### Thébault’s theorem

If you place squares on the sides of any parallelogram, their centers will always form a square.

### Geometric Illusion: Vertigo Pattern

Do you feel queasy when you look at this wallpaper? Though they appear to be sloped, the columns of stacked white and black patterns are perfectly straight and PARALLEL to each other.

Interested in my optical illusions? Feel free to visit my author page.

### Coxeter Disc

Infinite flavor in a finite fruit pastry space!

### Infinite Pythagorean Triplets

Consider the following simple progression of whole and fractional numbers (with odd denominators):
1 1/3, 2 2/5, 3 3/7, 4 4/9, 5 5/11, 6 6/13, 7 7/15, 8 8/17, 9 9/19, …
Any term of this progression can produce a Pythagorean triplet, for instance:
4 4/9 = 40/9; the numbers 40 and 9 are the sides of a right triangle, and the hypotenuse is one greater than the largest side (40 + 1 = 41).

### A curious right triangle

The sides of a pentagon, hexagon, and decagon, inscribed in congruent circles, form a right triangle.

### The Arithmetic-Geometric Mean Inequality

A visual intuitive proof that √ab cannot be larger than (a+b)/2, where a, b ∈ R*+

### When a plane intersects a dodecahedron

A cross-section of the dodecahedron can be an equilateral triangle, a square, a regular pentagon, a regular hexagon (two ways), or a regular decagon.