problem in Isosceles Triangles from the 2008 Austrian MO |
| June 7 |
Construction of Square from the 2008 Austrian MO |
| June 7 |
A Problem with Ratios from the 1969 Canadian MO |
| June 4 |
Cutting Triangles off Regular Hexagon |
| June 4 |
Asian Pacific Kite |
| June 3 |
Number Comparison - from the 1969 Canadian MO |
| June 3 |
Lucky Contest Winners |
| June 2 |
An Identity Involving the Integer Part - Problem from the 1981 Canadian MO |
| June 2 |
An Identity between the Roots of a Cubic Polynomial - Problem from the 2007 Irish MO |
| June 2 |
A Diophantine Equation with Square Roots - Problem from the 2008 British MO |
| June 2 |
Fixed Point in a Kite - Problem from the 1993 Asian Pacific MO |
| June 2 |
Ratios and Orthogonality in a Triangle - Problem from the 2006 Romania MO |
| June 1 |
A Diophantine Equation - Problem from the 2000 Belarus MO |
| May 30 |
Review of A Mathematician's Lament by Paul Lockhart |
| May 28 |
Sangaku with Angle between a Tangent and a Chord |
| May 27 |
Squares and Cubes - from the 1978 Canadian MO |
| May 27 |
Locus of the midpoints of concurrent chords - from the 1991 Canadian MO |
| May 27 |
Sum of 1984 consecutive squares - from the 1984 Canadian MO |
| May 27 |
Areas in a quadrilateral - from the 1978 Canadian MO |
| May 27 |
1986 Canadian MO, Problem 1 |
| May 27 |
Circle through the Incenter And Antiparallels |
| May 27 |
2001 IberoAmerican MO, Problem 2 |
| May 27 |
1980 Canadian MO, Problem 3 |
| May 27 |
1972 Canadian MO, Problem 5 |
| May 27 |
1969 Canadian MO, Problem 7 |
| May 27 |
1994 Ireland MO, Problem 1 |
| May 27 |
Another Look at Nagel's Theorem |
| May 26 |
1987 Canadian MO, Problem 2 |
| May 21 |
Need Mathematics Taught in School Be Relevant? |
| May 20 |
Yet another solution (by Vladimir Nikolin) to the "circle through 2 vertices and the incenter" problem |
| May 19 |
Equilateral triangles on the sides of a right triangle - a problem from the 2000 Belarus MO |
| May 19 |
Three Circles through the Incenter |
| May 18 |
2000 Belarus Mathematical Olympiad, Problem 7 |
| May 18 |
Construction with Optimization in Angle - Problem the 1979 USA Mathematical Olympiad |
| May 18 |
Problem 7 of the Australian Mathematical Olympiad 2009 |
| May 18 |
Problem 2 of the Australian Mathematical Olympiad 2008 |
| May 18 |
Circle through the Incenter |
| May 17 |
2010 Australian Mathematical Olympiad, Problem 6 |
| May 17 |
Inequality Between the Perimeters of Two Triangles and the Distances Between Their Vertices |
| May 16 |
Reflections of the circumcenter |
| May 15 |
Partial But General Case Of Fermat's Last Theorem 2 |
| May 14 |
Partial But General Case Of Fermat's Last Theorem |
| May 14 |
Simple Somos Sequence - a Russian Olympiad problem |
| May 14 |
Simple Somos Sequence Calculator |
| May 12 |
Inequality with Logarithms |
| May 12 |
Maximum Ratio of Similarity - Belarus Olympiad Problem |
| May 10 |
Simple dissection of an acute triangle |
| May 9 |
Three Orthogonal Circles Through Three Given Points |
| May 6 |
A Variant Of the Pythagorean Theorem |
| May 6 |
Triangle ABC is right iff sin^2(A) + sin^2(B) + sin^2(C) = 2 |
| May 5 |
1992 Asian Pacific Mathematical Olympiad, Problem 2 |
| May 5 |
1986 Vietnam Mathematical Olympiad, Problem 4 |
| May 4 |
Parallelogram Iterations |
| May 3 |
1962 Vietnam Mathematical Olympiad, Problem 4 |
| May 3 |
2010 USA Olympiad, Problem 1 |
| May 3 |
2010 USA Olympiad, Problem 3 |
| May 3 |
2010 USA Olympiad, Problem 4 |
| May 3 |
Nagel's Theorem: an Elementary Proof |
| May 3 |
Presence of the Antipodes on a Circle |
| May 3 |
Swapping Rows and Columns |
| May 2 |
Two Equilateral Triangles |
| May 1 |
Two Altitudes, One Midpoint |
| April 29 |
Constructions Related To An Inaccessible Point |
| April 29 |
A Telescoping Series |
| April 29 |
Yet Another Proof of the Concurrency of the Altitudes |
| April 27 |
Heron's Formula: a Proof |
| April 26 |
Approximation Of Roots |
| April 25 |
Nine Point Circle: an Elementary Proof |
| April 25 |
Existence of the Euler Line: An Elementary Proof |
| April 25 |
Problem 1 from the 1988 IberoAmerican Olympiad |
| April 24 |
Reflections of the Orthocenter II |
| April 23 |
Maximum Perimeter Property of the Incircle |
| April 21 |
Problem 5 from the USA Mathematical Olympiad |
