Chronology of Updates

Note

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, 2014, and 2015 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 31 Golden Ratio in Pentagon And Three Triangles
Dec 31 Stathis Koutras' Theorem
Dec 30 Equiangular p-gons
Dec 30 An Inequality for the Cevians through Circumcenter
Dec 29 An Inequality with Constraint in Four Variables
Dec 29 An Inequality in Triangle with Roots and Circumradius
Dec 29 The power of substitution II: proving an inequality with three variables
Dec 28 A Cyclic Inequality in Three Variables with Constraint
Dec 28 Two Products: Constraint and Inequality
Dec 27 An Inequality in Reciprocals II
Dec 26 An Inequality with Arctangents in Triangle
Dec 26 Leo Giugiuc's Second Lemma And Applications
Dec 26 Red and Pink Areas
Dec 25 Much from Little
Dec 25 Triangle in a 5x5 Square
Dec 24 Dorin Marghidanu's Believe It Or Not
Dec 24 Golden Ratio in Pentagon And Two Squares
Dec 23 Triangle in a 4x4 Square
Dec 23 Composition of Functions, an Exercise
Dec 23 A Cyclic Inequality in Three Variables VII
Dec 23 Graph without 3-Cycles
Dec 22 Distance Inequality
Dec 22 Average Number of Runs
Dec 22 Graph with Nodes of Even Degree
Dec 21 An Inequality with Sin, Cos, Tan, Cot, and Some
Dec 21 Orthocenter in Complex Plane
Dec 20 A Special Point: Intersection of the Diagonals in Quadrilateral
Dec 19 Complicated Constraint - Simple Inequality
Dec 18 An Inequality with Sides and Medians
Dec 17 First 1008 Digits
Dec 17 Volume of Fibonacci Tetrahedron
Dec 17 A Cyclic Inequality in Three Variables VI
Dec 17 A Not So Simple Inequality in Three Variables
Dec 15 An Inequality and Its Modifications
Dec 13 Exercise with Square Spiral
Dec 12 Barycenter of Cevian Triangle
Dec 11 When Is Triangle Equilateral: Marian Dinca's Criterion
Dec 11 Another Integral Inequality from the RMM
Dec 10 Dimensionless Inequality in the Euclidean Plane
Dec 10 Triangles on HO
Dec 10 What Is Red Herring
Dec 9 A Cyclic Inequality in Three Variables V
Dec 8 An Inequality with Determinants V
Dec 8 A Cyclic Inequality in Three Variables IV
Dec 7 An Inequality Where One Term Is More Equal Than Others
Dec 7 Quadratic Function for Solving Inequalities
Dec 6 Telescoping Tangents
Dec 6 A Cyclic Inequality in Three Variables III
Dec 4 Wonderful Inequality on Unit Circle
Dec 3 Centroid and Incenter in Isosceles Tetrahedra
Dec 3 A Cyclic Inequality in Three Variables II
Dec 3 An Inequality with Tangents and Cotangents
Dec 2 Chebyshev Holds a Key
Dec 1 Isosceles Tetrahedra Characterization via Inequalities
Nov 30 Centroid and Circumcenter in Isosceles Tetrahedra
Nov 29 The Joy of SET
Nov 29 A Relation in Inscribed Tetrahedra
Nov 28 Three Concurrent Chords at 60 Degrees Angles
Nov 27 Cevians Through the Circumcenter
Nov 26 An Inequality with Factorial
Nov 25 An Inequality with Just Two Variable II
Nov 25 An Inequality with Just Two Variable
Nov 24 How Long Are the Angle Bisectors of a Degenerate Triangle?
