## Six Points on a Circle

Take 6 points on a circle such that every second edge (green chords) has length equal to the radius of the circle. Then the midpoints of the other three sides of the cyclic hexagon form an equilateral triangle.

## Geometric Passe-muraille

A 3D regular hexahedron solid (cube) passing through a 2D plane:

## Math Hack of the Day: 66 + 99 = ?

Maths à la De Funès…

## Life, the Universe, and Maths

For years, mathematicians have worked to demonstrate that x3+y3+z3 = k, where k is defined as the numbers from 1 to 100. This theory is true in all cases except for an unproven exception: 42.

By 2016 and over a million hours of computation later, researchers of the UK’s Advanced Computing Research Center had its solution for 42.

More intriguing number facts here.

## Prime Square

3,139,971,973,786,634,711,391,448,651,577,269,485,891,759,419,122,938,744,591,877,656,925,789,747,974,914,319,422,889,611,373,939,731 produces reversible primes in each row, column and diagonal when distributed in a 10×10 square.
Diagram by HT Jens Kruse Andersen.

## Ellipse-Tracer

Two moving tangent circles can trace ellipses

## Wallace-Simson’s Line Theorem

The three blue points always lie on a straight line. The blue points are the closest points to the moving red point on the lines. In other words the blue points are the projections of the moving red point to the lines.