Can One Line Weave a 3D Star Crown?

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Can one line weave a 3D star crown?

One point makes five laps as t moves from 0 to 10π. The radius r(t) = 3.35 + 1.28 cos(5t) creates five rounded star-like lobes. The coordinates x(t) = r(t) cos(t) and y(t) = r(t) sin(t) turn the point around the center. The height z(t) = 0.78 sin(5t) + 0.92 sin(t/5) combines a fast ripple with a slow rise and fall, placing successive passes at different heights. One continuous line becomes a layered crown; the final rotation reveals its depth.

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

Music: 'Fire In The Sky' by Alex Jones & Xander Jones

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