Nov 24 Golden Ratio in an Isosceles Trapezoid with a 60 degrees Angle
Nov 24 A 60 degrees Rhombus in a 60 degrees Isosceles Trapezoid
Nov 23 Two-Sided Inequality - One Provenance
Nov 22 NonSquare Matrix as a Tool for Proving an Inequality
Nov 22 An Inequality in Cyclic Quadrilateral IV
Nov 22 9 Point Center on Angle Bisector
Nov 22 Euler Line Cuts Off Equilateral Triangle
Nov 21 Euler Line in a Triangle with a 60 Degrees Angle
Nov 21 Sangaku via Peru
Nov 20 Golden Ratio in 5-gon and 6-gon
Nov 19 A Cyclic Inequality in Three Variables
Nov 17 Wu's Inequality
Nov 16 Divide And Conquer in Cyclic Sums
Nov 16 An Easy Inequality with Three Integrals
Nov 15 A Property of Trapezoid with a Right Angle
Nov 14 An Inequality in Cyclic Quadrilateral III
Nov 14 Another Golden Ratio in Regular Pentagon
Nov 13 Inequality with Three Numbers, Not All Zero
Nov 13 An Inequality in Cyclic Quadrilateral II
Nov 12 Inequality with Three Linear Constraints
Nov 12 An Inequality in Cyclic Quadrilateral
Nov 11 An Inequality with Sines
Nov 10 Alice's Adventures in Wonderland
Nov 10 A Cycling Inequality with Integrals II
Nov 9 Marian Dinca's Refinement of Nesbitt's Inequality
Nov 8 Tangent, Cotangent and Square Roots Inequality
Nov 7 Inequality in Quadrilateral
Nov 6 Four Circles and a Line
Nov 6 Dorin Marghidanu's Example for Radon's Inequality
Nov 6 An All-Inclusive Inequality II
Nov 5 Inequality with Cubes and Cube Roots
Nov 5 Butterfly by Midline
Nov 3 A Two-Triangle Inequality II
Nov 3 Determinant on a Circle
Nov 2 Interpretation of the coordinate formula for the dot product in 3D
Nov 1 An Inequality in Parallelogram of Unit Area
Oct 31 A Cyclic Inequality in Triangle II
Oct 30 A Cyclic Inequality in Triangle
Oct 29 An Elementary Inequality by Non-elementary Means
Oct 27 One Triangle from Another II
Oct 27 One Triangle from Another
Oct 26 Butterfly via the Scale Factor of the Wings
Oct 26 Butterfly via Ceva
Oct 26 An Inequality from RMM with a Generic 5
Oct 26 Problem 3824 from Crux Mathematicorum
Oct 25 The Cosine Law: PWW by S. Kung
Oct 25 An Inequality with Absolute Values
Oct 24 An Inequality with Constraint XIII
Oct 22 ab + bc + ca does not exceed aa + bb + cc
Oct 22 A Cycling Inequality with Integrals
Oct 21 An Inequality from RMM with Powers of 2
Oct 20 Dan Sitaru's Inequality with Roots and Powers
Oct 20 A 4-variable Inequality from the RMM
Oct 19 Dan Sitaru's Inequality with Tangents
Oct 18 An Inequality with Constraint XII
Oct 17 Gregoie Nicollier's Proof of Napoleon's Theorem
Oct 14 Sladjan Stankovik's Inequality With Constraint
Oct 13 A One-Sided Inequality in Triangle
Oct 13 Dorin Marghidanu's Calculus Lemma
Oct 11 An Inequality with Exponents from a Calculus Lemma II
Oct 10 Leo Giugiuc's Proof of Napoleon's Theorem
Oct 9 Inequality with Roots, Squares and the Area
Oct 9 Yet Another Analytic Proof of Napoleon's Theorem
Oct 9 Problem 11804 from the AMM
Oct 7 5-Step Construction of the Golden Ratio, One of Many
Oct 5 An Inequality with Exponents from a Calculus Lemma
Oct 4 An All-Inclusive Inequality
