Dec 27 |
Infinitude of Primes - An Impossible Injection |

Dec 23 |
Prime Sums in Pairs |

Dec 23 |
Bertrand's Postulate - Paul Ërdos' First Published Paper |

Dec 22 |
Infinitude of Primes - via Bertrand's Postulate |

Dec 20 |
The Forgotten Art of Spherical Trigonomtery |

Dec 17 |
Infinitude of Primes - via Fibonacci Numbers |

Dec 16 |
Legendre's Theorem - The Prime Factorization of Factorials |

Dec 15 |
Lame's Theorem - First Application of Fibonacci Numbers |

Dec 12 |
The Law of Cosines - Another PWW |

Dec 11 |
Similarity Is About Proportion - And Ways to Look at It |

Dec 11 |
Property of Internal Angle Bisector - Hubert Shutrick's PWW |

Dec 4 |
The Cosine Law by Similarity |

Dec 1 |
Analytic Proof of Bottema's Theorem |

Nov 30 |
A Compass Only Construction - A Chord Tangent to an Inner circle |

Nov 26 |
Concurrency of Medians and Medial Triangles |

Nov 25 |
Properties of Flank Triangles |

Nov 24 |
A Property of Angle Bisectors III |

Nov 23 |
A Degenerate Case of Bottema's Configuration |

Nov 22 |
Orthic Semiperimeter |

Nov 22 |
Intersecting Chords Theorem - Hubert Shutrick's PWW |

Nov 21 |
Review of The Fractalist - Memoir by B. Mandelbrot |

Nov 19 |
24 with One Digit |

Nov 16 |
Intersecting Chords Theorem - a Visual Proof |

Nov 15 |
Pythagorean Identity and ODEs |

Nov 14 |
The Pythagorean Theorem from a Combinatorial Identity |

Nov 13 |
Ptolemy Theorem - Proof Without Word |

Nov 13 |
Midline in Quadrilateral |

Nov 12 |
Midline in Trapezoid |

Nov 11 |
Midline in Triangle |

Nov 10 |
Thales' Theorem |

Nov 9 |
Triangle Construction from Angle, Altitude and Median |

Oct 26 |
Irrationality from a Limit Lemma |

Oct 25 |
Expansion of Integers in an Integer Base |

Oct 24 |
Highway Musings |

Oct 23 |
The Best Writing on Mathematics |

Oct 22 |
A Property of the Power of 5 |

Oct 17 |
Graphing Equations Is Useful, IV |

Oct 17 |
Graphing Equations Is Useful, III |

Oct 17 |
Another Face and Proof of a Trigonometric Identity |

Oct 15 |
The Half-Life of Facts and Phase Transitions |

Oct 13 |
Binomial Theorem |

Oct 12 |
Volume of a Paraboloid of Revolution |

Oct 12 |
Volume of a Hyperboloid of Two Sheets |

Oct 12 |
Volume of a Hyperboloid of One Sheet |

Oct 11 |
Volume of a Paraboloid |

Oct 11 |
Volume of a Sphere and Volume of an Ellipsoid |

Oct 11 |
Area, Sector Area, and Segment Area of an Ellipse |

Oct 11 |
A Generalized Cavalieri-Zu Principle |

Oct 10 |
Pythagorean Theorem : A Variant of Proof by Tessellation |

Oct 8 |
Graphing Equations Is Useful, II |

Oct 8 |
Graphing Equations Is Useful |

Oct 4 |
A System of Equations Begging for Generalization |

Oct 4 |
Folding Square in a Line through the Center |

Oct 4 |
Review of Which Numbers Are Real? by Michael Henle |

Sep 26 |
Seven integers under 127 and their Ratios |

Sep 25 |
Review of A Mathematical Orchard: Problems and Solutions |

Sep 24 |
The Basics of Infinite Descent |

Sep 24 |
Guesstimation and Guesstimation 2.0 |

Sep 23 |
Tiling a 12x12 Square with Straight Trominoes |

Sep 22 |
Fermat's Only Published Proof |

Sep 21 |
What Is Infinite Descent? |

Sep 20 |
Area of Parallelogram Formula by Shearing |

Sep 20 |
Parallelogram and Ellipses |

Sep 20 |
Proof #98 of the Pythagorean theorem |

Sep 19 |
A Magical Incident due to the Paypal's Policy |

Sep 16 |
Candy Game (Change Discharged) |

Sep 14 |
Binet's Formula with Cosines |

Sep 14 |
Review of Fibonacci and Catalan Numbers: An Introduction by Ralph Gribaldi |

