Chronology of Updates

Note: I have placed chronology of updates for 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, and 2009 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 28 Semi-regular Tessellation on Hinges C
Dec 26 Semi-regular Tessellation on Hinges B
Dec 26 Semi-regular Tessellation on Hinges A
Dec 24 A Hinged Realization of a Plane Tessellation
Dec 23 A Corrected Version of the Calculus Proof of the Pythagorean Theorem
Dec 23 Proof #89 of the Pythagorean Theorem
Dec 22 Dancing Squares or a Hinged Plane Tessellation
Dec 21 Filling a Grid with Good Neighbors
Dec 20 Review of A Decade of the Berkley Math Circle
Dec 20 No Flipping without End
Dec 18 Viviani by Inversion
Dec 17 Absolute Value and 1998 integers
Dec 17 Word Ladders
Dec 16 Phantom Circle and Recaptured Symmetry
Dec 15 Eight Selections in Six Sectors
Dec 14 A Game of Candy Squares
Dec 13 Angles Inscribed in an Absent Circle
Dec 12 A Three Pegs Question
Dec 12 Escape of the Clones
Dec 11 Guests at a Round Table
Dec 11 Ptolemy by Inversion
Dec 9 Treasure Hunt from Outside the Grid
Dec 9 Treasure Hunt in a Square Grid
Dec 7 12 Coins in Verse
Nov 30 Menelaus from 3D
Nov 30 Chromatic Number of the Plane
Nov 29 The Rascal Triangle
Nov 29 Coloring Points in the Plane
Nov 28 Szilassi Polyhedron
Nov 28 Csaszar Polyhedron 4
Nov 28 Csaszar Polyhedron 1
Nov 27 Acute Angle Bisectors in a Right Triangle
Nov 27 1995 British Mathematical Olympiad, Problem 3
Nov 27 Circle through the Circumcenter
Nov 26 Skyscrapers Puzzle
Nov 25 Cevian Cradle
Nov 24 Diophantine Equations
Nov 24 Curious Identities Involving Integer Squares
Nov 24 AM-GM Inequality
Nov 23 VMO 1992 Problem 1
Nov 23 A Quickie Limit
Nov 23 Any Integer with Three 2s
Nov 21 Two-Parameter Solutions to Three Almost Fermat Equations
Nov 21 A Review of Geometric Etudes in Combinatorial Mathematics
Nov 20 Coloring Plane with Three Colors
Nov 17 Tiling Rectangles with L-Trominoes
Nov 15 Subtraction in a Rectangular Array
Nov 13 Not Exceeding 24
Nov 13 Knots on a Torus
Nov 12 Averaging Raindrops, Part 2
Nov 11 Averaging Raindrops - an exercise in geometric probability
Nov 10 Solution #4 to a three circles problem
Nov 7 100 Grasshoppers on a Triangular Board
Oct 31 Polygon in a Rectangle
Oct 31 Three Jugs - Equal Amounts
Oct 30 Many Jugs to One II
Oct 30 Many Jugs to One I
Oct 30 3 Jugs Problem - A Water Doubling Variant
Oct 29 Riemann Rearrangement Theorem
Oct 28 1/2 = 1
Oct 27 Review of An Introdcution to Diophantine Equations by T. Andreescu et al
Oct 27 A Short Equation in Reciprocals
Oct 25 An Equation in Reciprocals
Oct 25 Segment Trisection Induced by Parallels to Medians
Oct 23 Angle Bisectors In Rectangle
Oct 20 First Applications of Helly's Theorem
Oct 20 Helly's Theorem
Oct 19 Diophantine Quadratic Equation in Three Variables
Oct 18 Dissection of Triangle into Rhombus by Hubert Shutrick
Oct 18 Minus One But What a Difference
Oct 14 Homothety between In- and Excircles
Oct 13 Filling Pool with Fluids
Oct 12 Calculus Proof of the Pythagorean Theorem
Oct 11 Review of Mathematical Plums by R. Honsberger
Oct 9 Dissection of Triangle into Rhombus
Oct 8 Pentagon in a Semicircle
Oct 7 Extremal Problem in a Circular Segment
Oct 6 Counting Ordered Pairs
Oct 4 Asymmetric Propeller by Plane Tiling
Oct 2 A Mathematical Rabbit out of an Algebraic Hat
Oct 1 Carpets in Hexagon
Sep 29 Distinct Multisets with the Same Pairwise Sum
Sep 28 A Characterization of the Euler Line
Sep 27 Lennes' Polyhedron
Sep 24 Review of Classical Topics in Discrete Geometry by K. Bezdek
Sep 24 Morley's Theorem: Proof by H. Shutrick
Sep 23 A Chain of Touching Circles in a Polygon (a la Bui Quang Tuan)
Sep 23 A Chain of Touching Circles in a Polygon (a la Evelyn)
Sep 21 Fraction Comparison Sped up
Sep 19 Pythagoras' from the Star of David
Sep 17 Areas in Square by Dissection
Sep 14 Review of Charming Proofs by C. Alsina and R. B. Nelsen
Sep 11 Antiparallel via Three Reflections
Sep 10 Johnson Circles
Sep 8 Assigning Numbers to Points in the Plane
Sep 6 Squares in Semicircle and Circle
Sep 5 Are Most Triangles Obtuse?
