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, 2011, and 2012 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 30 Orthogonal Lines, Midpoints, and Collinearity
December 29 Integer Triangles with Two Angles in the Ratio 1 : 2
December 28 Concyclicity in Two Semicircles
December 26 Angles in 4-5-6 Triangle
December 25 Another Concurrence on the 9-Point Circle
December 24 Another Seven Circles Theorem
December 23 The 80-80-20 Triangle Problem, A Variant, Solution #2
December 23 Problem 4 from the IMO 2013 - Synthetic Solution
December 22 Problem 4 from the IMO 2013
December 21 Review of Origins of Mathematical Words
December 21 Equilateral Triangles formed by Circumcenters
December 20 Miquel Circumcenters
December 19 Three lines at 60 degres and Circumcenters
December 18 Infinitude of Primes Via Euler's Product Formula for Pi
December 18 Infinitude of Primes Via Euler's Product Formula
December 14 Telescoping Sums and Series
December 13 Puzzle of 30 Grid Points and 5 Circles
December 12 Puzzle of 25 Grid Points and 5 Circles
December 11 Review of Who's Bigger?
December 10 The Eutrigon Theorem
December 8 Billiard Handicap
December 8 Squeeze (Sandwich, Pinching ...) Theorem (Lemma): an Example
December 6 Review of Will You Be Alive 10 Years from Now?
December 6 Family Size
December 5 From One Collinearity to Another
December 4 Problem 1, 2012 IMO
December 4 Lighthouse at Fermat Points
December 3 Circle in Isosceles Triangle and a Fixed Point
December 2 A Nice Trig Formula
December 2 Double and Half Angle Formulas
November 29 Review of Problem-Solving and Selected Topics in Euclidean Geometry
November 26 Pythagorean Theorem via Geometric Progression
November 22 Morley's Theorem: A Proof That Needs Fixing
November 21 Carnot's Criterion via Aerial Coordinates
November 20 Cevians And Semicircles
November 20 Marking And Breaking Sticks
November 19 Ptolemy's Equality/Inequality via Inversion
November 19 Morley's Theorem: Second Proof by Roger Smyth
November 12 Review of Mathematical Olympiad in China (2009-2010). Problems and Solutions
November 12 Sums of the Elements of Three Element Subsets
November 10 Self-documenting Iterations
November 9 On the Intersection of kx and |sin(x)|
November 9 Conics Related To In- and Excircles
November 8 Carnot's Criterion
November 7 Triangles with Sides in Geometric Progression
October 17 Elementary Problems That Beg for Generalization
September 27 Involution on the Projective Line
September 25 Carnot's Theorem for Conics
September 25 Expressions Invariant under Projecive Mappings
September 19 Radical Simplification - Not That Simple!
September 16 Six Circles with Concurrent Pairwise Radical Axes
September 15 Center of Gravity and Motion of Material Points
September 13 Spiral Similarity and Collinearity
September 11 A Problem in Hinged Squares II
September 10 Cevian Cradle II
September 7 On Bottema's Shoulders with a Ladder
September 5 Four Isosceles Triangles Hinged at Vertices
September 4 Abutting Equilateral Triangles on a Line I - a finished version
September 3 Six Concyclic Circumcenters in Fermat's Configuration
September 1 Morley's Theorem - Taylor and Marr's Proof
August 31 Golden Ratio via Golden Rhombus
August 30 Concyclic Points from Midpoint of an Arc
August 17 Angle Bisectors Cross Circumcircle
August 16 Leech Trees and Taylor's Criterion
August 14 An Unexpected Rhombus
August 13 Eyeballing a Ball
August 13 Eye-to-Eye Theorem II
August 13 Eye-to-Eye Theorem I
August 12 Parabola and Abutting Equilateral Triangles
August 12 Focal Definition of Parabola
August 10 Abutting Equilateral Triangles on a Line I
August 7 Focus on the Eyeball Theorem
August 7 Praying Eyes Theorem
August 5 Fermat's Hexagon
August 5 Napoleon's Hexagon
August 3 An Unexpected Pair of Similar Triangles Which Are Equal
August 3 Some Properties of Common Tangents
August 1 Two Pascals Merge into One
July 29 Joined Common Chords of Napoleon's Circumcircles
July 29 An Extra Triple of Equilateral Triangles for Napoleon
July 25 Two Similar Triangles with Parallel Sides
July 24 Kiepert's Triangles Graduate to Ears of Arbitrary Shape
July 22 A Final Chapter of the Asymmetric Propeller Story
July 21 Conics Intersecting Sides Of A Triangle
July 21 Cassini's Ovals and Geometric Optimization
July 20 Napoleon on Hinges in GeoGebra
July 19 Kiepert's Centroid
July 18 Egyptian Triangle By Paper Folding III
July 17 Seven Equal Circles
July 16 Sum of Three Squares
July 15 Concyclic Points of Two Ellipses with Orthogonal Axes
July 13 Parallelogram in Four Circles
July 12 Two Triples of Concurrent Cevians and a Conic
July 11 Concurrent Cevians and a Conic through Their Feet
July 11 Conics Intersecting Sides Of A Triangle
July 9 Three pairs of Parallel Lines and a Conic
July 8 Representation of 3 with Three Equal Digits
July 8 Perimeters of Convex Polygons, One within the Other
July 7 Circle Rotations and Fixed Points
July 6 Weather Forecasting: A Story of Mathematical Triumph
July 3 Ellipse Touching Sides of Triangle at Midpoints
June 26 Kulikowski's Theorem
June 25 Yet Another Appearance of the Golden Ratio
June 19 Climbing Pyramidal Slopes
June 17 Property of Right Isosceles Triangle
June 17 Five Squares in Complex Numbers
June 11 Parallel Chords in Conics
June 7 Dynamic Software as Serendipity Enhancement
June 6 Rhombus in Circles
June 5 Naming Infinity - the book
June 5 Two Common Chords in Three Concurrent Circles
June 4 Three Common Chords in Three Concurrent Circles
June 4 Two Diameters and Longest Common Chord
June 4 Seven Concyclic Points
June 3 Three Collinear and Four Concyclic Points
May 29 Two Circles, Ellipse, and Parallel Lines
May 28 Elves and Gnomes
May 26 Is GLOBALHELLFRY a Prime?
