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Math'art: Colored Implicit Curves

Math'art: Colored Implicit Curves
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2019-09-12 14:46
Complex NumberTransformationSlider AnimationLocusGraphing
① This example demonstrates a series of colorful implicit curves generated on a plane through rotation and implicit curve commands, blending mathematics with visual art. ② Core mathematical concepts include implicit curves, rotational transformations, complex numbers, continuity, and variance, showing how curve families evolve with parameters. ③ Construction highlights: using GeoGebra's Rotate command to rotate base curves, ImplicitCurve to define implicit equations, and multiple objects (A, B, C, D, etc.) along with sliders (n, Vitesse) to control rotation angles and speed; several images (image1 to image4) are inserted as backgrounds or decorations, enriching the visual output. ④ Suitable for high school and above students or math enthusiasts, this example is ideal for exploring geometric properties of implicit curves, transformation rules, and mathematical aesthetics, and can serve as material for math-art creation or classroom demonstrations.

GeoGebra Commands & Parameters

  1. Rotate(C, b, A) → B
  2. ImplicitCurve({A, B, C, D, E, F, G, H, I}) → a_1
  3. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A1, A1)}) → B1
  4. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A2, A2)}) → B2
  5. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A3, A3)}) → B3
  6. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A4, A4)}) → B4
  7. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A5, A5)}) → B5
  8. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A6, A6)}) → B6
  9. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A7, A7)}) → B7
  10. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A8, A8)}) → B8
  11. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A9, A9)}) → B9
  12. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A10, A10)}) → B10
  13. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A11, A11)}) → B11
  14. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A12, A12)}) → B12
  15. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A13, A13)}) → B13
  16. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A14, A14)}) → B14
  17. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A15, A15)}) → B15
  18. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A16, A16)}) → B16
  19. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A17, A17)}) → B17
  20. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A18, A18)}) → B18
  21. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A19, A19)}) → B19
  22. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A20, A20)}) → B20
  23. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A21, A21)}) → B21
  24. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A22, A22)}) → B22
  25. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A23, A23)}) → B23
  26. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A24, A24)}) → B24
  27. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A25, A25)}) → B25
  28. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A26, A26)}) → B26
  29. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A27, A27)}) → B27
  30. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A28, A28)}) → B28
  31. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A29, A29)}) → B29
  32. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A30, A30)}) → B30
  33. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A31, A31)}) → B31
  34. ImplicitCurve({A, B, C, D, E, F, G, H, I + (A32, A32)}) → B32