The lute of Pythagoras is a geometric form made of pentagons with inscribed pentagrams where the sides of the pentagrams are the sides of the smaller pentagons. The form is a fractal, like the Koch snowflake where an infinite progression of forms fits into a finite space.

The lute of Pythagoras is a self-similar geometric figure made from a sequence of pentagrams.

The Lute of Pythagoras, named for Pythagoras of Samos (ca. 580-500 B.C.), demonstrates the interesting relationship between the pentagon and the Golden Triangle. The Sacred Cut, a construction dating to the sixth century B.C., was found in excavated brick remains in the ancient Roman port of Ostia.