Can One Line Weave a Braided Ring?

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Can one line weave a braided ring?

A single moving point follows the (7, 31) torus-knot equations: r(t) = 2.8 + 0.9 cos(31t), x(t) = r(t) cos(7t), y(t) = r(t) sin(7t), and z(t) = 0.9 sin(31t), with 0 ≤ t ≤ 2π.

The 7 turns move around the central hole. The 31 turns wind around the smaller tube. The radial term and z-coordinate work together to move the point around that tube, creating an interwoven path. Since 7 and 31 share no common divisor beyond 1, the path is one closed knot, not several separate loops. The final rotation reveals the rear strands and depth inside the ring.

This is one wire curve lying on a torus, not a filled surface or a physical weaving simulation.

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

Music: 'Helium' by TrackTribe

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