| 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 |
