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Möbius strip with rainbow unit normal vectors

Möbius strip with rainbow unit normal vectors
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2019-10-31 16:17
VectorSolid GeometryCalculusDerivativeGraphing
This example demonstrates the Möbius strip with its surface colored by rainbow unit normal vectors. Key math concepts include vectors, derivatives, surfaces, and transformations. Construction involves commands like Derivative, Surface, and Translate in GeoGebra. Suitable for university students in mathematics, physics, and learners interested in vector field visualization and spatial geometry.

GeoGebra Commands & Parameters

  1. Derivative(F, x) → dFx
  2. Derivative(F, y) → dFy
  3. Derivative(G, x) → dGx
  4. Derivative(G, y) → dGy
  5. Derivative(H, x) → dHx
  6. Derivative(H, y) → dHy
  7. Surface(F(u, v), G(u, v), H(u, v), u, 0, (2 * π), v, -1, 1) → Mobius
  8. Translate(Vector[(0, 0, 0), C1], B1) → D1
  9. Translate(Vector[(0, 0, 0), C2], B2) → D2
  10. Translate(Vector[(0, 0, 0), C3], B3) → D3
  11. Translate(Vector[(0, 0, 0), C4], B4) → D4
  12. Translate(Vector[(0, 0, 0), C5], B5) → D5
  13. Translate(Vector[(0, 0, 0), C6], B6) → D6
  14. Translate(Vector[(0, 0, 0), C7], B7) → D7
  15. Translate(Vector[(0, 0, 0), C8], B8) → D8
  16. Translate(Vector[(0, 0, 0), C9], B9) → D9
  17. Translate(Vector[(0, 0, 0), C10], B10) → D10
  18. Translate(Vector[(0, 0, 0), C11], B11) → D11
  19. Translate(Vector[(0, 0, 0), C12], B12) → D12
  20. Translate(Vector[(0, 0, 0), C13], B13) → D13
  21. Translate(Vector[(0, 0, 0), C14], B14) → D14
  22. Translate(Vector[(0, 0, 0), C15], B15) → D15
  23. Translate(Vector[(0, 0, 0), C16], B16) → D16
  24. Translate(Vector[(0, 0, 0), C17], B17) → D17
  25. Translate(Vector[(0, 0, 0), C18], B18) → D18
  26. Translate(Vector[(0, 0, 0), C19], B19) → D19
  27. Translate(Vector[(0, 0, 0), C20], B20) → D20
  28. Translate(Vector[(0, 0, 0), C21], B21) → D21
  29. Translate(Vector[(0, 0, 0), C22], B22) → D22
  30. Translate(Vector[(0, 0, 0), C23], B23) → D23
  31. Translate(Vector[(0, 0, 0), C24], B24) → D24
  32. Translate(Vector[(0, 0, 0), C25], B25) → D25
  33. Translate(Vector[(0, 0, 0), C26], B26) → D26
  34. Translate(Vector[(0, 0, 0), C27], B27) → D27
  35. Translate(Vector[(0, 0, 0), C28], B28) → D28
  36. Translate(Vector[(0, 0, 0), C29], B29) → D29
  37. Translate(Vector[(0, 0, 0), C30], B30) → D30
  38. Translate(Vector[(0, 0, 0), C31], B31) → D31
  39. Translate(Vector[(0, 0, 0), C32], B32) → D32
  40. Translate(Vector[(0, 0, 0), C33], B33) → D33

AI Drawing Prompt Reference

Draw a Möbius strip with its surface colored by rainbow unit normal vectors to demonstrate vectors, derivatives, surfaces, and transformations. Compute the partial derivatives of functions, construct the Möbius strip surface, then distribute and color the unit normal vectors evenly over the surface, and finally present the complete figure.
The prompt above was compiled from the original drawing commands and is for reference only.