Watch One Line Turn From a Circle Into a Square

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Can one continuous 3D curve be two different shapes?

From above, every point satisfies x² + y² = R², so the projection is a perfect circle. From the side, the same points satisfy max(|x|, |z|) = R, producing a square. The line is drawn once, then the completed curve rotates 90 degrees to reveal both shadows.

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

Music: 'Sleep Music No. 1' by Chris Haugen

#MathArt #Geometry #Projection