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, 2012 and 2013 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 30 Pedal Triangles of Inverse Points
Dec 28 Proclivity of Conjoint Archimedean Twins for Proliferation
Dec 26 A Pedal Property in Equilateral Triangle
Dec 26 Pedal Similarity
Dec 25 Sides and Area of Pedal Triangle
Dec 24 Extension of Euclid's Game
Dec 23 Parallelogram with Side Lines through Fixed Points
Dec 22 BMO 2014, Problem 3
Dec 21 An Inequality Involving Fermat Point
Dec 20 Inequalities in Triangle
Dec 18 Bounds for the Sum of Distances to the Vertices
Dec 17 Garcia-Feuerbach Collinearity
Dec 15 Archimedean Siblings out of Wedlock, i.e., Arbelos
Dec 6 Tangent to the Incircle
Dec 4 Sum of All Natural Numbers
Dec 3 Dao Thanh Oai's Invariant
Dec 3 Chain of Six Intersecting Circles
Dec 3 Chain of Four Intersecting Circles
Dec 2 Review of The Best Writing on Mathematics 2014
Nov 24 Further properties of Van Aubel Configuration
Nov 22 Extra Feature of Van Aubel Configuration
Nov 21 Triangle from angle A, m_b, h_a
Nov 21 Law of Cosines by Ancient Sliding
Nov 20 Midpoint Reciprocity in Napoleon's Configuration
Nov 19 Longitude, Latitude and Distance to the Equator
Nov 18 A Problem for the 2015 New Year's Eve
Nov 17 Property of Two Pencils of Parallel Lines
Nov 16 Triangle by Inradius, Circumradius, Side or Angle
Nov 14 Train on Bridge
Nov 12 Uncommon Triangle Constructions
Nov 6 Equilateral Triangles On Sides of a Parallelogram II
Nov 4 Fermat Point Several Times Over
Nov 3 Van Schooten's and Pompeiu's Theorems
Nov 2 The Law of Cosines - Yet Another PWW
Nov 1 Triangle from Side, Median, and Altitude
Oct 31 Mathematicians and Musicians
Oct 30 Tables for Multiplication
Oct 29 Using Math Rules: An Example
Oct 28 Broken Line in Triangle
Oct 27 Cutting Circle to Rearrange Two Dots
Oct 27 Two Jugs - One's Volume Unknown
Oct 23 Triangle from Side, Circumradius, and Median
Oct 21 Vietnamese Extension of a Japanese Theorem
Oct 21 Chasing Angles Among Angle Bisectors
Oct 19 Vietnamese Lemma towards an Extension of a Japanese Theorem
Oct 17 Eyeball theorem
Oct 16 Construct Triangle by Angle Bisector, Altitude, and Side
Oct 14 Properties of the Harmonic Ratio
Oct 13 A. G. Samosvat's Proof by Dissection of the Pythagorean Theorem (#104)
Oct 10 Two Circles in Square II
Oct 9 (Un)fair Division by Consensus
Oct 9 Circle Concurrence on Circumcircle
Oct 9 Isogonal Lemma
Oct 7 Review of 'Zombies and Calculus' by Colin Adams
Oct 3 Dao's Archimedean Twins - Third Pair
Oct 2 Dao's Archimedean Twins - Second Pair
Oct 1 Beauty and the Beast - in Trigonometry
Oct 1 Gladiator Game
Sep 30 Twins Beget Twins
Sep 29 Construction of Triangle from Side, Angle, and that Angle's Bisector
Sep 24 Projective Invariants For Pascal And Desargues
Sep 19 Deceptive Appearances
Sep 18 Another Seven Circles Theorem, now with proof
Sep 17 Morley's Equilaterals, Spiridon A. Kuruklis' proof
Sep 15 Backward Proof of Morley's Theorem by B. Stonebridge
Sep 14 Review of Coffee, Love and Matrix Algebra
