December 30 
Orthogonal Lines, Midpoints, and Collinearity 
December 29 
Integer Triangles with Two Angles in the Ratio 1 : 2 
December 28 
Concyclicity in Two Semicircles 
December 26 
Angles in 456 Triangle 
December 25 
Another Concurrence on the 9Point Circle 
December 24 
Another Seven Circles Theorem 
December 23 
The 808020 Triangle Problem, A Variant, Solution #2 
December 23 
Problem 4 from the IMO 2013  Synthetic Solution 
December 22 
Problem 4 from the IMO 2013 
December 21 
Review of Origins of Mathematical Words 
December 21 
Equilateral Triangles formed by Circumcenters 
December 20 
Miquel Circumcenters 
December 19 
Three lines at 60 degres and Circumcenters 
December 18 
Infinitude of Primes Via Euler's Product Formula for Pi 
December 18 
Infinitude of Primes Via Euler's Product Formula 
December 14 
Telescoping Sums and Series 
December 13 
Puzzle of 30 Grid Points and 5 Circles 
December 12 
Puzzle of 25 Grid Points and 5 Circles 
December 11 
Review of Who's Bigger? 
December 10 
The Eutrigon Theorem 
December 8 
Billiard Handicap 
December 8 
Squeeze (Sandwich, Pinching ...) Theorem (Lemma): an Example 
December 6 
Review of Will You Be Alive 10 Years from Now? 
December 6 
Family Size 
December 5 
From One Collinearity to Another 
December 4 
Problem 1, 2012 IMO 
December 4 
Lighthouse at Fermat Points 
December 3 
Circle in Isosceles Triangle and a Fixed Point 
December 2 
A Nice Trig Formula 
December 2 
Double and Half Angle Formulas 
November 29 
Review of ProblemSolving and Selected Topics in Euclidean Geometry 
November 26 
Pythagorean Theorem via Geometric Progression 
November 22 
Morley's Theorem: A Proof That Needs Fixing 
November 21 
Carnot's Criterion via Aerial Coordinates 
November 20 
Cevians And Semicircles 
November 20 
Marking And Breaking Sticks 
November 19 
Ptolemy's Equality/Inequality via Inversion 
November 19 
Morley's Theorem: Second Proof by Roger Smyth 
November 12 
Review of Mathematical Olympiad in China (20092010). Problems and Solutions 
November 12 
Sums of the Elements of Three Element Subsets 
November 10 
Selfdocumenting Iterations 
November 9 
On the Intersection of kx and sin(x) 
November 9 
Conics Related To In and Excircles 
November 8 
Carnot's Criterion 
November 7 
Triangles with Sides in Geometric Progression 
October 17 
Elementary Problems That Beg for Generalization 
September 27 
Involution on the Projective Line 
September 25 
Carnot's Theorem for Conics 
September 25 
Expressions Invariant under Projecive Mappings 
September 19 
Radical Simplification  Not That Simple! 
