| 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 |
