A heptadecagon (or a 17-gon) is a seventeen sided polygon.
Constructing the Heptadecagon
In 1796, Gauss proved, at the age of 19 (let that sink in…) that the heptadecagon is constructible with a compass and a straightedge, such as a ruler. His proof of the constructibility of an n-gon relies on two things:
the fact that “constructibility is equivalent to expressibility of the trigonometric functions of the common angle in terms of arithmetic operations and square root extractions“;
The Sierpinski Triangle, or Sierpinski Sieve, is a fractal described by Polish Mathematician Sierpinski in 1915, although it appeared in Italian art from the 13th century. It has an overall shape of an equilateral triangle, and is subdivided recursively into smaller equilateral triangles.
Constructing a Sierpinski Triangle
Start with an equilateral triangle.
Connect the midpoints of each side, hence dividing it into 4 smaller congruent equilateral triangles.
Now cut out the triangle in the centre.
Repeat steps 2 and 3 with each of the remaining smaller triangles.
If we let be the number of black triangles after iteration n, be the length of a side of a triangle, and be the fractional area which is black after the nth iteration, then: