| Dec 30 |
Building Bridges |
| Dec 29 |
Join Circles by Given Segment |
| Dec 23 |
Review of Prime Curios: The Dictionary of Prime Number Trivia |
| Dec 21 |
Is .999... = 1? A Non-standard View |
| Dec 17 |
Problem 4, 1975 USA Math Olympiad: The Final Touch |
| Dec 15 |
Two Circles and Two More |
| Dec 14 |
Secant, Normal, Tangent |
| Dec 12 |
Two Circles and One More |
| Dec 11 |
Problem 4, 1975 USA Math Olympiad: Normals and Tangents |
| Dec 11 |
Problem 4, 1975 USA Math Olympiad and Isosceles Triangles |
| Dec 9 |
Rabbits Reproduce; Integers Don't |
| Dec 9 |
Four Weighings Suffice |
| Dec 9 |
All Powers of x are Constant |
| Nov 28 |
Problem 4, 1975 USA Math Olympiad and the Radical Axis |
| Nov 26 |
Changing Colors II |
| Nov 25 |
Long Up Short Down |
| Nov 25 |
Sums Of Successive Squares |
| Nov 21 |
What Is Absolute Value? |
| Nov 20 |
Make It All Zeros |
| Nov 18 |
GCD and LCM via Factoring |
| Nov 17 |
Euclid's Algorithm: An Interactive Illustration |
| Nov 17 |
Factoring with the Factor Tree |
| Nov 14 |
Compare Fractions: Interactive Practice |
| Nov 12 |
Nested Subsets |
| Nov 12 |
Napoleon's Theorem: A third proof with complex numbers |
| Nov 11 |
Shifting Digits and a Point of View |
| Nov 11 |
Tangent as a Radical Axis |
| Nov 10 |
APMO 1995 Problem 3 |
| Nov 10 |
The Size is in the Eyes of the Beholder |
| Nov 9 |
Base (Binary, Decimal, etc.) Converter |
| Nov 8 |
Ambassadors at a Round Table |
| Nov 7 |
USA 1975 Problem 4 |
| Nov 5 |
Importance of the Absolute Value |
| Nov 4 |
APMO 2002 Problem 3 |
| Nov 4 |
USA 1975 Problem 3 |
| Nov 2 |
Archimedes' Law of the Lever |
| Oct 31 |
Sine of a Sum Formula |
| Oct 30 |
Addition and Subtraction Formulas for Sine and Cosine II |
| Oct 30 |
Addition and Subtraction Formulas for Sine and Cosine |
| Oct 29 |
Chasing Angles in Pascal's Hexagon |
| Oct 28 |
Theorems of Ceva and Menelaus, an Illustrated Generalization |
| Oct 27 |
Simultaneous Generalization of the Theorems of Ceva and Menelaus |
| Oct 26 |
Trigonometric Proof of the Pythagorean Theorem |
| Oct 25 |
Escher's Theorem |
| Oct 24 |
Inequality from Math Magazine 2009 |
| Oct 24 |
Lagrange's identity, Proof |
| Oct 24 |
Fermat Points and Concurrent Euler Lines II |
| Oct 22 |
Fermat Points and Concurrent Euler Lines I |
| Oct 22 |
Some Properties of Napoleon's Configuration |
| Oct 20 |
Mixing maths and fiction for a higher purpose |
| Oct 19 |
Scheduling and Critical Path Algorithm |
| Oct 17 |
Problem 3, APMO 1989 |
| Oct 15 |
Problem 4, APMO 1995 |
| Oct 12 |
Ptolemy on Hinges |
| Oct 12 |
Jan Stevens' proof of E. W. Dijkstra's Generalization of the Pythagorean theorem |
| Oct 9 |
Traveling Salesman Problem |
| Oct 8 |
APMO 1991 Problem 1 |
| Oct 5 |
Finding Hamilton Paths and Circuits |
| Oct 4 |
Method of Markers II |
| Oct 1 |
Problem A2, 69th Putnam Competition |
| Oct 1 |
Problem A1, 69th Putnam Competition |
| Sept 30 |
Rational Points On a Circle |
| Sept 29 |
A Sushi Morsel |
| Sept 29 |
Rhombus in a Cyclic Quadrilateral |
| Sept 29 |
Proof #82 of the Pythagorean theorem |
| Sept 27 |
Fleury's Algorithm and Euler's Paths and Cycles |
| Sept 24 |
Five Methods of Apportionment |
| Sept 20 |
Hunting Right Angles |
| Sept 16 |
An Identity in a Regular Heptagon |
| Sept 15 |
Fair Division: Method of Sealed Bids II |
| Sept 10 |
APMO 2003, Problem 2 |
| Sept 6 |
Sum of Squares of Distances to Vertices |
| Sept 4 |
Distance between the Orthocenter and Circumcenter |
| Sept 3 |
APMO 1998, Problem 4 |
| Sept 2 |
APMO 2004, Problem 2 |
| Aug 29 |
Geometric Optimization from the Asian Pacific Mathematical Olympiad |
| Aug 29 |
Yet Another Puzzle with Hats |
| Aug 28 |
Banzhaf Power Index Calculator |
| Aug 28 |
Shapley-Shubik Power Index Calculator |
| Aug 17 |
Four Voting Methods |
| Aug 17 |
Simple Graph Practice |
| July 26 |
Cabart's Collinearity |
| July 26 |
Napoleon-Barlotti Theorem |
| July 23 |
Napoleon's Relatives |
| July 22 |
Three Dimensional Cross |
| July 21 |
Napoleon on Hinges |
| July 20 |
Cavalieri's Principle |
| July 19 |
Problem 1 from the IMO 2009 |
| July 19 |
