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Rainbow Figure 8 Surface

Rainbow Figure 8 Surface
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2018-07-05 18:21
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates a rainbow-colored Figure 8 surface. It involves the concepts of trigonometric functions and surfaces. By using the sequence command, users can dynamically change the color and shape of the surface. This example is suitable for high school and above students, for teaching geometric construction and function graphs.

GeoGebra Commands & Parameters

  1. Sequence(Surface[gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, i + π / n, i + (2 * π / n)], i, 0, (2 * π), (2 * π / n)) → black
  2. Sequence(Surface[gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, i, i + π / n], i, 0, (2 * π), (2 * π / n)) → white
  3. Length(black) → b
  4. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A1, A1 + (2 * π / n)) → B1
  5. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A2, A2 + (2 * π / n)) → B2
  6. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A3, A3 + (2 * π / n)) → B3
  7. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A4, A4 + (2 * π / n)) → B4
  8. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A5, A5 + (2 * π / n)) → B5
  9. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A6, A6 + (2 * π / n)) → B6
  10. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A7, A7 + (2 * π / n)) → B7
  11. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A8, A8 + (2 * π / n)) → B8
  12. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A9, A9 + (2 * π / n)) → B9
  13. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A10, A10 + (2 * π / n)) → B10
  14. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A11, A11 + (2 * π / n)) → B11
  15. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A12, A12 + (2 * π / n)) → B12
  16. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A13, A13 + (2 * π / n)) → B13
  17. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A14, A14 + (2 * π / n)) → B14
  18. Surface(gx(u, v), gy(u, v), gz(u, v), u, (-π), π, v, A15, A15 + (2 * π / n)) → B15