Note: I have placed chronology of updates for 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006 and 2007 into separate files. Starting with 1997, the most recent entries appear topmost. Besides providing an insight into this site's evolution, chronology of updates may be used for word searches.

 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