| 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 4-5-6 Triangle |
| December 25 |
Another Concurrence on the 9-Point Circle |
| December 24 |
Another Seven Circles Theorem |
| December 23 |
The 80-80-20 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 Problem-Solving 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 (2009-2010). Problems and Solutions |
| November 12 |
Sums of the Elements of Three Element Subsets |
| November 10 |
Self-documenting 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 |
Eye-to-Eye Theorem II |
| August 13 |
Eye-to-Eye 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 2n |
| 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 classical-experimental 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 |