Sep 3 Volumes of Two Pyramids
Sep 3 Squares in Triangles
Sep 1 Pythagorean Theorem: An Algebraic Proof with Three Trapezoids
Aug 27 A Maximum Area Property of the Medial Triangle
Aug 26 The Broken Chord Theorem: proof by Mariano Perez de la Cruz
Aug 26 The Illustrated Law of Cosines
Aug 16 Pythagoras' from Bottema's
Aug 15 A Lemma of Equal Areas
August 4 Touching Circles with Given Centers II
August 4 Review of Numbers Rule by G. Szpiro
August 3 2001 Poland Mathematical Olympiad, Problem 2
August 2 Are Australian Elections Fair As Claimed?
August 2 Nested Radicals
August 1 Pythagoras' from Broken Chords (proof #85)
August 1 The Broken Chord Theorem: proof by Bui Quang Tuan
August 1 Three Equal Circles in a Semicircle
July 31 Shuffling Probability
July 27 Two Triples of Concurrent Circles
July 23 Six Circles Theorem (Bui Quang Tuan)
July 23 Finger Counting
July 16 Circle in a Square Inscribed in a Circle
July 11 J. Casey's Additions to Euclid I.47
July 6 A Circle Rolling in an Equilateral Triangle
June 27 Line, Circle, and Fixed Points
June 26 An inequality from 1971 Canadian Mathematical Olympiad
June 26 Problem with angle bisector from 1975 Canadian Mathematical Olympiad
June 26 Fixed points from 2007 Irish Mathematical Olympiad
June 25 Problem with equal angles from 1987 IberoAmerican Mathematical Olympiad
June 24 Perpendicular lines in a cyclic quadrilateral from 1975 Canadian Mathematical Olympiad
June 23 Review of What's Luck Has to Do with It? by Joseph Mazur
June 22 A Trigonometric Identity in a Right Triangle from the 1960 IMO
June 22 Ancient Problem = Ancient Solution
June 21 Euclid's Game on a Square Grid
June 18 Square in a Circle Inscribed in a Square
June 17 Parametric Problem in Quartic Polynomial from 1984 USAMO
June 16 Example: A Poker Hand
June 15 A Property of Centrally Symmetric Hexagons
June 14 Chain of Circles on a Chord
June 9 Circle, Isosceles Triangle and Fixed Point
June 9 A Circle in an Isosceles triangle from the 2006 Irish MO
June 8 Circles on the sides of a triangle from the 2005 Austrian MO
June 8 Problem of divisibility from the 1970 Canadian MO
June 8 Concurrency from the 2009 Austrian MO
June 8 Problem in Isosceles Triangles from the 2008 Austrian MO
June 7 Construction of Square from the 2008 Austrian MO
June 7 A Problem with Ratios from the 1969 Canadian MO
June 4 Cutting Triangles off Regular Hexagon
June 4 Asian Pacific Kite
June 3 Number Comparison - from the 1969 Canadian MO
June 3 Lucky Contest Winners
June 2 An Identity Involving the Integer Part - Problem from the 1981 Canadian MO
June 2 An Identity between the Roots of a Cubic Polynomial - Problem from the 2007 Irish MO
June 2 A Diophantine Equation with Square Roots - Problem from the 2008 British MO
June 2 Fixed Point in a Kite - Problem from the 1993 Asian Pacific MO
June 2 Ratios and Orthogonality in a Triangle - Problem from the 2006 Romania MO
June 1 A Diophantine Equation - Problem from the 2000 Belarus MO
May 30 Review of A Mathematician's Lament by Paul Lockhart
May 28 Sangaku with Angle between a Tangent and a Chord
May 27 Squares and Cubes - from the 1978 Canadian MO
May 27 Locus of the midpoints of concurrent chords - from the 1991 Canadian MO
May 27 Sum of 1984 consecutive squares - from the 1984 Canadian MO
May 27 Areas in a quadrilateral - from the 1978 Canadian MO
May 27 1986 Canadian MO, Problem 1
May 27 Circle through the Incenter And Antiparallels
May 27 2001 IberoAmerican MO, Problem 2
May 27 1980 Canadian MO, Problem 3
May 27 1972 Canadian MO, Problem 5
May 27 1969 Canadian MO, Problem 7
May 27 1994 Ireland MO, Problem 1
May 27 Another Look at Nagel's Theorem
May 26 1987 Canadian MO, Problem 2
May 21 Need Mathematics Taught in School Be Relevant?
