Chronology of Updates


I have placed chronology of updates for 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 and 2010 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 29 Vector proof of Monge's Theorem of three circles
Dec 28 Concyclicity in Rectangle
Dec 25 In Pursuit of the Traveling Salesman
Dec 24 Sample Probability Problems from AMC
Dec 24 Property of Semicircles
Dec 22 The Contest Problem Book I-IV
Dec 21 Star of David Theorems in Pascal Triangle
Dec 20 Two Cevians and Proportions in a Triangle
Dec 16 Mathematics and Physics in the car market
Dec 16 Fermat's Like Equation
Dec 16 Viviani by Vectors
Dec 15 Review of How To Fold It by J. O'Rourke
Dec 13 Pantograph
Dec 13 What Is Linkage?
Dec 8 Probabilistic Method
Dec 7 A problem for the innocent minds
Dec 4 What Is Random?
Dec 3 Gauss' theorem on constructibility of regular polygons
Dec 2 Review of Leonardo's Mirror and The Monty Hall Probalem by Ivan Moscovich
Dec 1 Review of An Invitation to Mathematics by Dierk Schleicher and Malte Lackmann
Nov 28 Serendipitous Proofs Of The Pythagorean Theorem
Nov 27 Solve the equation cos^n(x) - sin^n(x) = 1
Nov 27 cos(pi/7)-cos(2pi/7)+cos(3pi/7) = 1/2
Nov 22 Collinearity via Concyclicity
Nov 20 Collinearity with the Orthocenter
Nov 17 Orbital Resonance and the Existence of Irrational Numbers
Nov 15 A Newly Born Pair of Siblings to Archimedes' Twins
Nov 11 On the Perimeters of Embedded Polygons
Nov 11 The Extreme Principle
Nov 9 A Proof of the Pythagorean Theorem with Orthocenter and Right Isosceles Triangles
Nov 9 Enchanted by Fascinating Mathematical People
Nov 7 Thought provokers to start a class with, II
Nov 7 Golden Section in Two Equilateral Triangles, II
Nov 6 Golden Section in Two Equilateral Triangles
Nov 5 A Characteristic Property Of Right Triangles
Nov 2 Solve cos2x + cos22x + cos23x = 1
Oct 31 Finicky Diophantine Equations
Oct 31 Given the Probability, Find the Sample Space
Oct 31 Review of Magical Mathematics
Oct 28 Constructive Existence of the de Bruijn Cycles
Oct 27 Existence of the de Bruijn Cycles via Graphs
Oct 27 Euler Cycles in Digraph
Oct 26 Infinitude of Primes Via Lower Bounds
Oct 22 Order and Chaos in Multiple Pendulums
Oct 22 The Parabolic Sieve of Prime Numbers
Oct 22 Tiling a Rectangle with L-tetrominoes
Oct 22 Tiling a Square with T-, L-, and a Square Tetrominoes
Oct 21 Tiling a Square with Tetrominoes Fault-Free
Oct 20 1961 IMO, Problem 4. An exercise in barycentric coordinates
Oct 18 1961 IMO. Problem 1. A system of three equations with two parameters
Oct 18 Curvy Dissection
Oct 16 Dissection of a Vase
Oct 13 A Decomposition of Isosceles Triangles into 4 Isosecles Triangles
Oct 13 1960 IMO, Problem 5: Loci of points in a cube
Oct 11 1959 IMO, Problem 3
Oct 9 Flipping Items Simultaneously III
Oct 7 Geometric Application of Ramsey's Theory
Oct 7 Viete's Formulas
Oct 7 Ramsey Number R(5, 3)
Oct 6 Derivative in Heron's Formula
Oct 5 A Proof by Game for a Sum of a Convergent Series
Oct 4 Tiling a Chessboard with Dominoes
Oct 3 Round Carpets
Oct 3 Review of The IMO Compendium
Oct 3 Angle Trisection
Oct 2 Ramsey Number R(4, 4)
Oct 2 Ramsey Number R(4, 3)
Oct 1 Ramsey Number R(3, 3, 3)
Sep 29 Sylvester's Problem
Sep 27 1962 IMO, Problem 2: an inequality with a twist
Sep 26 1=2 via Continued Fractions
Sep 26 Another proof of the Pythagorean theorem
Sep 23 Viviani in Isosceles Triangle
Sep 20 Majority Judgement: Measuring, Ranking and Electing by Michel Balinski and Rida Laraki
Sep 19 Review of Number-Crunching by Paul H. Nahin
Sep 19 The leapfrog problem - who is right?
Sep 16 Rectilinear Paradox
Sep 13 Finite Sums of Terms 2^(n-i) i^2
Sep 12 Countability of Rational Numbers via Conitnued Fractions
Sep 12 Ptolemy via Cross-Ratio
Sep 11 Countability Principle
Sep 11 Negative on the left, positive on the right: how come?
Sep 11 Physics Minus Mathematics: The Week of Creation
Sep 9 Pythagorean Guess
Sep 8 Asymmetric Propeller
Sep 8 All Integers Are Even
Sep 8 All Powers of 2 Are Equal to 1
Aug 15 One Sheet Hyperboloid
Aug 12 Pairs of Areas in Equilateral Triangle
Aug 11 Review of The Man of Numbers: Fibonacci's Arithmetic Revolution by Keith Devlin
Aug 11 Pompeiu's Theorem
Aug 10 Proof #20 of the Butterfly Theorem
Aug 10 Identities with Triangular Numbers
Aug 10 Involution on the Projective Line
Aug 9 Quadrilateral with 3 Equal Sides
Aug 8 Biblical pi and Gematria
Aug 7 Fixed Point in Isosceles and Equilateral Triangles
Aug 7 Proportions in Square
Aug 7 Review of Viewpoints: Mathematical Perspective and Fractal Geometry in Art by Marc Frantz and Annalisa Crannell
Aug 5 Regular Polygons in a Triangular Grid
July 31 Disapperances a la Sam Loyd
July 29 Fibonacci Numbers in Equilateral Triangle
July 26 Fleas on a Chessboard
July 23 Wisdom of Kozma Prutkov
July 23 Solving an Equation with Inverse Functions
July 21 What Is Finite?
July 17 Cross Points in a Polygon
July 17 White and Black Balls in Urn. 1 in, 2 out. What Color Remains?
July 15 Inverse to a Curious Partition Problem, Correct Solution
July 15 The 80-80-20 Triangle. Inverse to a Curious Partition Problem (Solution with a flaw)
July 11 Three Colors on a Chessboard
July 11 Rooks on a Chessboard
July 8 Coloring a Cube with Subdivided Faces
July 7 Angle Bisectors in a Quadrilateral - Cyclic and Otherwise
July 2 Harmonic Mean in Geometry
June 25 Angle Bisector Theorem
June 25 Filling an Array with 0s and 1s - and Counting
June 24 Shuttle Puzzle Practice II
June 23 David Richeson's Extention of an Old Japanese Theorem
June 19 Three Points Casey's Theorem
June 18 Sum of two Cantor sets
June 18 Casey's Theorem
June 12 Moving Chips in Pairs Down a Checkerboard
June 12 An Olympiad Problem for a Kindergarten Investigation
June 10 Parallel Lines in a Cyclic Quadrilateral
June 9 Butterfly theorem, a Projective Proof
June 9 A Property of the fusc() Function
June 7 Brahmagupta-Mahavira Identities
June 5 Construction of a Cyclic Quadrilateral
June 5 Circle Centers on Radical Axes
June 5 Three Concurrent Circles and Simultaneous Diameters
June 4 PWW: How Geometry Helps Algebra
June 4 Simultaneous Diameters in Concurrent Circles
June 3 Jack D'Aurizio Proof of Sawayama's Lemma
June 2 Area of a Bicentric Quadrilateral
June 1 An Area Inequality
June 1 Brahmagupta's Formula and Theorem
May 31 Simson Line in Disguise
May 30 Terquem's Theorem
May 27 Tromino Puzzle: Deficient Squares
May 25 Vandermonde Determinant
May 24 Divisibility Of Prod-Dif And The Vandermonde Determinant
May 23 Countability of Rational Numbers: PWW
May 23 Covering a Chessboard with a Hole with L-Trominoes
May 21 In Calculus too 1 = 0
May 21 Cyclic Quadrilateral, Concurrent Circles and Collinear Points
May 20 Equal Areas in Regular 2n-gons
May 19 Problems with Many Solutions
May 19 Inclusion-Exclusion Principle: an Example
May 17 Sums of Geometric Series - Proofs Without Words
May 16 Solution #11 to a Classical Problem in the 80-80-20 Triangle
May 15 Two Circles and a Limit - Trigonometric Solution
May 15 The 80-80-20 Triangle Problem, A Derivative, Solution #7
May 15 Number of Factors of an Integer
May 14 Two Circles and a Limit - Analytic Proof
May 12 An Age Conundrum with Men of the Cloth
May 10 Two Problems from a Serbian 7 Grade Math Competition
May 10 Golden Ratio is Irrational
May 8 Cantor's First Uncountability Proof
May 7 Every Parallelogram Is a Rectangle
May 5 Mascheroni Construction of a Regular Pentagon
May 4 Let Them Count by My Boys
May 4 Math Behind Counting
May 1 A Proof Perigal and All Others After Him Missed
April 30 Is a Point a Part of a Line?
