December 31 
MacLaurin's Construction of Conics 
December 26 
Chasles' Theorem, a Simple Proof 
December 25 
What Is Ellipse? 
December 25 
Focus and Directrix of Ellipse 
December 25 
Focal Definition of Ellipse 
December 24 
Conjugate Diameters in Ellipse 
December 22 
Bisector of an imaginary angle may be real 
December 21 
Angle Bisectors in Ellipse II 
December 20 
Infinite Discent for x^{4} + y^{4} = z^{4} 
December 20 
Ellipse Between Two Circles 
December 19 
Pairs of Homologous Lines under Spiral Similarities 
December 17 
NoPedal Collinearity 
December 17 
Angle Bisectors in Ellipse 
December 17 
Spiral Similarity 
December 16 
Fermat's Little Theorem 
December 16 
Pencils of Cubics 
December 16 
Three Tangents, Three Chords in Ellipse 
December 15 
Urquhart's Theorem For And By Conics 
December 12 
Miquel's Theorem for Circles 
December 12 
SixPoints, ThreeLines 
December 10 
Thébault's Problem IV 
December 9 
Homologous Lines under Three Spiral Similarities 
December 7 
Derivatives without Limits 
December 7 
Sum without Adding 
December 7 
Stereographic Projection and Inversion 
December 6 
Proof #80 of the Pythagorean theorem 
December 5 
Product Of Four Consecutive Integers 
December 2 
Cubic Formula 
November 25 
Morley's Theorem: Proof by B. Stonebridge and B. Millar 
November 24 
Regular Polyhedra: Tetrahedron, Octahedron, Cube, Icosahedron, Dodecahedron 
November 23 
Nested Radicals 
November 23 
Monotone Convergence Theorem 
November 22 
Possible or Impossible? 
November 19 
Given Parabola, Find Axis 
November 19 
Parallel Chords in Ellipse 
November 18 
Pedal Collinearities 
November 17 
Two Simsons in a Triangle 
November 17 
Infinite Rod 
November 16 
Generalization That Solves the Problem 
November 9 
What Is Symmetry? 
October 30 
What Is Percent? 
October 28 
A Market Day 
October 27 
Review of The Princeton Companion to Mathematics 
October 26 
The Many Ways to Construct a Triangle IV 
October 22 
Newton's Method by Newton 
October 19 
Newton's Method 
October 18 
Four Touching Circles III 
October 17 
Four Touching Circles II 
October 13 
Riemann Sphere and Möbius Transformation 
October 8 
Stereographic Projection of a Coffin Problem 
October 4 
Stereographic Projection and Radical Axes 
October 4 
Bevan's Point and Theorem 
October 3 
What Is Abstraction? 
October 2 
Shearing Butterflies in Quadrilaterals 
October 1 
Construction of a Triangle from the Circumcenter, Orthocenter and Incenter 
September 22 
Review of Kiselev's Geometry: Book II. Stereometry 
Septembe 21 
Fermat point and 9point Centers 
Septembe 21 
Principle of Proportionality 
Septembe 20 
120° Breeds 90° 
Septembe 20 
Four Centroids and Parallels 
September 18 
Graph and Roots of a Third Degree Polynomial 
September 17 
Graph and Roots of Quadratic Polynomial 
September 16 
Completing a Square and Quadratic Formula 
September 13 
Why a Diameter Is the Longest Chord? 
September 12 
Projective infinity 
September 11 
Infinity in Compactification 
September 10 
Five Concyclic Points 
September 9 
6 to 9 Point Circle 
September 7 
Y. Sawayama's Theorem 
September 6 
Circles Tangent to Circumcircle 
September 5 
Geometric Proof of Wilson's Theorem 
September 3 
Divisibility and Modulo Arithmetic at IMO 2007 
September 3 
Proof #79 of the Pythagorean Theorem 
September 2 
A Clique of Acquaintances 
September 2 
Round Robin Tournament 
August 29 
Bulls and Cows,
Vowel Movement,
Thugs and Bowmen

August 26 
Triangles with Equal Area, Solutions 5 and 6 
August 26 
Angle Bisector in Parallelogram 
August 25 
Triangles with Equal Area, Solutions 2, 3, 4 
August 24 
Triangles with Equal Area 
August 22 
Six Concyclic Points 
August 21 
Circles through the Orthocenter 
August 15 
Two Intersecting Circles 
August 14 
Concyclic Points in Equilateral Bumps 
August 13 
Review of Arithmetic for Parents: A Book for Grownups about Children's Mathematics by R. Aharoni 
August 8 
Diameters and Chords 
August 8 
A Line in Triangle Through the Circumcenter 
July 30 
Geometric Construction of Roots of Quadratic Equation 
July 24 
How to Ask an Embarrassing Question 
July 23 
Review of Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills by P. Nahin 
July 22 
Review of Duelling Idiots and Other Probability Puzzlers by P. Nahin 
July 21 
What Is Limit? 
