Two Hilbert curve.

Science and Math
Science and Math World

Triangulating a circle.

How to do a drawing like this? Start with a circle and divide it into n equal parts. I choose n=100 for this drawing. There is an easy formula for this, the i-th point is (radius*cos(i*2*PI/n),

radius*sin(i*2*PI/n)). Then for each i connect the i-th point to the point (radius*cos(PI-2*i*2*PI/n), radius*sin(PI-2*i*2*PI/n)). This might not be one of the original points, but it is on the circle. And that is it 🙂

Why is this mathematically interesting? This way we get a set of nonparallel lines such that there are a lot of triple intersections between them.

Pattern

Based on Joan Taylor’s wanderer tiling. http://tilings.math.uni-bielefeld.de/substitution/wanderer-refl/

Reuleaux triangles. These shapes have a very nice property, their width is the same in any direction.