May 20 Yet another solution (by Vladimir Nikolin) to the "circle through 2 vertices and the incenter" problem
May 19 Equilateral triangles on the sides of a right triangle - a problem from the 2000 Belarus MO
May 19 Three Circles through the Incenter
May 18 2000 Belarus Mathematical Olympiad, Problem 7
May 18 Construction with Optimization in Angle - Problem the 1979 USA Mathematical Olympiad
May 18 Problem 7 of the Australian Mathematical Olympiad 2009
May 18 Problem 2 of the Australian Mathematical Olympiad 2008
May 18 Circle through the Incenter
May 17 2010 Australian Mathematical Olympiad, Problem 6
May 17 Inequality Between the Perimeters of Two Triangles and the Distances Between Their Vertices
May 16 Reflections of the circumcenter
May 15 Partial But General Case Of Fermat's Last Theorem 2
May 14 Partial But General Case Of Fermat's Last Theorem
May 14 Simple Somos Sequence - a Russian Olympiad problem
May 14 Simple Somos Sequence Calculator
May 12 Inequality with Logarithms
May 12 Maximum Ratio of Similarity - Belarus Olympiad Problem
May 10 Simple dissection of an acute triangle
May 9 Three Orthogonal Circles Through Three Given Points
May 6 A Variant Of the Pythagorean Theorem
May 6 Triangle ABC is right iff sin^2(A) + sin^2(B) + sin^2(C) = 2
May 5 1992 Asian Pacific Mathematical Olympiad, Problem 2
May 5 1986 Vietnam Mathematical Olympiad, Problem 4
May 4 Parallelogram Iterations
May 3 1962 Vietnam Mathematical Olympiad, Problem 4
May 3 2010 USA Olympiad, Problem 1
May 3 2010 USA Olympiad, Problem 3
May 3 2010 USA Olympiad, Problem 4
May 3 Nagel's Theorem: an Elementary Proof
May 3 Presence of the Antipodes on a Circle
May 3 Swapping Rows and Columns
May 2 Two Equilateral Triangles
May 1 Two Altitudes, One Midpoint
April 29 Constructions Related To An Inaccessible Point
April 29 A Telescoping Series
April 29 Yet Another Proof of the Concurrency of the Altitudes
April 27 Heron's Formula: a Proof
April 26 Approximation Of Roots
April 25 Nine Point Circle: an Elementary Proof
April 25 Existence of the Euler Line: An Elementary Proof
April 25 Problem 1 from the 1988 IberoAmerican Olympiad
April 24 Reflections of the Orthocenter II
April 23 Maximum Perimeter Property of the Incircle
April 21 Problem 5 from the USA Mathematical Olympiad
April 21 Addition and Subtraction of Integers
April 19 Faulty Symmetry
April 18 Triangulated Dinosaur
April 17 Problem 9 from the 2009 Middle European Mathematical Olympiad
April 16 Counting and Equivalent Fractions
April 16 Scoring Misere: Two Heaps Perfect Strategy
April 12 Problem 2 from the 1992 China Mathematical Olympiad
April 12 Problem 3 from the 1992 IberoAmerican Mathematical Olympiad
April 12 Problem 2 from the 2007 British Mathematical Olympiad
April 9 Sine and Cosine of 15 Degrees Angle
April 8 Equal Areas in Equilateral Triangle
April 6 Angle Bisector in Equilateral Trapezoid
April 6 Problem 1 of the 2010 China Mathematical Olympiad
April 5 Two Lines - Two Circles
April 4 What Is Line?
