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Sphere Scanning by Juan Carlos Ponce Campuzano

Sphere Scanning by Juan Carlos Ponce Campuzano
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2019-04-24 19:45
Solid GeometryCalculusParametric EquationGeometric ConstructionGraphing
This example demonstrates the interaction between a sphere and geometric elements like planes and polygons through scanning, generating unique mathematical art. Core math concepts include solid geometry, derivatives, linear regression, parametric equations, and transformations. Construction highlights the use of GeoGebra commands like Polygon, Translate, Sphere, Plane, and IntersectPath. Suitable for high school students and math enthusiasts exploring spatial geometry and mathematical art.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, C) → p0, f, g, h, i
  2. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (1 - 1)) - 1, 0)]) → P1
  3. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (2 - 1)) - 1, 0)]) → P2
  4. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (3 - 1)) - 1, 0)]) → P3
  5. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (4 - 1)) - 1, 0)]) → P4
  6. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (5 - 1)) - 1, 0)]) → P5
  7. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (6 - 1)) - 1, 0)]) → P6
  8. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (7 - 1)) - 1, 0)]) → P7
  9. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (8 - 1)) - 1, 0)]) → P8
  10. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (9 - 1)) - 1, 0)]) → P9
  11. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (10 - 1)) - 1, 0)]) → P10
  12. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (11 - 1)) - 1, 0)]) → P11
  13. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (12 - 1)) - 1, 0)]) → P12
  14. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (13 - 1)) - 1, 0)]) → P13
  15. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (14 - 1)) - 1, 0)]) → P14
  16. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (15 - 1)) - 1, 0)]) → P15
  17. Sphere((0, t, 0), 0.75) → s
  18. Plane(P1) → PO1
  19. Plane(P2) → PO2
  20. Plane(P3) → PO3
  21. Plane(P4) → PO4
  22. Plane(P5) → PO5
  23. Plane(P6) → PO6
  24. Plane(P7) → PO7
  25. Plane(P8) → PO8
  26. Plane(P9) → PO9
  27. Plane(P10) → PO10
  28. Plane(P11) → PO11
  29. Plane(P12) → PO12
  30. Plane(P13) → PO13
  31. Plane(P14) → PO14
  32. Plane(P15) → PO15
  33. IntersectPath(PO1, s) → S1
  34. IntersectPath(PO2, s) → S2
  35. IntersectPath(PO3, s) → S3
  36. IntersectPath(PO4, s) → S4
  37. IntersectPath(PO5, s) → S5
  38. IntersectPath(PO6, s) → S6
  39. IntersectPath(PO7, s) → S7
  40. IntersectPath(PO8, s) → S8
  41. IntersectPath(PO9, s) → S9
  42. IntersectPath(PO10, s) → S10
  43. IntersectPath(PO11, s) → S11
  44. IntersectPath(PO12, s) → S12
  45. IntersectPath(PO13, s) → S13
  46. IntersectPath(PO14, s) → S14
  47. IntersectPath(PO15, s) → S15