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 |