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, 2013, and 2014 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 Three Circles and Area
Dec 29 Is X a Midpoint of a Chord
Dec 27 Proportions and the Incenter
Dec 25 Limit of a Recursive Sequence
Dec 23 An Inequality with Constraint VI
Dec 21 Pythagorean Perimeter Theorem
Dec 21 Generalized Carnot's theorem
Dec 19 Inequality with Csc And Sin
Dec 19 Euler Inequality in Triangle
Dec 19 Concurrence on Angle Bisector
Dec 18 An Inequality with Constraint V
Dec 18 Jensen's Inequality
Dec 17 An Inequality with Constraint IV
Dec 16 An Inequality from Morocco
Dec 16 An Inequality from Morocco, with a Proof, or Is It?
Dec 15 A Limit of Another Sequence
Dec 14 A Limit of a Sequence
Dec 13 Optimization in Parallelepiped
Dec 12 Dao's Variant of Thebault's First Problem
Dec 11 Jordan Curve Theorem
Dec 9 An Inequality with Constraint III
Dec 8 Solution #10 to a variant of the 80-80-20 triangle problem
Dec 8 Solution #9 to a variant of the 80-80-20 triangle problem
Dec 8 Solution #8 to a variant of the 80-80-20 triangle problem
Dec 7 A Problem with Two Isosceles Triangles
Dec 4 Advancing a Millenium Problem
Dec 4 An Inequality with Constraints II
Dec 3 An Inequality with Constraint
Nov 30 Review of Problems for Metagrobologists by David Singmaster
Nov 29 Steiner's Circumellipse in Barycentric Coordinates
Nov 28 Steiner's Inellipse in Barycentric Coordinates
Nov 27 Area of the Intersection of Two Equal Rectangles
Nov 26 Pedal Parallelogram
Nov 26 Cevian Parallelogram
Nov 24 Constrained Area in Triangle
Nov 24 Area of Cutoff Triangles
Nov 24 Area of Cevian Triangle
Nov 24 Area Inequalities in Triangle
Nov 22 Inequality from Math Phenomenon
Nov 22 Chebyshev Inequality
Nov 21 Rearrangement Inequality
Nov 19 Sanchez's Viviani's Area Analogue
Nov 19 Equal areas In Circle
Nov 18 A Problem with Right Isosceles Triangles
Nov 17 Bicubal Domino
Nov 16 Constrained Intermarriages
Nov 15 Bisectors and Proportions
Nov 10 Newton's and Maclaurin's Inequalities
Nov 9 Getting Your Rightful Share Back
Nov 6 An Inequality from Tibet
Nov 4 Application of Cauchy-Schwarz Inequality
Nov 3 Optimal Quadrilateral Inscribed in Square, PWW
Nov 2 Optimal Quadrilateral Inscribed in Square
Oct 29 Simple But Uncommon Equation from 1968 IMO
Oct 29 A Functional Equation from 1968 IMO
Oct 27 Inequalities and Quadratic Forms
Oct 27 An Application of Schur's Inequality
Oct 26 Schur's Inequality
Oct 25 An Inequality in Determinants
Oct 23 Fold Square into Equilateral Triangle
Oct 22 Areas in Three Squares
Oct 21 Orthogonality in Two Squares
Oct 19 An Equation in Matrices
Oct 19 The Shortest Crease
Oct 17 An Equation in Integers and Rational Numbers
Oct 16 Pythagorean Theorem, Proof 114
Oct 16 Pythagorean Theorem by Inscribed Semicircle
Oct 15 Golden Ratio in Isosceles Right Triangle, Square, and Semicircle
Oct 14 Trisect Segment: 2 Circles, 4 Lines
Oct 13 Extremal Problem in a Quadrilateral
Oct 11 Centroids and Circumcenters
Oct 9 Butterfly in Inscriptible Quadrilateral
Oct 8 Prove 2[sqrt(n) - sqrt(n-1)] > 1/sqrt(n)
Oct 7 Angles in a Triangle: an Exercise
Oct 2 Thales on Angle Bisectors
Sep 25 Angle Chasing on Radical Axis
Sep 24 Angle in Square
Sep 21 An Application of Hlawka's Inequality
Sep 19 Scalar Product Optimization
Sep 17 Tangents And Bisectors
Sep 14 Equation in Permutations
Sep 12 Triangle by HM segments
Sep 9 Transversal Trigonometry
Sep 9 A Property of Cyclic Quadrilateral
Sep 8 Miguel Ochoa's van Schooten is a Slanted Viviani
Sep 8 Miguel Ochoa's van Schooten Like Theorem III
Sep 7 Miguel Ochoa's van Schooten Like Theorem II
Sep 6 On the Intersection of 1+x and e^x and Trigonometric Consequences
Sep 4 A Problem of Acute Triangle
Sep 3 When a Triangle is A-cute