Sep 9 |
Butterfly with Menelaus |

Sep 8 |
Butterfly in Kite |

Aug 16 |
Lipogrammatic Proof of the Pythagorean Theorem |

Aug 15 |
Butterfly Trigonometry |

Aug 14 |
The 5 Elements of Effective Thinking |

Aug 13 |
Multifaceted Cork |

Aug 8 |
Leonardo's Petals |

Aug 7 |
Four Incircles in an Equilateral Triangle, a Sangaku |

Aug 7 |
Evolution of a problem and an answer II |

Aug 2 |
Evolution of a problem and an answer |

Aug 1 |
A second solution to Problem from 2012 IMO |

Aug 1 |
Evolution of a problem and an answer |

July 29 |
GCD of Fibonacci Numbers |

July 26 |
Fibonacci Idendtities with Matrices |

July 25 |
Number of Trials to First Success |

July 24 |
Flatland 2: Sphereland |

July 21 |
Neuberg Cubic |

July 19 |
Another Geometry Problem from 2012 IMO - Problem 1 |

July 18 |
A Geometry Problem from 2012 IMO - Problem 5 |

July 18 |
A Functional Equation from the 2012 IMO |

July 13 |
Cevian triangle of the Cevian triangle |

July 11 |
The Shape of the Colosseum |

July 11 |
Construction of an Oval - the Roman Way |

July 4 |
Cassini's Identity |

July 3 |
Candido's Identity |

July 2 |
Fibonacci Numbers Trick |

July 2 |
An Engaging Algebraic Identity |

June 30 |
Two Pairs of Parallel Lines in a Triangle |

June 26 |
Parallel Lines in a Triangle upgraded |

June 24 |
Parallel Lines in a Triangle |

June 22 |
Desargues' Hexagon |

June 21 |
More Trigonometric Proofs of the Pythagorean Theorem |

June 14 |
Curious Identities In Pythagorean Triangles |

June 14 |
A review of A Cultural History of Physics by Karoly Simonyi |

June 10 |
Vertical and Horizontal Dominoes on a Chessboard |

June 9 |
Archimedes' Law of Buoyancy |

June 8 |
Serendipity and Luck |

June 7 |
A Kindergarten Activity As a Problem for Adolescents |

June 7 |
Two Perspective Triangles |

June 5 |
On Dedekind Cuts |

June 2 |
Square Root of 2 as a Continued Fraction |

May 28 |
Vecten-Nikolin Hexagon |

May 26 |
Optimization in a Crooked Trapezoid |

May 26 |
Indivisibles and Infinitesimals |

May 25 |
Huygens' Problem |

May 25 |
Distance Between Projections |

May 25 |
Residence at an Optimal Distance |

May 24 |
Three Checker Game on a One Row Board |

May 23 |
A Crooked Polygon |

May 21 |
Butterflies in Similar Co-axial Conics |

May 21 |
Engaging Math Activities for the Summer Break |

May 21 |
Parity Games |

May 20 |
X and the City - a Review |

May 19 |
How Fast Does One's Shadow Grow? |

May 15 |
Areal Butterflies |

May 15 |
The Weierstrass Substitution |

May 14 |
Geometric Proofs Of the Irrationality of Square Roots |

May 13 |
Gauss' Lemma |

May 12 |
Proof #97 of the Pythagorean theorem |

May 11 |
A Hundred Years War |

May 10 |
Escher the Mathematician |

May 8 |
Spilling Molasses and Defying Conservation Laws |

Apr 28 |
Sums and Products, a Generalization |

Apr 27 |
Poincare And Standardized Testing |

Apr 26 |
