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Difference of Two Cubes - Part 2

Difference of Two Cubes - Part 2
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2016-03-19 12:51
Solid GeometryCalculusOptimizationGeometric Construction
This example demonstrates the geometric representation and related phenomena of the difference of two cubes, involving core math concepts like the difference of cubes formula, similar triangles, median value theorem, solid geometry optimization problems, and tangent lines. It constructs using GeoGebra commands such as Intersect, Point, and Polygon. Suitable for high school and above learners to understand the connection between algebra and geometry and optimization problems.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, xAxis) → A
  2. Point(yAxis) → B
  3. Point(yAxis) → C
  4. Point(xAxis) → D
  5. Point(xAxis) → E
  6. Point(zAxis) → J
  7. Point(zAxis) → K
  8. Intersect(yAxis, zAxis) → M
  9. Polygon(F, B, C, G) → poly2, f_1, b_1, c, g
  10. Polygon(H, F, G, I) → poly3, h, f_2, g_1, i
  11. Polygon(E, D, F, H) → poly4, e, d_1, f_3, h_1
  12. Polygon(D, L, J, A) → poly5, d_2, l, j, a_1
  13. Polygon(J, N, B, A) → poly6, j_1, n, b_2, a_2
  14. Polygon(L, O, F, D) → poly7, l_1, o, f_4, d_3
  15. Polygon(O, N, B, F) → poly8, o_1, n_1, b_3, f_5
  16. Polygon(K, J, N, R) → poly13, k_1, j_3, n_4, r_2
  17. Polygon(S, E, D, P) → poly15, s, e_1, d_4, p_3
  18. Polygon(E, H, V, S) → poly16, e_2, h_2, v, s_1
  19. Polygon(H, V, T, I) → poly18, h_3, v_2, t, i_1
  20. Polygon(T, W, G, I) → poly19, t_1, w, g_2, i_2
  21. Polygon(U, C, G, W) → poly22, u_1, c_1, g_3, w_3
  22. Polygon(U, R, B, C) → poly23, u_2, r_4, b_4, c_2
  23. Polygon(N, O, L, J) → poly1, n_5, o_5, l_5, j_5
  24. Polygon(K, P, L, J) → poly14, k_2, p_2, l_4, j_4
  25. Polygon(A, D, F, B) → poly24, a, d, f, b
  26. Polygon(L, O, F, D) → poly9, l_2, o_2, f_6, d_5
  27. Polygon(O, N, B, F) → poly10, o_3, n_2, b_5, f_7
  28. Polygon(Q, R, N, O) → poly11, q, r, n_3, o_4
  29. Polygon(P, Q, O, L) → poly12, p, q_1, o_6, l_3
  30. Polygon(V, Q, F, H) → poly17, v_1, q_2, f_8, h_4
  31. Polygon(Q, W, G, F) → poly20, q_3, w_1, g_4, f_9
  32. Polygon(P, Q, R, K) → poly21, p_1, q_4, r_1, k
  33. Polygon(Q, R, K, P) → poly25, q_5, r_3, k_3, p_4
  34. Polygon(W, U, R, Q) → poly26, w_2, u, r_5, q_6
  35. Polygon(V, T, W, Q) → poly27, v_3, t_2, w_4, q_7
  36. Polygon(S, P, Q, V) → poly28, s_2, p_5, q_8, v_4