Lute of Pythagoras
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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,[citation needed] like the Koch snowflake 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. the sides of the lute are part of the golden triangle which is constructed using the golden rectangle.
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