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Earth as a Sphere by WONG FAU CHOO

Earth as a Sphere by WONG FAU CHOO
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2018-12-02 10:18
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the geometric model of the Earth as a sphere and related calculations. It involves core mathematical concepts such as sphere, cube, tangent function, root, ratios, and numbers. The construction uses GeoGebra commands like Circle, Segment, PointIn, Intersect, CircleSector, Angle, Point, CircumcircleArc, and Line. It is suitable for high school and above students to learn and understand the geometric properties and calculations of spheres.

GeoGebra Commands & Parameters

  1. Circle(N, E, S) → c
  2. Circle(D, E, C) → d
  3. Segment(N, S) → f
  4. PointIn(a) → G
  5. Circle(zAxis, G) → e
  6. Circle(N, G, S) → g
  7. Intersect(g, e) → H, I, ,
  8. Segment(G, I) → h
  9. Intersect(h, f) → J
  10. Intersect(e, c) → K, L, ,
  11. Intersect(d, g) → M, N_1, ,
  12. CircleSector(J, G, L) → p
  13. CircleSector(O, G, N_1) → q
  14. Angle(N_1, O, G) → α
  15. Angle(N_1, O, E) → β
  16. Point(c) → P
  17. Circle(f, P) → r
  18. Point(c) → Q
  19. Point(c) → R
  20. Point(c) → S_1
  21. Point(c) → T
  22. Circle(f, Q) → s
  23. Circle(f, S_1) → t
  24. Circle(f, R) → c_1
  25. Circle(f, T) → d_1
  26. Point(d) → U
  27. Point(d) → V
  28. Point(d) → W
  29. Point(d) → Z
  30. Point(d) → A_1
  31. Circle(N, V, S) → e_1
  32. Circle(N, W, S) → f_1
  33. Circle(N, U, S) → g_1
  34. Circle(N, Z, S) → h_1
  35. PointIn(a) → A
  36. Intersect(h_1, g_1, 1) → B
  37. CircumcircleArc(N, A, S) → k_1
  38. Circle(f, A) → p_1
  39. Intersect(k_1, d) → B_1, C_1, ,
  40. CircleSector(O, A, B_1) → q_1
  41. Segment(O, B_1) → i
  42. Line(A, i) → j
  43. Intersect(j, f) → D_1
  44. Intersect(p_1, c) → E_1, F_1, ,
  45. CircleSector(D_1, E_1, A) → r_1