A Review of Dana Mackenzie's "The Universe in Zero Words" |

Apr 25 |
When Friends Are Right |

Apr 24 |
Euclidean Constructions vs Ruler And Compass |

Apr 22 |
Regarding the Mess We Are In |

Apr 20 |
Probability Paradoxes |

Apr 19 |
The Regula Falsi - Iterated |

Apr 19 |
The Secant Method |

Apr 18 |
A Representation of Rational Numbers |

Apr 18 |
A Middle School Problem from a Moscow Olympiad |

Apr 17 |
An Anti-cultural Aspect of Consructivism |

Apr 16 |
When Two Wrongs Make One Right |

Apr 5 |
Review of The Lost Millennium |

Mar 29 |
Chinese Remainder Theorem: an Application to Chronology |

Mar 24 |
Binet's Formula via Generating Functions |

Mar 23 |
Binet's Formula by Induction |

Mar 18 |
Decimal Sums of Successive Integers |

Mar 17 |
A Note on Cavalieri's Indivisibles |

Mar 16 |
Pinocchio as Epimenides |

Mar 14 |
Generating Functions from Recurrences |

Mar 12 |
The Joy of Homogeneity, a Sequel |

Mar 10 |
Review of Beautiful Mathematics by Martin Erickson |

Mar 7 |
Laplace's Rule of Succession |

Mar 6 |
Short Runs from an Urn |

Mar 6 |
Gauss and Euler Integrals |

Mar 5 |
Plane Isometries As Complex Functions |

Feb 28 |
Conditional Probability of Recurrence |

Feb 27 |
Quadrilateral from a Segment |

Feb 26 |
Is the Triangle Inequality Necessary? |

Feb 24 |
The Joy of Homogeneity |

Feb 21 |
Mathematical Legends |

Feb 20 |
Probability of Two Integers Being Coprime |

Feb 20 |
Can one learn from people who do not know what they are talking about? |

Feb 19 |
Mach's Conservation of Area and the Pythagorean Theorem |

Feb 19 |
Thought Provokers to Start a Class With, VI |

Feb 15 |
An Extra Illustration of J. E. Bottcher's Proof of the Pythagorean Theorem |

Feb 14 |
Watt's and Chebyshev's Linkage |

Feb 12 |
Polygonal Ears and Triangulation Duals |

Feb 10 |
Meisters' Two Ears Theorem |

Feb 6 |
Bimedians and Diagonals in a Quadrilateral |

Feb 4 |
The Concurrency of the Altitudes in a Triangle - Trigonometric Proof |

Feb 4 |
An Extension of the AM-GM Inequality: A second look |

Feb 1 |
Existence of the Incenter: a Second Look |

Feb 1 |
Medians in a Triangle Meet at the Center: a Second Look |

Jan 31 |
An Extension of the AM-GM Inequality |

Jan 30 |
Altitudes Concur at a Point: a Second Look |

Jan 24 |
Finding a Parallelogram in 3D |

Jan 23 |
Two Planar Constructions Related to a 3D Problem |

Jan 21 |
An Equation in Radicals |

Jan 19 |
Griffiths' Theorem |

Jan 17 |
Review of InsurmountableSimplicities: Thirty-nine Philosophical Conundrums |

Jan 12 |
Integers With Digits 1 and 2 and Residues Modulo Powers of 2 |

Jan 10 |
Fibonacci Tilings |

Jan 9 |
Rolle's Theorem in Action |

Jan 7 |
Divisibility by Powers of 2 |

Jan 6 |
Propositiones ad acuendos juvenes |

Jan 3 |
Sylvester's Problem, a Second Look |

Jan 2 |
Trigonometric Identities with Arctangents |

Jan 1 |
Negative Coconuts |