Surface Knot

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2018-03-23 05:55

In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1

This example demonstrates the construction of a surface knot, a special type of three-dimensional topological structure that cannot be continuously deformed into a plane. Using the Sequence command in GeoGebra, the formation process of the surface knot can be dynamically displayed. Suitable for high school math enthusiasts and topology beginners.

GeoGebra Commands & Parameters

Sequence(Surface[(cos(u) * cos((p * u) + v)) + ((3 * cos(u)) * (1.5 + sin((u * 5 / 3)) / 2)), (sin(u) * cos((p * u) + v)) + ((3 * sin(u)) * (1.5 + sin((u * 5 / 3)) / 2)), sin((p * u) + v) + (2 * cos((u * 5 / 3))), u, (-3 * π), (3 * π), v, i + π / n, i + (2 * π / n)], i, 0, (2 * π), (2 * π / n)) → black
Sequence(Surface[(cos(u) * cos((p * u) + v)) + ((3 * cos(u)) * (1.5 + sin((u * 5 / 3)) / 2)), (sin(u) * cos((p * u) + v)) + ((3 * sin(u)) * (1.5 + sin((u * 5 / 3)) / 2)), sin((p * u) + v) + (2 * cos((u * 5 / 3))), u, (-3 * π), (3 * π), v, i, i + π / n], i, 0, (2 * π), (2 * π / n)) → white

AI Drawing Prompt Reference

Draw a 3D surface knot to show its formation process, dynamically displaying its topological structure through a sequence, primarily in black with white details, presenting a complex yet orderly geometric beauty.

The prompt above was compiled from the original drawing commands and is for reference only.