The lute of Pythagoras

Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...

is a geometric form made of pentagon

Pentagon

In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The sum of the internal angles in a simple pentagon is 540°. A pentagram is an example of a self-intersecting pentagon.- Regular pentagons :In a regular pentagon, all sides are equal in length and...

s with inscribed pentagram

Pentagram

A pentagram is the shape of a five-pointed star drawn with five straight strokes...

s where the sides of the pentagrams are the sides of the smaller pentagons. The form is a fractal

Fractal

A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...

, like the Koch snowflake

Koch snowflake

The Koch snowflake is a mathematical curve and one of the earliest fractal curves to have been described...

 where an infinite progression of forms fits into a finite space. The sides of the lute are based on the number phi, which is the golden ratio and an irrational number like pi. If you measure any line in the lute it is the ratio of phi.