Problem 4 from the IMO 2009 |
| July 14 |
Mechanical Proofs of the Pythagorean Theorem |
| July 14 |
Invariant Area Sweep Implies Pythagorean Theorem |
| July 9 |
Uncountability of the Reals - via a Game |
| July 6 |
Integer Iterations on a Circle III |
| July 5 |
Minumum Spanning Trees and Kruskal's Algorithm |
| July 2 |
Structure of Hyperreal Numbers |
| June 29 |
One Dimensional Ants |
| June 19 |
What Is Demagoguery? |
| June 17 |
Hyperintegers and Hyperreal Numbers |
| June 9 |
Models and Metamathematics |
| June 5 |
Fibonacci's Quickies |
| June 1 |
May the Product of Planes Be a Sphere? |
| May 31 |
Dollars in Pockets |
| May 31 |
One Trigonometric Formula and Its Consequences |
| May 29 |
Bimedians in a Regular Tetrahedron |
| May 29 |
Two Parallels in a Triangle and One More |
| May 28 |
Clifford Algebras |
| May 27 |
A better solution to a difficult sangaku problem |
| May 27 |
A Restored Sangaku |
| May 26 |
Probability of Divisibility |
| May 26 |
Product of Simple Fractions |
| May 26 |
IMO 2007, Problem 2, solution by Vo Duc Dien |
| May 25 |
Sum of Squares in Equilateral Triangle |
| May 21 |
Bisection of Yin and Yang |
| May 19 |
Counting Squares in a Square |
| May 15 |
A Review of Pythagoras' Revenge by Arturo Sangalli |
| May 15 |
A Line in a Square Grid |
| May 14 |
Two Color Coloring of the Plane |
| May 11 |
Two Sangaku with Equal Incircles |
| May 8 |
Formal Systems - an Example |
| May 5 |
GCD(M, N) × LCM(M, N) = M × N |
| May 4 |
What Is Fraction? |
| May 3 |
Fraction Comparison |
| Apr 29 |
Gödel's Incompleteness Theorem |
| Apr 29 |
Theories and Proofs |
| Apr 28 |
Morley's Theorem, Proof by R. Smyth |
| Apr 27 |
Napoleon's Theorem via Two Rotations |
| Apr 26 |
Morley's theorem, Proof by Nolan L Aljaddou |
| Apr 23 |
Möbius' Strip |
| Apr 11 |
Intuitive Probability |
| Apr 10 |
Dawson's Kayles |
| Apr 10 |
Dawson's Chess |
| Apr 3 |
On the Games of Hex and Y |
| Apr 3 |
Infinitesimals. Non-standard Analysis |
| Apr 2 |
Infinitude of Primes - A Topological Proof without Topology |
| Apr 1 |
A Triangle of Antreas Hatzipolakis |
| Mar 31 |
Six Concyclic Points II |
| Mar 30 |
Solutions to the Third Millennium Olympiad |
| Mar 29 |
Grebe: from Ladies' Diary to Carroll's Pillow |
| Mar 25 |
A Parallelogram in Triangle |
| Mar 24 |
Is Every Trapezoid Parallelogram? |
| Mar 23 |
On the Difference of Areas |
| Mar 21 |
Matrix Groups |
| Mar 18 |
Number 8 Is Interesting |
| Mar 14 |
Iterations on a Circle Through Three Points |
| Mar 14 |
Pigeonhole in Clubs |
| Mar 8 |
Angles in a Cube III |
| Mar 7 |
Squares in Circles |
| Mar 7 |
Circles with Tangent Diameters |
| Mar 3 |
Four Hinged Squares: using complex numbers |
| Feb 28 |
A Minesweeper Theorem |
| Feb 20 |
Proof 19 of irrationality of √2 |
| Feb 17 |
Angles in a Cube I |
| Feb 17 |
Angles in a Cube II |
| Feb 12 |
Pascal: Necessary and Sufficient |
| Feb 6 |
Butterflies in Hyperbola |
| Feb 4 |
Problem 5 from IMO 2004 |
| Feb 4 |
Morley's theorem, a proof by B. Stonebridge |
| Feb 2 |
Urquhart's theorem - From Leningrad Mathematical Olympiad |
| Jan 31 |
An Inequality for Grade 8 |
| Jan 30 |
Proof 81 of the Pythagorean theorem |
| Jan 29 |
Morley's theorem, B. Bollobás' proof |
| Jan 27 |
Stereographic Projection |
| Jan 23 |
Problem 1 from IMO 2006 |
| Jan 20 |
Irrationality of √2, Proof #14 and Proof #8'' |
| Jan 18 |
Tangent Circles and an Isosceles Triangle II |
| Jan 17 |
Problem 4 from IMO 2007, Solution VII |
| Jan 16 |
Three Pyramids are Better Than Two |
| Jan 15 |
Orthocenter and Three Equal Circles |
| Jan 14 |
Equal Circles, Medial Triangle and Orthocenter |
| Jan 13 |
Cut the Cube |
| Jan 13 |
Cut the Cylinder |
| Jan 11 |
Cut the Cone |
| Jan 8 |
Between Major and Minor Circles |
| Jan 6 |
An Interesting Example of Angle Trisection by Paperfolding |
| Jan 5 |
Fundamental Theorem of Algebra: A Simple Complex Analysis Proof and An Advanced Calculus Proof |
| Jan 3 |
Irrationality of √2, Proof #17, Proof #18, Proof #19 |
| Jan 2 |
Construction of Conics from Pascal's Theorem |
| Jan 1 |
Irrationality of √2, Proof #16 |