May 26 The Number of Judges and the Number of Votes
May 25 Egyptian Triangle By Paper Folding II
May 24 Maxwell's Theorem by Way of Trigonometric Ceva
May 23 A square in parallel lines
May 20 Area and Perimeter Splitters in a Triangle
May 20 Probabilities in a Painted Cube
May 14 Cutting Triangle in Two by a Line through a Point
May 9 e in the Pascal Triangle
May 7 Applying Daniel Dennett's New Book
May 6 Length of a Median
May 3 Francois Viete's Reduction of CCC to PCC
May 2 LCC: Apollonius' Problem with Two Circles and a Line
May 2 LLC: Apollonius' Problem with Two Lines and a Circle
May 1 PLC: Apollonius Problem with a point, a line, and a circle
April 30 PPL: An Elementary Solution
April 29 PCC: Apollonius' Problem with Two Circles and a Point
April 28 Apollonius's Construction
April 28 Combo Playground: Calculating the Number of Paths on a Square Grid
April 28 In the Spirit of Thebault I
April 27 CCC: Gergonnes's Solution to Apollonius' Problem
April 27 Poles, Polars and Orthogonal Circles
April 25 The Four Touching Circles Problem IV
April 23 How to Construct Orthogonal Circle
April 22 How to Construct Common Tangents to Two Circles
April 19 CCC: Apollonius' Problem with Three Intersecting Circles
April 15 PLL: Apollonius' Problem with Two Lines and a Point
April 14 PPL: Apollonius' Problem with Two Points and a Line
April 14 PPC: Apollonius' Problem with Two Points and a Circle
April 14 The Problem of Apollonius
April 13 How to Construct Tangents from a Point to a Circle
April 13 How to Construct a Radical Axis
April 7 Two Triangles Inscribed in a Conic - with Elementary Solution
April 5 Apollonian Circle for Two Lines and a Circle
April 4 A dissection puzzle. Proof #99 of the Pythagorean theorem
April 4 Counting Fat Sets
March 24 Vandermonde's Convolution Formula
March 21 Lucas' Theorem II
March 20 The Golden Ticket: P, NP, and the Search for the Impossible
March 18 A review of a biography of Vito Volterra
March 13 Two Triangles Inscribed in a Conic - with Solution
March 12 Why cats land on their feet - a problem of 80 years standing!
March 4 Napoleon's Theorem by Vectors and Trigonometry
March 3 An Inequality by Uncommon Induction
March 2 Concurrence of the Altitudes As Seen from 3D
March 1 3D Concurrency Of Altitudes
March 1 Photo Cameras I owned
Feb 27 Computers - then and now - from personal experience
Feb 25 Two Triangles Inscribed in a Conic
Feb 21 An Euclidean Construction with Inversion
Feb 20 Exeter Point
Feb 20 Concurrence Not from School Geometry
Feb 15 The Butterfly Effect
Feb 12 The Eutrigon Theorem
Feb 10 cos/sin inequality
Feb 5 An Application of Quadratic Formula
Feb 3 What happens to the area when the radius of circle is doubled?
Jan 31 Excircles Variant of Thebault's Problem III
Jan 30 A Lemma on the Road to Sawayama
Jan 30 A Double Meaning of an Arc's Midpoint
Jan 29 A Property of Right Trapezoids
Jan 28 Review of Mathematical Circle Diaries: Complete Curriculum for Grades 5 to 7 by Anna Burago
Jan 24 Review of Xu Jiagu's Lecture Notes on Mathematical Olympiad Courses for Senior Section
Jan 24 Roots and Tangents
Jan 22 Inequality with Harmonic Differences
Jan 21 An Identity From the 2010 China Mathematical Competition
Jan 20 Solve - an Olympiad Problem - in Your Mind
Jan 18 Square from Four Points, One on Each Side
Jan 18 Square from Four Points, One on Each Side, Solution 1
Jan 18 Square from Four Points, One on Each Side, Solution 2
Jan 17 For any k greater than 3, Decompose Cyclic Quadrilaterals into k Cyclic Quadrilaterals
Jan 17 Problem 4 from the 1959 IMO: Construction of a Right Triangle
Jan 16 A Problem of Divisibility by 2n
Jan 15 Henri Poincaré: A Scientific Biography
Jan 14 Inspiration, Perspiration and Satisfaction
Jan 12 A Pair of Probability Games for Beginners
Jan 11 A Diameter As a Diagonal of Inscribed Quadrilateral
Jan 10 Countability of Rational Numbers as a Union of Finite Sets
Jan 9 5x5 Square Grid and 5 Circes
Jan 9 Linear Function with Coefficients in Arithmetic Progression
Jan 7 Review of Numbers and Functions. From a classical-experimental mathematician's point of view by Victor H. Moll
Jan 5 Infinitude of Primes - from Infinitude of Mutual Primes
Jan 2 Bottema's Theorem - Proof Without Words
Jan 1 Tangent of 22.5° - Proof Wthout Words

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Copyright © 1996-2017 Alexander Bogomolny


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