Oct 1 Circumcenter and Orthocenter
Sep 29 The Golden Pentacross
Sep 29 Miguel Ochoa's Chords And Tangents
Sep 29 A Tricky Integral Inequality
Sep 27 Quadrilateral Inequality
Sep 27 Golden Ratio in a Butterfly Astride an Equilateral Triangle
Sep 27 Addition and Subtraction Formulas for Sine and Cosine IV
Sep 26 Inequality by Calculus
Sep 24 Three Junior Problems from Vietnam
Sep 21 An Integral Inequality from the RMM
Sep 18 Hlawka in Convex Quadrilateral
Sep 10 Points on Incircle: Another Look
Sep 9 Incircle in Equilateral Triangle
Sep 9 Circles in Barycentric Coordinates
Sep 6 Another Property of Points on Incircle
Sep 5 Two Conditions for a Triangle to Be Equilateral
Sep 4 Completing the Square Where It Matters
Sep 2 Another Refinement of the Ionescu-Weitzenbock Inequality
Aug 31 Two Refinements of Ionescu-Weitzenbock Inequality
Aug 29 A Two-Triangle Inequality
Aug 27 Problem 4020 from Crux Mathematicorum
Aug 24 Hung Viet's Inequality
Aug 23 An Inequality with Determinants IV
Aug 22 An Inequality in Acute Triangle, Courtesy of Ceva's Theorem
Aug 21 An Inequality with Finite Sums
Aug 19 An Inequality with Determinants III
Aug 16 An Inequality In Triangle That Involves the Four Basic Centers
Aug 14 Area Optimization in Trapezoid
Aug 10 Radon's Inequality and Applications
Aug 9 Dorin Marghidanu's Example
Aug 9 Bergstrom's inequality
Aug 6 Two Butterflies Theorem as a Porism of Cyclic Quadrilaterals
Aug 4 The Devil is in the Exceptions
Aug 3 Prasolov's Pythagorean Identity
Aug 3 Inequality In Triangle: Sides and Angle Bisectors
Aug 2 A Trigonometric Inequality from the RMM
Aug 2 Equation in Radicals as a System of Equations
Aug 1 An Inequality in Triangle, X
Jul 31 An Inequality in Triangle, IX
Jul 30 When Is Triangle Isosceles: Miguel Ochoa Sanchez's Criterion
Jul 28 Sum of Squares in Equilateral Triangle
Jul 28 Construction of a Triangle from the Circumradius, Inradius, and an Altitude
Jul 27 Cospherical Points
Jul 27 A System of Equations in Determinants
Jul 25 Powers and Fractions Inequality
Jul 24 Miguel's Tangents: Modern Day Sangaku
Jul 23 Miguel's Area of Square
Jul 21 Proof by A. Robson
Jul 18 Greatest Difference in Arithmetic Progression
Jul 12 An Inequality in Triangle, VIII
Jul 6 Hlawka-like Dinca's Inequality
Jul 5 Quadratic Formula: Completing And Not Completing the Square
Jun 27 An Inequality with Cot, Cos, and Sin
Jun 25 Miguel's Special Trapezoid
Jun 18 An Inequality with Integrals and Rearrangement
Jun 18 A Problem from the Danubius Contest 2016
Jun 15 Monthly Problem 11199
Jun 14 Muirhead's Inequality
Jun 14 Infinitude of Primes - A. Thue's Proof
Jun 13 An Inequality in Reciprocals
Jun 12 The power of substitution: solving an equation in a right triangle
Jun 11 An Inequality with Constraint XI
Jun 10 An Inequality with Determinants II
Jun 9 Modern Vietnamese Classic
Jun 8 An Inequality with Determinants
Jun 8 Golden Ratio in Equilateral and Right Isosceles Triangles
Jun 8 Golden Ratio With Two Unequal Circles And a Line II
Jun 7 Golden Ratio In a 2x2 Square: Without And Within
