# Bernhard Rietzl

Freelance artist

Schwabmuenchen, Germany

I am interested in the combination of art and mathematics especially number theory. Prime numbers can be seen as the elements of the whole numbers, compound numbers literally are the products of these basic elements. It is like in chemistry where the chemical elements are the basis for all compound molecules.

Nautilus theodori

15 x 20 x 12 cm

plastics, 3D printed

2016

The spiral of Theodorus is a spiral composed of contiguous right triangles. It was first constructed by Theodorus of Cyrene (Greece, 5th century BC).

The spiral is started with an isosceles right triangle, with each leg having unit length. Another right triangle is formed with one cathetus being the hypotenuse of the prior triangle (with length √2) and the other leg having length of 1; the length of the hypotenuse of this second triangle is √3. This repeats; the i th triangle in the sequence is a right triangle with side lengths √i and 1, and with hypotenuse √i + 1.

In German this spiral is called "Wurzelschnecke" (root snail), which inspired the idea for constructing this 3D work.

The spiral is started with an isosceles right triangle, with each leg having unit length. Another right triangle is formed with one cathetus being the hypotenuse of the prior triangle (with length √2) and the other leg having length of 1; the length of the hypotenuse of this second triangle is √3. This repeats; the i th triangle in the sequence is a right triangle with side lengths √i and 1, and with hypotenuse √i + 1.

In German this spiral is called "Wurzelschnecke" (root snail), which inspired the idea for constructing this 3D work.