September 16 
Six Circles with Concurrent Pairwise Radical Axes 
September 15 
Center of Gravity and Motion of Material Points 
September 13 
Spiral Similarity and Collinearity 
September 11 
A Problem in Hinged Squares II 
September 10 
Cevian Cradle II 
September 7 
On Bottema's Shoulders with a Ladder 
September 5 
Four Isosceles Triangles Hinged at Vertices 
September 4 
Abutting Equilateral Triangles on a Line I  a finished version 
September 3 
Six Concyclic Circumcenters in Fermat's Configuration 
September 1 
Morley's Theorem  Taylor and Marr's Proof 
August 31 
Golden Ratio via Golden Rhombus 
August 30 
Concyclic Points from Midpoint of an Arc 
August 17 
Angle Bisectors Cross Circumcircle 
August 16 
Leech Trees and Taylor's Criterion 
August 14 
An Unexpected Rhombus 
August 13 
Eyeballing a Ball 
August 13 
EyetoEye Theorem II 
August 13 
EyetoEye Theorem I 
August 12 
Parabola and Abutting Equilateral Triangles 
August 12 
Focal Definition of Parabola 
August 10 
Abutting Equilateral Triangles on a Line I 
August 7 
Focus on the Eyeball Theorem 
August 7 
Praying Eyes Theorem 
August 5 
Fermat's Hexagon 
August 5 
Napoleon's Hexagon 
August 3 
An Unexpected Pair of Similar Triangles Which Are Equal 
August 3 
Some Properties of Common Tangents 
August 1 
Two Pascals Merge into One 
July 29 
Joined Common Chords of Napoleon's Circumcircles 
July 29 
An Extra Triple of Equilateral Triangles for Napoleon 
July 25 
Two Similar Triangles with Parallel Sides 
July 24 
Kiepert's Triangles Graduate to Ears of Arbitrary Shape 
July 22 
A Final Chapter of the Asymmetric Propeller Story 
July 21 
Conics Intersecting Sides Of A Triangle 
July 21 
Cassini's Ovals and Geometric Optimization 
July 20 
Napoleon on Hinges in GeoGebra 
July 19 
Kiepert's Centroid 
July 18 
Egyptian Triangle By Paper Folding III 
July 17 
Seven Equal Circles 
July 16 
Sum of Three Squares 
July 15 
Concyclic Points of Two Ellipses with Orthogonal Axes 
July 13 
Parallelogram in Four Circles 
July 12 
Two Triples of Concurrent Cevians and a Conic 
July 11 
Concurrent Cevians and a Conic through Their Feet 
July 11 
Conics Intersecting Sides Of A Triangle 
July 9 
Three pairs of Parallel Lines and a Conic 
July 8 
Representation of 3 with Three Equal Digits 
July 8 
Perimeters of Convex Polygons, One within the Other 
July 7 
Circle Rotations and Fixed Points 
July 6 
Weather Forecasting: A Story of Mathematical Triumph 
July 3 
Ellipse Touching Sides of Triangle at Midpoints 
June 26 
Kulikowski's Theorem 
June 25 
Yet Another Appearance of the Golden Ratio 
June 19 
Climbing Pyramidal Slopes 
June 17 
Property of Right Isosceles Triangle 
June 17 
Five Squares in Complex Numbers 
June 11 
Parallel Chords in Conics 
June 7 
Dynamic Software as Serendipity Enhancement 
June 6 
Rhombus in Circles 
June 5 
Naming Infinity  the book 
June 5 
Two Common Chords in Three Concurrent Circles 
June 4 
Three Common Chords in Three Concurrent Circles 
June 4 
Two Diameters and Longest Common Chord 
June 4 
Seven Concyclic Points 
June 3 
Three Collinear and Four Concyclic Points 
May 29 
Two Circles, Ellipse, and Parallel Lines 
May 28 
Elves and Gnomes 
May 26 
Is GLOBALHELLFRY a Prime? 
May 26 
The Number of Judges and the Number of Votes 
May 25 
Egyptian Triangle By Paper Folding II 
May 24 
Maxwell's Theorem by Way of Trigonometric Ceva 
May 23 
A square in parallel lines 
May 20 
Area and Perimeter Splitters in a Triangle 
May 20 
Probabilities in a Painted Cube 
May 14 
Cutting Triangle in Two by a Line through a Point 
May 9 
e in the Pascal Triangle 
May 7 
Applying Daniel Dennett's New Book 
May 6 
Length of a Median 
May 3 
Francois Viete's Reduction of CCC to PCC 
May 2 
LCC: Apollonius' Problem with Two Circles and a Line 
May 2 
LLC: Apollonius' Problem with Two Lines and a Circle 
May 1 
PLC: Apollonius Problem with a point, a line, and a circle 
April 30 
PPL: An Elementary Solution 
April 29 
PCC: Apollonius' Problem with Two Circles and a Point 
April 28 
Apollonius's Construction 
April 28 
Combo Playground: Calculating the Number of Paths on a Square Grid 
April 28 
In the Spirit of Thebault I 
April 27 
CCC: Gergonnes's Solution to Apollonius' Problem 
April 27 
Poles, Polars and Orthogonal Circles 
April 25 
The Four Touching Circles Problem IV 
April 23 
How to Construct Orthogonal Circle 
April 22 
How to Construct Common Tangents to Two Circles 
April 19 
CCC: Apollonius' Problem with Three Intersecting Circles 
April 15 
PLL: Apollonius' Problem with Two Lines and a Point 
April 14 
PPL: Apollonius' Problem with Two Points and a Line 
April 14 
PPC: Apollonius' Problem with Two Points and a Circle 
April 14 
The Problem of Apollonius 
April 13 
How to Construct Tangents from a Point to a Circle 
April 13 
How to Construct a Radical Axis 
April 7 
Two Triangles Inscribed in a Conic  with Elementary Solution 
April 5 
Apollonian Circle for Two Lines and a Circle 
April 4 
A dissection puzzle. Proof #99 of the Pythagorean theorem 
April 4 
Counting Fat Sets 
March 24 
Vandermonde's Convolution Formula 
March 21 
Lucas' Theorem II 
March 20 
The Golden Ticket: P, NP, and the Search for the Impossible 
March 18 
A review of a biography of Vito Volterra

March 13 
Two Triangles Inscribed in a Conic  with Solution 
March 12 
Why cats land on their feet  a problem of 80 years standing! 
March 4 
Napoleon's Theorem by Vectors and Trigonometry 
March 3 
An Inequality by Uncommon Induction 
March 2 
Concurrence of the Altitudes As Seen from 3D 
March 1 
3D Concurrency Of Altitudes 
March 1 
Photo Cameras I owned 
Feb 27 
Computers  then and now  from personal experience 
Feb 25 
Two Triangles Inscribed in a Conic 
Feb 21 
An Euclidean Construction with Inversion 
Feb 20 
Exeter Point 
Feb 20 
Concurrence Not from School Geometry 
Feb 15 
The Butterfly Effect 
Feb 12 
The Eutrigon Theorem 
Feb 10 
cos/sin inequality 
Feb 5 
An Application of Quadratic Formula 
Feb 3 
What happens to the area when the radius of circle is doubled? 
Jan 31 
Excircles Variant of Thebault's Problem III 
Jan 30 
A Lemma on the Road to Sawayama 
Jan 30 
A Double Meaning of an Arc's Midpoint 
Jan 29 
A Property of Right Trapezoids 
Jan 28 
Review of Mathematical Circle Diaries: Complete Curriculum for Grades 5 to 7 by Anna Burago 
Jan 24 
Review of Xu Jiagu's Lecture Notes on Mathematical Olympiad Courses for Senior Section 
Jan 24 
Roots and Tangents 
Jan 22 
Inequality with Harmonic Differences 
Jan 21 
An Identity From the 2010 China Mathematical Competition 
Jan 20 
Solve  an Olympiad Problem  in Your Mind 
Jan 18 
Square from Four Points, One on Each Side 
Jan 18 
Square from Four Points, One on Each Side, Solution 1 
Jan 18 
Square from Four Points, One on Each Side, Solution 2 
Jan 17 
For any k greater than 3, Decompose Cyclic Quadrilaterals into k Cyclic Quadrilaterals 
Jan 17 
Problem 4 from the 1959 IMO: Construction of a Right Triangle 
Jan 16 
A Problem of Divisibility by 2^{n} 
Jan 15 
Henri Poincaré: A Scientific Biography 
Jan 14 
Inspiration, Perspiration and Satisfaction 
Jan 12 
A Pair of Probability Games for Beginners 
Jan 11 
A Diameter As a Diagonal of Inscribed Quadrilateral 
Jan 10 
Countability of Rational Numbers as a Union of Finite Sets 
Jan 9 
5x5 Square Grid and 5 Circes 
Jan 9 
Linear Function with Coefficients in Arithmetic Progression 
Jan 7 
Review of Numbers and Functions. From a classicalexperimental mathematician's point of view by Victor H. Moll 
Jan 5 
Infinitude of Primes  from Infinitude of Mutual Primes 
Jan 2 
Bottema's Theorem  Proof Without Words 
Jan 1 
Tangent of 22.5°  Proof Wthout Words 