Jun 7 An Inequality in Triangle, VII
Jun 6 Characterization of the Symmedian Point with Medians and Orthic Triangle
Jun 3 An Inequality in Integers II
Jun 2 Area of Isosceles Triangle
Jun 2 Golden Ratio In Rectangles
Jun 1 Golden Ratio Next to the Poster
Jun 1 Golden Ratio Poster
Jun 1 Simple Inequality with Many Faces And Variables
May 31 Golden Ratio In Right Isosceles Triangle
May 30 An Inequality with Cycling Sums
May 30 Golden Ratio In Three Tangent Circles
May 29 An Application of Hlawka's Inequality II
May 29 Golden Ratio In a 3x3 Square II
May 28 Golden Ratio In a 3x3 Square
May 28 Biochemical Algorithms and School Algebra
May 28 Golden Ratio With Two Unequal Circles And a Line
May 27 Inequality with Two Minima
May 27 Golden Ratio in a Chain of Polygons, So to Speak
May 24 Golden Ratio With Two Equal Circles And a Line
May 18 An Arctan Identity and its Consequence
May 16 Inequality with Powers And Radicals
May 14 Surprise: Right Angle in Circle
May 13 Inequality with Nested Radicals II
May 12 Symmedian and the Simson
May 11 Pythagorean Theorem through Angles 60 and 120
May 11 The Law of Cosines for 60 and 120
May 7 Rectangle Inscribed in Triangle
May 6 An Inequality from Gazeta Matematica, March 2016 IV
May 6 Perimeters of Parallelogram And Rhombus
May 5 Symmedian via Parallel Transversal and Two Circles
May 4 Ascending Bases and Exponents in Pascal's Triangle
May 3 No Need To Lose the Battle
May 1 Problem 3980 from Crux Mathematicorum
May 1 Symmedian via Squares and a Circle
Apr 30 Steiner's Ratio Theorem
Apr 30 Vector Algebra in Tetrahedron
Apr 29 An Inequality from Gazeta Matematica, March 2016 III
Apr 26 Not too easy - not too difficult
Apr 18 A Generalization of Van Aubel's Theorem
Apr 16 Pythagorean Theorem through Equilateral Triangles
Apr 14 A Sum by Dorin Marghidanu
Apr 13 7 or 22
Apr 10 cos 75 + cos 45 = cos 15
Apr 10 RomanoNorwegian Inequality
Apr 9 Another Equilateral Triangle in Napoleon's Configuration
Apr 8 An Inequality from Gazeta Matematica, March 2016 II
Apr 4 Weekly report, the week of March 28, 2016
Apr 3 An Inequality from Gazeta Matematica, March 2016
Apr 1 Doodling on April 1st
Mar 30 Parallelogram in Trapezoid
Mar 30 Heron in Trapezoid
Mar 29 Construction of a Triangle from an Angle, Circumcenter and Incenter
Mar 29 Construction of a Triangle from a Side, the Median and the Angle Bisector
Mar 29 Spectral Decomposition of a Planar Quadrilateral: an Illustration
Mar 29 Spectral Decomposition of a Planar Quadrilateral
Mar 27 Weekly report, March 21-27, 2016
Mar 27 Arbelos' Morsels
Mar 26 Improving an Inequality
Mar 26 Area Inequality in Trapezoid
Mar 25 Geometric Mean In Trapezoid
Mar 24 An Application of Schur's Inequality II
Mar 24 An Inequality in Triangle, VI
Mar 23 Squares on Sides of a Parallelogram
Mar 23 Squares on Sides of a Quadrilateral II
Mar 21 A Property of a Median
Mar 19 Equilateral Triangles on Sides of a Parallelogram III
Mar 18 Sums of Unit Vectors
Mar 14 Inradii Relation in Right Triangle
Mar 13 Integral of a Piece-wise Function
Mar 13 Sums of Squares in Circle