April 4 What Is Point?
April 1 Problem 7 of the Canadian Mathematical Olympiad 1971
March 31 Problem 2 of the Canadian Mathematical Olympiad 2010
March 31 Problem 3 of the Balkan Mathematical Olympiad 1988
March 30 Properties of GCD and LCM
March 29 GCD and LCM by Plain Factorization
March 26 Common Multiples and the Least Common Multiple
March 25 Factors And Multiples
March 24 IMO 1998 Problem 1
March 22 Cantor-Bernstein-Schroeder theorem, a Second Proof
March 17 Addition and Subtraction Formulas for Sine and Cosine III
March 17 Linear System with Parameter
March 16 Listing All the Composite Numbers
March 16 Lucky Numbers
March 12 Factorial Products
March 11 Function in the Plane That Vanishes
March 10 The Size of a Class: Two Viewpoints
March 9 Less than, Equal to, Greater Than Symbols
March 9 Points Generated by the Nine Points
March 8 Tangent Lines and Circles in Convex Quadrilateral
March 7 The Ballot Lemma
March 5 The Reflection Lemma
March 4 Getting a Scout out of Desert
March 3 Random Walks
March 2 Van Schooten's Locus Problem
March 2 Square out of a Quadrilateral
Feb 27 Diagonal Argument
Feb 25 A Trigonometric Solution to a Difficult Sangaku Problem
Feb 24 A Possibly First Proof of the Concurrence of Altitudes
Feb 24 Patterns in Pascal's Triangle
Feb 23 Construction of Pascal's Triangle
Feb 23 Short Construction of the Geometric Mean
Feb 22 Treatise on Arithmetical Triangle
Feb 19 A Fair Game of Chance
Feb 19 Isosceles Tetrahedron
Feb 13 Concyclic Points in Bride's Chair
Feb 13 Joseph Keech in Bride's Chair
Feb 12 New Proof of Euclid's Theorem
Feb 12 Properties of the Figures in Euclid I.47
Feb 11 Four Crossing Circles
Feb 10 Two Circles on Angle Bisector
Feb 10 Coaxal Circles on Perpendicular Bisector
Feb 6 Equal Chords in Crossing Circles
Feb 6 Parallel Chords in Crossing Circles
Feb 3 Monty Hall Problem Redux
Jan 31 Monty Hall Dilemma's Simulation
Jan 30 The Plain Butterfly Theorem
Jan 29 Proof 18 of the Butterfly Theorem
Jan 28 Unproperty of the Powers of 2
Jan 27 The Local-Global Principle
Jan 25 Infinitude Of Primes From Legendre's Formula
Jan 25 Legendre's Formula
Jan 24 Half Turn, Reflection in Point
Jan 23 Clubs in a Vector Space
Jan 21 Triangulating Squares
Jan 20 A Proof of the Coincidence of Altitudes by W. Chapple (1749)
Jan 19 p-adic Expansions
Jan 18 p-adic Numbers
Jan 18 What Is Space Completion?
Jan 15 Line through a Point in an Angle
Jan 13 Mutually (Jointly) Independent Events
Jan 12 Morley's Trisector Theorem: Proof by R. J. Webster
Jan 12 Morley's Trisector Theorem: Proof by H. D. Grossman
Jan 11 However You Solve It ... A Wonderful Equation
Jan 11 Trigonometry by Paper Folding
Jan 10 Isoperimetric Property of Equilateral Triangles
Jan 10 Maximum Area Property of Equilateral Triangles
Jan 9 Sangaku with Quadratic Optimization
Jan 7 Equilateral Triangle on Parallel Lines
Jan 5 Circles with Equal Collinear Chords
Jan 3 Translated Triangles
Jan 2 Find a Common Chord of Given Length
Jan 1 Equilateral and 3-4-5 Triangles

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Copyright © 1996-2018 Alexander Bogomolny