Sep 12 Powers of 6 and 7771
Sep 11 With One Weighing
Sep 11 Solutions of F(x)=x and F(F(x))=x
Sep 8 Review of Really Big Numbers
Sep 7 Dijkstra's Proof of Morley's Theorem
Sep 4 A Property of Unimodal Integers as a Whole
Sep 3 Symmetries in Triangle II
Sep 1 Symmedian in Right Triangle
Aug 10 Concyclicity from Collinearity
Aug 5 Moment of Inertia of a Regular Polygon
Aug 4 Novel Concurrency of Perpendicular Bisectors
Aug 4 Garcia's Two Circles Lemmas
Aug 1 Distance to the Horizon on the Fourth of July
Jul 29 Butterflies in a Pencil of Conics
Jul 28 Theorem of Three Tangents to a Conic
Jul 25 Projections of Convex Quadrilateral
Jul 23 A New Proof That the Rationals Are Countable
Jul 22 Three Parabolas with Common Directrix
Jul 19 The 80-80-20 Triangle Problem, 20-30 case
Jul 19 The 80-80-20 Triangle Problem, Solution #12
Jul 17 Equilateral Triangle on Three Lines
Jul 16 There is no Difference Between Equilateral Triangles
Jul 15 Equilateral Triangle on Angle Bisectors
Jul 10 Concyclic Points at the IMO 2014
Jul 10 Butterfly in Parabola
Jul 10 Reflection in a Triangle Tangent to Parabola
Jul 9 Eyeballs Projected
Jul 8 An Increasing Sequence from 2014 IMO
Jul 8 Multiplication of Points on an Ellipse
Jul 6 Multiplication of Points on a Circle
Jul 4 Shedding Light on the Ball for Eyeballing
Jul 3 Invert Two Circles Into Equal Ones
Jul 2 Seven and the Eighth Circle Theorem
Jul 1 Two Triangles Sharing the Circumcenter
Jul 1 Gergonne's Apollonian Circles
Jun 30 Golden Ratio in Regular Pentagon
Jun 28 Line Through a Center of Similarity
Jun 28 Line Not Through a Center of Similarity
Jun 25 Six Concyclic Points on Sides of a Triangle
Jun 23 Bespectacled Eyeballs Extension
Jun 23 Segment Projections in Equilateral Triangle
Jun 23 A Property of Perspective Triangles
Jun 20 Rectified, Halved, Sheared, Eyeballs Still Surprise
Jun 20 Symmetry in an Asymmetric Configuration
Jun 19 Eyeball Theorem Rectified
Jun 18 Dao's Archimedean Twins
Jun 17 Tangent Circles, Similarity and Equal Segments
Jun 16 Updated Garcia's Archimedean Twins
Jun 16 Updated the Praying Eyes Theorem
Jun 15 Garcia's Archimedean Twins
Jun 15 Eyeballing a ball
Jun 14 Lines Crossing Circles at Vertices of Equilateral Triangle
Jun 13 Square, Semicircle, and Other Curves
Jun 12 A Property of Points on Excircle
Jun 12 Similar Triangles in Crossing Circles
Jun 12 Semicircle on Square
Jun 11 Sequences of Concyclic Points on a Conic
Jun 9 Lines through Circles at Vertices of Equilateral Triangle
Jun 9 Circles Tangent to Medians at the Centroid
Jun 7 Shifted by the Inradius Tangent Collinearities
Jun 3 A Property of Points on Incircle
Jun 2 Tangent Curiosity in Equilateral Triangle
Jun 1 Pythagoras, with a Nod to the Carpets Theorem
May 30 An Equation in Squares
May 28 Bottema in Three Rotations
May 27 Bottema with Similar Triangles
May 27 Bottema with a Product of Rotations
May 25 Concurrent and Parallel Lines in Parallelogram
May 25 Looking Back at Bottema
May 24 Parallelogram and Four Equilateral Triangles
May 23 A Series with k-Permutations