Sep 1 Homothety in Equilateral Triangles
Aug 31 What 1, 6, and 14 Have to Do with 5
Aug 30 Concurrence in Equilateral Triangle
Aug 28 Inequality in Rectangle
Aug 27 The Dual of Maxwell's Theorem
Aug 25 Area of Trapezoid
Aug 24 Extremal Distance Ratio
Aug 23 An Identity in Triangle II
Aug 5 Algebraic-Geometric Equation
Aug 4 Modern Day Sangaku
Aug 2 Amazing Mix of Triangular Numbers and Golden Ratio
Jul 28 An Unusual Quadratic Equation
Jul 27 Regular Hexagon from Arbitrary Triangle
Jul 26 Inequality for Integer Sequences II
Jul 26 Inequality in Acute Triangle
Jul 26 Inequality for Integer Sequences
Jul 25 Perspective Triangles in Circle
Jul 24 Relation Engendered By Medians
Jul 24 Relation Engendered By Altitudes
Jul 23 Cubic Equation for the Sides of a Triangle
Jul 23 Property of Quadratic Polynomials
Jul 22 Pleasant Proportions in Triangle
Jul 21 An Inequality via Young's Theorem
Jul 21 An Angle Inequality in Simple Polygons
Jul 20 Reuleaux's Triangle, Extended
Jul 14 Triangle from Two Side Lines and the Euler Line
Jul 10 An Universal Inequality for Cevians
Jul 1 Iterations on Monotone Functions
Jun 30 Tangential Chaos
Jun 29 An innovative recurrence
Jun 25 An Equation in Determinants
Jun 24 Two Related Triangles of Equal Areas
Jun 22 Leo's Lemma, Second Application
Jun 21 Two Sequences Defined by Recurrence
Jun 19 Three visions of a fact
Jun 17 Simpson Paradox
Jun 17 Importance of Having an Angle of 60 Degrees
Jun 17 Triangle with a 60 degrees angle
Jun 16 A Sum of a Double Series
Jun 16 Leo Giugiuc's Trigonometric Lemma
Jun 15 Is There a Limit
Jun 14 A One-Line Proof of the Infinitude of Primes
Jun 11 Clough's theorem: the simplest proof
Jun 10 Beyond Viviani
Jun 10 Slanted Viviani, PWW
Jun 8 Area Inequality in Triangle II
Jun 7 Slanted Viviani
Jun 6 YATPOPT, Yet Another Trigonometric Proof of the Pythagorean Theorem
Jun 5 Problem in Direct Similarity
Jun 4 Inverse Similarity through Reflections
Jun 2 An Inequality with Nested Radicals
May 31 From Triangle Inequality to Inequality in Triangle
May 28 A Curious Identity in Triangle
May 26 An Inequality in Triangle, II
May 26 The Jeweler's Observation, a look back
May 25 Isotomic Reciprocity
May 20 Construct Triangle from Altitude, Median and Inradius
May 18 An Affine Property of Barycenter
May 18 An Identity for Regular Tetrahedra
May 16 Van Khea's Fourth Identity in Triangle
May 12 Parabolas Related to the Orthic Triangle
May 11 An Inequality in Triangle
May 11 Parabolic Reciprocity
May 10 Miguel Ochoa's van Schooten Like Theorem
May 10 Elegant Minimum of a Function
May 7 One More Seven Circles Theorem
May 7 William Wallace's 1803 Statement of the Butterfly Theorem
May 6 Third Unusual Identity in Triangle
May 4 Dan-Stefan Marinescu Inequality
May 4 Twin Segments in Four Semicircles
May 2 Characterization of Trapezoid
May 1 A wrapping surprise
Apr 30 Review of The Proof and The Pudding by Jim Henle
Apr 28 From Arbitrary Pentagon to Regular One
Apr 25 A Geometric Proof of Proizvolov's Identity
Apr 24 From Arbitrary Hexagon to Regular One
Apr 22 Extras in Bottema's Configuration
Apr 22 From Straight Line to Regular Hexagon
Apr 21 Parallelogram in Parallelogram And in Projection
Apr 20 A Problem in Three Pentagons
Apr 19 A Generalization of Simson Line
Apr 17 A Combinaton Locus
Apr 16 Golden Ratio in Mixtilinear Circles
Apr 16 Proofs of the Pythagorean Theorem via Heron's Formula II
Apr 15 Further Properties of Peculiar Circles
Apr 14 An Inequality from the 2015 Romanian TST
Apr 6 Another Identity in Triangle
Apr 5 Circle of Apollonius in Equilateral Triangle
Apr 5 Integer Triangle That Sums to Cube
Apr 5 Another Sangaku in Square
Apr 3 An Identity in Triangle
Apr 3 Square Roots and Triangle Inequality
Apr 1 Why Learn Mental Math Tricks?
