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Cube and Sphere with Equal Surface Area

Cube and Sphere with Equal Surface Area
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2019-05-26 02:33
CircleSolid GeometryGeometric Construction
This example demonstrates a geometric model where a cube and a sphere have equal surface areas. It involves core math concepts like solid geometry, surface area calculations, and the approximate value of Pi. Construction highlights include using GeoGebra commands such as Point, Segment, Polygon, Line, Midpoint, Circle, Intersect, Semicircle, Distance, Rotate, and Angle. Suitable for high school mathematics education, exploring spatial geometry and the relationship with Pi.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 12]) → B
  2. Segment(A, B) → f
  3. Polygon(A, B, 4) → poly1, g, h, i, j, C, D
  4. Point(h) → E
  5. Point(h) → F
  6. Line(E, F) → k
  7. Midpoint(C, B) → G
  8. Circle(G, 13.41640786499874) → c
  9. Point(j) → H
  10. Line(H, I) → l
  11. Point(c) → J
  12. Circle(B, J) → d
  13. Intersect(d, l, 2) → K
  14. Segment(K, A) → m
  15. Midpoint(A, K) → L
  16. Midpoint(K, A) → M
  17. Circle(L, 4) → e
  18. Point(Circle[A, 4]) → N
  19. Segment(A, N) → n
  20. Polygon(N, A, 4) → poly2, p, q, r, s, O, P
  21. Segment(N, O) → t
  22. Semicircle(D, O) → c_1
  23. Distance(A, f) → distanceAf
  24. Intersect(c_1, f, 1) → Q
  25. Segment(A, Q) → a
  26. Distance(A, Q) → distanceAQ
  27. Circle(N, 6.821178167174472) → d_1
  28. Circle(A, 5.525257603798908) → e_1
  29. Intersect(d_1, e_1, 2) → R
  30. Segment(A, R) → b
  31. Midpoint(R, A) → S
  32. Circle(S, 2.762628801899454) → f_1
  33. Segment(N, R) → g_1
  34. Distance(A, R) → distanceAR
  35. Rotate(O, 45°, N) → O'
  36. Angle(O, N, O') → α
  37. Circle(O, 8) → h_1
  38. Intersect(h_1, l, 1) → T
  39. Polygon(T, O, 4) → poly3, i_1, j_1, k_1, l_1, U, V
  40. Segment(V, O) → m_1
  41. Polygon(P, O, 4) → poly4, n_1, p_1, q_1, r_1, W, Z
  42. Segment(P, W) → s_1
  43. Polygon(O, A, 4) → poly5, t_1, a_1, b_1, f_2, A_1, B_1
  44. Segment(A, B_1) → g_2
  45. Polygon(O, B_1, 4) → poly6, h_2, i_2, j_2, k_2, C_1, D_1