May 22 Regular Hexagon and Triangle Joined at Vertex
May 22 Yet Another Generalization of Bottema's Theorem
May 22 A DIY Proof of the Irrationality of sqrt(2)
May 21 Irrationality of k-th roots
May 20 Entry 1.414... in Ramanujan's Notebooks
May 18 Carpets in Triangle, II
May 18 Irrationality of sqrt(2) via a Difference Equation
May 17 An Inequality with Permutations, II
May 15 An Inequality with Permutations, I
May 14 Spiral Similarity Leads to Equilateral Triangle
May 13 A Matter of Collinearity: Metamorphosis of a Problem
May 12 Four Incircles in an Equilateral Triangle, Third Solution
May 12 Reflection in the Circumcenter
May 11 Another Algebraic Proof of the Pythagorean Theorem
May 6 Two Pencils of Parallel Lines
May 4 Telescoping Squares
May 3 Telescoping Cubes
May 2 An Olympiad Problem With the Floor Function
May 2 A Number Theoretic Problem With the Floor Function
Apr 30 Pythagorean Triples via Fibonacci Numbers
Apr 29 Viviani's 3D Analogue
Apr 29 Tiling Sphere by Four Equal Triangles
Apr 28 Tetrahedron with Orthogonal Perpendiculars to Opposite Edges
Apr 28 Tetrahedron with Equiareal Faces, II
Apr 28 Isosceles Tetrahedron
Apr 27 Tetrahedron with Equiareal Faces
Apr 26 An Algebraic Lemma with Geometric Consequences
Apr 24 Tetrahedron in Parallelepiped
Apr 23 Review of Count Like an Egyptian
Apr 22 Fixed Point on Perpendicular Bisector
Apr 21 Sum of Absolute Values
Apr 19 A Quartic Equation
Apr 18 ln(2) in Pascal's Triangle
Apr 17 pi^e vs e^pi
Apr 17 Pi in Pascal's Triangle via Triangular Numbers
Apr 16 Hjelmslev's Theorem on Canvas
Apr 14 Pi in Pascal's Triangle
Apr 13 L. Giugiuc's Proof of Morley's Theorem
Apr 12 B. Bollobás' Trigonometric Proof of Morley's Theorem
Apr 9 Review of Math Bytes by Tim Chartier
Apr 9 Cubes in Pascal's Triangle
Apr 8 Sylvester's Problem, Lang's solution
Apr 8 Sylvester's Problem, Steinberg's solution
Apr 8 Sylvester's Problem, Gallai's solution
Apr 8 Sylvester's Problem, Kelly's solution
Apr 7 Sylvester's Problem
Apr 6 Brahmagupta-Fibonacci Identity
Apr 3 Number of Regions N Lines Divide Plane
Apr 3 What Is the Extremal Principle?
Apr 1 Three Euler Lines That Are Four
Mar 31 A View on the Circle of Apollonius
Mar 31 What Is Indirect Proof?
Mar 30 Existence of the Circumcenter, Indirect Proof
Mar 27 Seven Problems in Equilateral Triangle, Solution to Problems 5, 6, 7
Mar 27 Seven Problems in Equilateral Triangle, Solution to Problem 4
Mar 26 Seven Problems in Equilateral Triangle, Solution to Problem 3
Mar 26 Seven Problems in Equilateral Triangle, Solution to Problem 2
Mar 26 Seven Problems in Equilateral Triangle, Solution to Problem 1
Mar 25 When Two Segments Intersect
Mar 24 Voronoi Diagram
Mar 23 Another Property of Circle Through the Incenter
Mar 21 Properties of Circle Through the Incenter
Mar 21 A Property of Circle Through the Incenter
Mar 20 Central and Inscribed Angles in Complex Numbers
Mar 19 Simple Property of Circle Through the Incenter
Mar 19 Conics in Triangle
Mar 19 Seven Problems in Equilateral Triangle
Mar 18 What Is Angle Chasing?