| April 21 |
Addition and Subtraction of Integers |
| April 19 |
Faulty Symmetry |
| April 18 |
Triangulated Dinosaur |
| April 17 |
Problem 9 from the 2009 Middle European Mathematical Olympiad |
| April 16 |
Counting and Equivalent Fractions |
| April 16 |
Scoring Misere: Two Heaps Perfect Strategy |
| April 12 |
Problem 2 from the 1992 China Mathematical Olympiad |
| April 12 |
Problem 3 from the 1992 IberoAmerican Mathematical Olympiad |
| April 12 |
Problem 2 from the 2007 British Mathematical Olympiad |
| April 9 |
Sine and Cosine of 15 Degrees Angle |
| April 8 |
Equal Areas in Equilateral Triangle |
| April 6 |
Angle Bisector in Equilateral Trapezoid |
| April 6 |
Problem 1 of the 2010 China Mathematical Olympiad |
| April 5 |
Two Lines - Two Circles |
| April 4 |
What Is Line? |
| April 4 |
What Is Point? |
| April 1 |
Problem 7 of the Canadian Mathematical Olympiad 1971 |
| March 31 |
Problem 2 of the Canadian Mathematical Olympiad 2010 |
| March 31 |
Problem 3 of the Balkan Mathematical Olympiad 1988 |
| March 30 |
Properties of GCD and LCM |
| March 29 |
GCD and LCM by Plain Factorization |
| March 26 |
Common Multiples and the Least Common Multiple |
| March 25 |
Factors And Multiples |
| March 24 |
IMO 1998 Problem 1 |
| March 22 |
Cantor-Bernstein-Schroeder theorem, a Second Proof |
| March 17 |
Addition and Subtraction Formulas for Sine and Cosine III |
| March 17 |
Linear System with Parameter |
| March 16 |
Listing All the Composite Numbers |
| March 16 |
Lucky Numbers |
| March 12 |
Factorial Products |
| March 11 |
Function in the Plane That Vanishes |
| March 10 |
The Size of a Class: Two Viewpoints |
| March 9 |
Less than, Equal to, Greater Than Symbols |
| March 9 |
Points Generated by the Nine Points |
| March 8 |
Tangent Lines and Circles in Convex Quadrilateral |
| March 7 |
The Ballot Lemma |
| March 5 |
The Reflection Lemma |
| March 4 |
Getting a Scout out of Desert |
| March 3 |
Random Walks |
| March 2 |
Van Schooten's Locus Problem |
| March 2 |
Square out of a Quadrilateral |
| Feb 27 |
Diagonal Argument |
| Feb 25 |
A Trigonometric Solution to a Difficult Sangaku Problem |
| Feb 24 |
A Possibly First Proof of the Concurrence of Altitudes |
| Feb 24 |
Patterns in Pascal's Triangle |
| Feb 23 |
Construction of Pascal's Triangle |
| Feb 23 |
Short Construction of the Geometric Mean |
| Feb 22 |
Treatise on Arithmetical Triangle |
| Feb 19 |
A Fair Game of Chance |
| Feb 19 |
Isosceles Tetrahedron |
| Feb 13 |
Concyclic Points in Bride's Chair |
| Feb 13 |
Joseph Keech in Bride's Chair |
| Feb 12 |
New Proof of Euclid's Theorem |
| Feb 12 |
Properties of the Figures in Euclid I.47 |
| Feb 11 |
Four Crossing Circles |
| Feb 10 |
Two Circles on Angle Bisector |
| Feb 10 |
Coaxal Circles on Perpendicular Bisector |
| Feb 6 |
Equal Chords in Crossing Circles |
| Feb 6 |
Parallel Chords in Crossing Circles |
| Feb 3 |
Monty Hall Problem Redux |
| Jan 31 |
Monty Hall Dilemma's Simulation |
| Jan 30 |
The Plain Butterfly Theorem |
| Jan 29 |
Proof 18 of the Butterfly Theorem |
| Jan 28 |
Unproperty of the Powers of 2 |
| Jan 27 |
The Local-Global Principle |
| Jan 25 |
Infinitude Of Primes From Legendre's Formula |
| Jan 25 |
Legendre's Formula |
| Jan 24 |
Half Turn, Reflection in Point |
| Jan 23 |
Clubs in a Vector Space |
| Jan 21 |
Triangulating Squares |
| Jan 20 |
A Proof of the Coincidence of Altitudes by W. Chapple (1749) |
| Jan 19 |
p-adic Expansions |
| Jan 18 |
p-adic Numbers |
| Jan 18 |
What Is Space Completion? |
| Jan 15 |
Line through a Point in an Angle |
| Jan 13 |
Mutually (Jointly) Independent Events |
| Jan 12 |
Morley's Trisector Theorem: Proof by R. J. Webster |
| Jan 12 |
Morley's Trisector Theorem: Proof by H. D. Grossman |
| Jan 11 |
However You Solve It ... A Wonderful Equation |
| Jan 11 |
Trigonometry by Paper Folding |
| Jan 10 |
Isoperimetric Property of Equilateral Triangles |
| Jan 10 |
Maximum Area Property of Equilateral Triangles |
| Jan 9 |
Sangaku with Quadratic Optimization |
| Jan 7 |
Equilateral Triangle on Parallel Lines |
| Jan 5 |
Circles with Equal Collinear Chords |
| Jan 3 |
Translated Triangles |
| Jan 2 |
Find a Common Chord of Given Length |
| Jan 1 |
Equilateral and 3-4-5 Triangles |
