| 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 x4 + y4 = z4 |
| December 20 |
Ellipse Between Two Circles |
| December 19 |
Pairs of Homologous Lines under Spiral Similarities |
| December 17 |
No-Pedal 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 9-point 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 |
Cantor-Bernstein-Schroeder 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. Well-ordered 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 |
3-4-5 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 49th 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 |