April 29 Areas on the Graphs of Power Functions
April 29 Rational Solutions to xy = yx
April 28 An Elementary Proof of Bottema's Theorem
April 22 Four Numbers, Six Differences, GCD of the Products
April 20 Dissection of a Square Pyramid
April 20 Octahedron In Tetrahedron
April 18 50th IMO - 50 Years of International Mathematical Olympiad
April 16 A Multiplicative Identity of Areas in a Triangle
April 15 Invariance in Orthodiagonal Quadrilaterals
April 14 Curious Identities Involving Integer Products
April 11 A Review of Rediscovering Mathematics by Shai Simonson
April 10 Adding a Long List of Numbers
April 6 William Wallace's Proof of the Butterfly Theorem
April 5 Golden Ratio and Midpoints
April 5 From Equilateral Triangle and Square to Golden Ratio
April 4 Sicherman Dice
April 2 Probability Generating Functions
April 2 Hexagons in a Square
April 1 A Review of The Cambridge Dictionary of Statistics
March 30 The Futurama Theorem and Puzzle
March 28 Bear Born on a Tuesday
March 21 Geometry, Algebra, and Illustrations
March 18 Five Digits Magic Prediction
March 18 Four Digits Magic Prediction
March 17 Inequality of a Series of Square Roots
March 16 1089 and a Property of 3-digit Numbers
March 14 Serendipitous Beauty
March 12 Schwarz Lantern
March 10 The Mean Property of the Mean
March 5 Circle Chains on Napoleon Triangles
March 2 The Law of Cosines (Independent of the Pythagorean Theorem)
Feb 28 Plane Filling Curves: One of Sierpinski's Curves
Feb 26 Following the Hilbert Curve
Feb 26 Six Misnamed Coins, Two Weighings
Feb 26 Plane Filling Curves: the Lebesgue Curve
Feb 24 What Is Area?
Feb 17 Mikhalev's Octahedrons
Feb 17 Psychology of 0.99999...
Feb 16 Area of a Circle by Leonardo da Vinci
Feb 13 Difference of two Cantor sets, II
Feb 11 Grandfather's Bill
Feb 10 A review of two combinatorics books
Feb 8 Intersections of a Circle with the Four Quadrants
Feb 6 Algebraic proof of the theorem of butterflies in quadrilaterals
Feb 4 Squares and Straight Tetrominoes
Feb 4 Areas In Circle
Feb 4 Determinant and Divisibility
Feb 3 What Is Determinant?
Feb 1 4 addtional proofs of the incidence of the altitudes
Feb 1 Midpoints and Orthogonality in Isosceles Triangles
Jan 31 Square, Similarity and Slopes
Jan 30 Bayesian Odds
Jan 25 Area of a Circle by Rabbi Abraham bar Hiyya Hanasi
Jan 24 Torque as a Mathematical Object
Jan 23 Pythagorean Theorem via an Isosceles Triangle
Jan 21 Dancing Rectangles Model Auxetic Behavior
Jan 19 Hinged Greek Cross Tessellation
Jan 18 Circles in a Regular Polygon
Jan 16 Subsets and Intersections
Jan 15 A Low Bound for 1/2 * 3/4 * 5/6 * ... * (2n-1)/2n
Jan 14 Pythagorean Theorem from the Shoelace Formula
Jan 13 Regular Pentagon Inscribed in Circle by Paper Folding
Jan 11 Odd Scoring
Jan 8 Right Triangles on Sides of a Square
Jan 7 Golden Window
Jan 5 Equal Incircles Theorem, Angela Drei's Proof
Jan 4 Circles Cover a Quadrilateral

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Copyright © 1996-2018 Alexander Bogomolny