Mar 30 Four Golden Circles
Mar 27 Construct Triangle by Angle, Median, and Circumradius
Mar 27 Two Conics, Pascal, Chasles, and Cross-Ratio
Mar 26 Construct Triangle by Angle, Altitude and Median
Mar 24 A Conic in a Triangle
Mar 22 Concurrence in Arbelos
Mar 21 Areas in Two Parallelograms and a Translation
Mar 19 Triangle from Angle Bisector, Altitude and Inradius
Mar 19 Triangle from Median, Altitude and Circumradius
Mar 18 An Equation Involving the Total Number of Digits
Mar 16 Triangle from Angle Bisector, Altitude and Circumradius
Mar 16 An Equation Involving Four Collinear Points
Mar 16 Hlawka's Inequality
Mar 13 Area Inequality in Triangle
Mar 11 Construct Triangle from Angle, Inradius, and Altitude
Mar 11 Triangle from Angle, Inradius, and Difference of Sides
Mar 10 Infinitude of Primes As a Quickie
Mar 5 Between a Cross and a Square
Mar 4 Infinitude of Primes Via Powers of 2
Mar 4 Sophie Germain's Identity
Mar 3 A Property of Number 4
Mar 2 Equilateral Triangle on a Closed Curve
Mar 1 Review of Single Digits by Marc Chamberland
Mar 1 Pythagorean Theorem by Analytic Geometry
Feb 28 An Infinite Product from Recursion
Feb 27 Isosceles Configuration in Triangle
Feb 26 Pythagorean Theorem via Half-Angle Formulas
Feb 25 Isogonal Concurrencies
Feb 25 Cutting a Hole in Half
Feb 21 Getting the first digits of Pi by counting collisions
Feb 21 A Median Surprise
Feb 20 A Property of Altitudes
Feb 20 All about altitudes
Feb 18 Beyond Pythagoras
Feb 18 Golden Ratio in Five Steps
Feb 17 An Unusual Generalization of the Pythagorean Theorem
Feb 17 An Unusual Generalization of the Pythagorean Theorem, a Variant
Feb 16 Triangle from Side, Inradius, and Altitude
Feb 15 Regular Octagon by Paper Folding
Feb 10 Triangle from a, A, m_{c}/m_{b}
Feb 9 Perrin Sequence
Feb 6 Carnot's Theorem from Ptolemy's Theorem
Feb 4 Golden Ratio in a Rhombus
Feb 3 What Is Counterexample
Feb 2 Golden Ratio in Inscribed Equilateral Triangles
Feb 2 Golden Ratio As a Mathematical Morsel
Feb 1 Golden Ratio in Two Equilateral Triangles
Feb 1 Golden Ratio in Two Squares
Jan 31 Golden Ratio in Hexagon
Jan 31 Why sin(x)/x tends to 1
Jan 31 The Squeeze Theorem
Jan 30 Golden Ratio in Equilateral Triangles
Jan 30 Golden Ratio in Square
Jan 29 Undefined vs Indeterminate in Mathematics
Jan 28 The Very Last, for 2014, proof of the Irrationality of sqrt(2)
Jan 28 Isoperimetric Property of Equilateral Triangles II
Jan 26 Isoperimetric Theorem For Quadrilaterals II
Jan 25 Triangular Areas in Circle
Jan 24 Rectangular Areas in Circle
Jan 23 Without Loss of Generality
Jan 22 Divergence of {cos(n)}
Jan 21 Golden Ratio via van Aubel's Theorem
Jan 20 Sine And Cosine Are Continuous Functions
Jan 16 The Fascinating World of Graph Theory
Jan 15 Golden Ratio in Circle - in Droves
Jan 14 Pythagoras, from the Power of a Point - Again
Jan 13 Associativity from 1977 IMO
Jan 8 Another Golden Ratio in Semicircle
Jan 6 From 3 to Golden Ratio in Semicircle
Jan 1 A Property of Orthic Triangle
Jan 1 Circumcenter and Orthocenter Are Isogonal Conjugate

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Copyright © 1996-2018 Alexander Bogomolny