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Curve Stitching in a Cube

Curve Stitching in a Cube
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2016-02-13 19:21
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates curve stitching within a cube. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Point, Sequence, Cube, and Polygon, the faces and edges of the cube are constructed. Suitable for middle school and above students or math enthusiasts.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Sequence(A + (k * (B - A)), k, 0, 1, 1 / s) → edge1
  5. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  6. Sequence(H + (k * (E - H)), k, 0, 1, 1 / s) → edge2
  7. Sequence(C + (k * (G - C)), k, 0, 1, 1 / s) → edge3
  8. Sequence(Polygon[Element[edge1, k], Element[edge2, k], Element[edge3, k]], k, 1, 11) → twist
  9. Polygon(Element[edge1, h], Element[edge2, h], Element[edge3, h]) → poly1, b, c, d
  10. Sequence(Segment[Element[edge1, k], Element[edge2, k]], k, 1, s + 1) → string12
  11. Sequence(Segment[Element[edge3, k], Element[edge2, k]], k, 1, s + 1) → string23
  12. Sequence(Segment[Element[edge1, k], Element[edge3, k]], k, 1, s + 1) → string31

AI Drawing Prompt Reference

Create a curve stitching pattern inside a cube. Construct the faces and edges of the cube first. Then, draw three continuous curves starting from one vertex of the cube, each curve composed of multiple points along the corresponding edges, with points evenly distributed. Finally, connect each segment of these curves to form an interwoven pattern, showcasing the geometric construction within the cube.
The prompt above was compiled from the original drawing commands and is for reference only.