Can the Pythagorean Theorem Grow 511 Squares?

BEHIND THE WORK

Can the Pythagorean theorem grow a tree from 511 connected squares?

Begin with one square and build a right triangle on its top edge. If the parent side is s, the two new sides are a = s cos θ and b = s sin θ, so a² + b² = s². Repeating the same construction on both children for nine levels creates 2⁹ − 1 = 511 squares. One continuous glowing line retraces shared edges as the recursive canopy grows.

Artismathic turns equations into visual art—one function at a time.

Music: 'The Beast Within' by The Soundlings

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