Mar 18 Strategy and Tactics in Problem Solving
Mar 17 Pure Angle Chasing III
Mar 16 Pure Angle Chasing II
Mar 15 Pure Angle Chasing
Mar 14 Probability of Matching Socks
Mar 12 Conic in Hexagon
Mar 12 McDougall's Generalization of Ptolemy's Theorem
Mar 11 Conic from Parallel Chords
Mar 11 Concurrence of Ten Nine-Point Circles
Mar 10 Reim's Similar Coins IV
Mar 10 Euler-Poncelet Point
Mar 10 Reim's Similar Coins III
Mar 9 Reim's Similar Coins II
Mar 9 Reim's Similar Coins I
Mar 6 Thales' Theorems
Mar 5 Probability of Two Integers Being Comprime
Mar 3 Probability on Discrete Infinite Sets
Mar 2 Squares in Pascal's Triangle
Mar 2 Isoperimetric Theorem For Quadrilaterals
Mar 2 Parallelograms among Quadrilaterals
Mar 2 Rectangles among Parallelograms
Mar 1 Carpets in Triangle
Feb 28 Triangle of Minimum Perimeter
Feb 27 Sums of Binomial Reciprocals in Pascal's Triangle
Feb 26 Equilateral Triangle in Equilateral Triangle
Feb 20 d'Alembert's Misstep
Feb 19 Pythagorean Theorem for Reciprocals
Feb 18 Area and Perimeter of Circle
Feb 17 Beating a Dead Horse: Mathematics Education Reform - Again
Feb 17 Volume and Area of Torricelli's Trumpet
Feb 16 Weighted Dice Problem
Feb 15 The Schwarz Lantern Explained
Feb 15 Hidden Orthogonality
Feb 14 A Generalization of the Pythagorean Theorem
Feb 14 Elementary Introduction into the Concept of Area
Feb 14 Area of Rectangle
Feb 12 Trigonometry According to Ptolemy
Feb 12 A Family of Cyclic Quadrilaterals
Feb 11 Altitudes have ears, foot, stem, and root
Feb 11 Another Property of the 9-Point Circle
Feb 11 Divide Triangle by Lines Parallel to Base
Feb 9 A Not Symmetric Inequality
Feb 9 Infinitude of Primes - Golomb's Topological Proof
Feb 8 Two Cyclic Inequalities
Feb 7 Practical Relativity
Feb 7 e and pi Spoof
Feb 5 Catalan Numbers in Pascal's Triangle
Feb 4 Infinitely many proofs that there are infinitely many primes
Feb 3 Projections of Isogonal Conjugate are Concyclic
Feb 3 A Property of Isogonal Lines
Feb 2 Another Pair of Archimedean Twins - a Redux
Feb 1 Hardy's Example of Non-Serious Theorems
Jan 31 Outline Mathematics: Diophantine Equation I
Jan 31 Outline Mathematics: Improving on an Escalator
Jan 30 Counting Permutations with Fixed Points
Jan 29 Wizards, Aliens, and Starships
Jan 29 How to write an equation of the union of two sets
Jan 27 Symmetry Principle in Probability
Jan 27 An Identity in (Cyclic) Quadrilaterals
Jan 26 The Law of Cosines by Larry Hoehn
Jan 26 A Formula for sin(3x)
Jan 26 A Vector-based Proof of Morley's Trisector Theorem
Jan 25 Concyclic Incenters in Bicentric Quadrilateral
Jan 24 Inscriptible Quadrilateral of Triangle Incenters
Jan 24 Concyclic Points in Inscriptible Quadrilateral
Jan 23 Two Quadruplets of Concyclic Points
Jan 22 Checkmate Puzzle
Jan 21 Random Points on a Segment
Jan 20 A Geometric Limit
Jan 20 A Property of Thebault Circles
Jan 18 Kordemsky's Palindrome Problem
Jan 16 Anticenter and Orthocenters
Jan 14 Not So Hidden Homotheties
Jan 11 A Property of Thebault Circles
Jan 10 Construction of Thebault Circles
Jan 10 What is the Color of the Remaining Ball?
Jan 9 Concurrence on a Circle
Jan 9 Angle in Right Triangle
Jan 9 Two Circles, Tangents and Two Collinearities
Jan 9 Construction and Properties of Mixtilinear Incircles 2
Jan 8 Conic in Mixtilinear Incircles
Jan 8 Construction and Properties of Mixtilinear Incircles
Jan 8 Collinear Intersections and Products of Ratios
Jan 7 Yet Another Seven Circles Theorem
Jan 6 Garfield's Ghost Revisited - by Tony Foster
Jan 6 Isosceles Trapezoid In Cyclic Quadrilateral
Jan 6 Droz-Farny Theorem - an Analytic Solution
Jan 4 A Property of Pascal's Hexagon Pascal May Have Overlooked
Jan 2 Yet Another Concurrence on the 9-Point Circle
Jan 1 Six Concyclic Points via Antipedal Triangle

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Copyright © 1996-2018 Alexander Bogomolny