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Sphere Scanning

Sphere Scanning
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2019-06-02 13:57
Solid GeometryTransformationGeometric Construction
This example demonstrates the scanning process of a sphere on a plane and geometric transformations. It involves core mathematical concepts such as sphere, rational numbers, geometric transformations, plane figures, median line, LCM and GCD. The construction utilizes GeoGebra commands and objects like Polygon, Translate, Sphere, Plane, and IntersectPath. Suitable for high school and above, it serves as a teaching tool for solid geometry and transformations.

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