July 18 
Surreal Numbers 
July 14 
Review of The Mathematician's Brain by David Ruelle 
July 11 
What Is Algorithm? 
July 10 
What Is Calculus? 
July 9 
Review of The Calculus Gallery: Masterpieces from Newton to Lebesgue by William Dunham 
July 2 
Right Replacement 
June 27 
Butterfly in Ellipse 
June 25 
Shaggy Dog Theorem 
June 24 
Proofreading Example 
June 23 
Binomial Distribution 
June 22 
Bernoulli Trials 
June 19 
Pinning Butterfly on Radical Axes 
June 10 
Algorithm for Computing LCM 
June 7 
CantorBernsteinSchroeder theorem 
June 5 
Gergonne and Soddy Lines Are Perpendicular 
June 3 
Chess Players Truel 
June 3 
Weitzenböck Inequality 
June 1 
Ordinal Numbers 
May 30 
Order. Wellordered sets. 
May 28 
Cardinal Numbers 
May 21 
Review of A Course in the Geometry of n Dimensions 
May 13 
Infinity As a Limit 
May 12 
Projective Generalization of Maxwell's Theorem 
May 11 
Projective Proof of Maxwell's Theorem 
May 10 
What Is Infinity? 
May 8 
345 Triangle by a Kid 
May 7 
Bayes' Theorem 
May 6 
Trigonometric Functions 
May 6 
What Is Trigonometry? 
May 5 
The Lepidoptera of the Quadrilateral II 
May 5 
3D Quadrilateral  a Coffin Problem 
May 5 
Maxwell Theorem via the Center of Gravity 
May 2 
Japanese Art and Mathematics 
May 1 
A Sangaku by a Teen 
May 1 
Review of Sacred Mathematics: Japanese Temple Geometry 
May 1 
Peacock's Tail Sangaku 
April 30 
Circles and Semicircles in Rectangle 
April 30 
Four Hinged Squares 
April 28 
Neuberg Sangaku 
April 25 
What Is Analytic Geometry? 
April 25 
Guessing Two Consecutive Integers 
April 24 
A Certain Ambiguity 
April 22 
Sangaku with Three Mixtilinear Circles 
April 16 
Continuous Sample Spaces 
April 15 
Conditional Probability and Independent Events 
April 10 
Square in Chair 
April 9 
E. W. Dijkstra's Proof of the Pythagorean Theorem 
April 6 
Paper Folding & Cutting Sangaku 
April 3 
Gion Shrine Problem 
April 3 
A 49^{th} Degree Challenge 
April 2 
Another simple integral 
March 31 
Vecten's Mesh 
March 29 
Touching Circles and Concurrency 
March 28 
Pappus' Generalization of Euclid I.47 
March 23 
Isoperimetric Theorem for Rectangles 
March 17 
Sangaku: Critique of My View and a Response 
March 17 
Construction of a Triangle from Two Vertices and the Centroid 
March 2 
Another proof of irrationality of √N 
March 2 
Boys and Girls Solving Problems 
February 25 
Huygens' proof of the Pythagorean Theorem 
February 21 
Three Congruent Circles by Reflection III 
February 20 
Fermat's Point, Solution #7 
February 19 
Fermat's Point, Solution #6 
February 18 
Gergonne in Ellipse 
February 17 
Seven Circles Theorem 
February 13 
Expectation 
February 10 
A Hard but Important Sangaku 
February 6 
Fundamental Theorem of Algebra  Yet Another Proof 
February 2 
Concyclic Points in a Triangle 
January 29 
Two Congruent Circles by Reflection 
January 27 
Independent Events and Independent Experiments 
January 26 
Fuss' Theorem 
January 26 
Intouch Triangle in Poncelet Porism 
January 26 
Extouch Triangle in Poncelet Porism 
January 25 
Euler's Formula and Poncelet Porism 
January 22 
Three Congruent Circles by Reflection II 
January 21 
Three Congruent Circles by Reflection 
January 12 
Zeros and Nines 
January 8 
Random Variables 
January 7 
Chevalier de Méré's Problem 
January 6 
Dependent and Independent Events 
January 5 
Conditional Probability 
January 4 
Geometric view of the Sieve of Eratosthenes 
January 1 
Pythagorean Theorem: J. Adams' Proof by Dissection 