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 |