Mar 13 Camouflaged Butterfly
Mar 11 Golden Ratio in Pentagon: Once More
Mar 11 Constant Ratio on Circle
Mar 8 Curious Irrationality in Square
Mar 7 Perpendiculars in Parallelogram
Mar 7 JCT - K3,3 on a Torus or Moebius Strip
Mar 6 Pythagorean Theorem: Some False Proofs
Mar 2 Proof #116 of the Pythagorean Theorem
Mar 2 Sum of Two Squares
Feb 29 Linear Algebra Tools for Proving Inequalities: Cauchy-Binet Formula
Feb 28 An Inequality with Constraint X
Feb 26 An Inradii Relation in Inscriptible Quadrilateral
Feb 25 An Inequality in Triangle, V
Feb 24 An Inequality with Constraint IX
Feb 23 Two Squares In Circle
Feb 23 A First Look at The Population Explosion Book
Feb 22 A Generalization of an Inequality from a Romanian Olympiad
Feb 22 Doubling Investment for a Fee And Getting Zero
Feb 20 An Inequality in Triangle IV
Feb 19 Common Centroids Lead to Equilateral Triangle
Feb 18 Proportions with Two Orthocenters
Feb 18 An Inequality with a Generic Proof
Feb 16 Linear Algebra Tools for Proving Inequalities
Feb 15 A Problem in Complex Numbers Sets 3 Aside
Feb 14 A Problem from Croatian TST, Proof Variants
Feb 13 A Problem from Croatian TST
Feb 11 Extrema of x^3+y^3+z^3-xyz on the unit sphere
Feb 11 An Asymmetric Inequality
Feb 10 Equilateral Triangle on Parallel Lines II
Feb 10 Matrices and Determinants as Optimization Tools: an Example
Feb 9 Integral Is Area
Feb 8 An Inequality in Triangle III
Feb 7 $\sin 1^\circ+\sin 2^\circ+\sin 3^\circ+\cdots+\sin 180^\circ=\tan 89.5^\circ$
Feb 6 Condition to Have a 60 Degrees Angle
Feb 6 A Simple Inequality in Three Variables
Feb 5 Cyclic Quadrilateral from the USAMO
Feb 5 An Elementary Proof for Euler's Series
Feb 5 Exponential Inequalities for Means
Feb 4 Areas between Two Parallelograms
Feb 4 Fermat in a Triangle with a 60 Degrees Angle
Feb 2 An Inequality with Constraint VIII
Feb 1 How Jost Burgi Computed the Sines of All Integer Angles in 1586
Jan 31 Two Equations in Three Variables
Jan 30 The Roads We Take
Jan 30 Birth of an Inequality
Jan 30 A Property of Inscriptible Quadrilaterals
Jan 29 Beatty Sequences II
Jan 26 Antiparallel and Circumradius
Jan 26 Batman's Problem
Jan 25 A Followup on Solving A Fourth Degree Equation
Jan 24 Surprising 60 degrees in Equilateral Triangle
Jan 23 Solve A Fourth Degree Equation
Jan 23 2006 Hellenic Mathematical Olympiad, Problem 4
Jan 22 Chasing Secant Angles
Jan 22 Review of The Best Writing on Mathematics 2015
Jan 20 Pythagorean Theorem, Proof 115
Jan 19 Triangle of Maximum Area II
Jan 16 Triangle of Maximum Area
Jan 14 When Circle Meets Hyperbola
Jan 13 An Inequality with Exponents
Jan 9 For Equality Choose Angle Bisector
Jan 8 Sanchez's Areas in Bottema's
Jan 8 An Inequality with Constraint VII
Jan 6 An Inequality in Integers
Jan 6 Orthogonality in Isogonal Conjugacy
Jan 5 Non-transitive Dice
Jan 2 An Inequality for Mixed Means

|Mail| |Fron page| |Contents|

Copyright © 1996-2018 Alexander Bogomolny

[an error occurred while processing this directive]
[an error occurred while processing this directive]