Chronology of Updates


I have placed chronology of updates for 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, and 2011 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.

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

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Copyright © 1996-2017 Alexander Bogomolny


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