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Difference of Two Cubes

Difference of Two Cubes
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2016-03-19 12:31
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric shape of the difference between two cubes. Key mathematical concepts include cubes, differences, and slopes. Using GeoGebra commands such as Intersect, Point, and Polygon, complex geometric shapes can be constructed. Suitable for high school mathematics education and learning.

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(D, F, B, A) → poly1, d, f, b, a
  10. Polygon(F, B, C, G) → poly2, f_1, b_1, c, g
  11. Polygon(H, F, G, I) → poly3, h, f_2, g_1, i
  12. Polygon(E, D, F, H) → poly4, e, d_1, f_3, h_1
  13. Polygon(D, L, J, A) → poly5, d_2, l, j, a_1
  14. Polygon(J, N, B, A) → poly6, j_1, n, b_2, a_2
  15. Polygon(L, O, F, D) → poly7, l_1, o, f_4, d_3
  16. Polygon(O, N, B, F) → poly8, o_1, n_1, b_3, f_5
  17. Polygon(L, J, N, O) → poly9, l_2, j_2, n_2, o_2
  18. Polygon(Q, P, L, O) → poly10, q, p, l_3, o_3
  19. Polygon(O, N, R, Q) → poly11, o_4, n_3, r, q_1
  20. Polygon(P, K, R, Q) → poly12, p_1, k, r_1, q_2
  21. Polygon(K, J, N, R) → poly13, k_1, j_3, n_4, r_2
  22. Polygon(K, J, L, P) → poly14, k_2, j_4, l_4, p_2
  23. Polygon(S, E, D, P) → poly15, s, e_1, d_4, p_3
  24. Polygon(E, H, V, S) → poly16, e_2, h_2, v, s_1
  25. Polygon(V, Q, P, S) → poly17, v_1, q_3, p_4, s_2
  26. Polygon(H, V, T, I) → poly18, h_3, v_2, t, i_1
  27. Polygon(T, W, G, I) → poly19, t_1, w, g_2, i_2
  28. Polygon(Q, W, T, V) → poly20, q_4, w_1, t_2, v_3
  29. Polygon(W, U, R, Q) → poly21, w_2, u, r_3, q_5
  30. Polygon(U, C, G, W) → poly22, u_1, c_1, g_3, w_3
  31. Polygon(U, R, B, C) → poly23, u_2, r_4, b_4, c_2

AI Drawing Prompt Reference

Draw the difference between two cubes. Start by creating points B and C on the y-axis, D and E on the x-axis, J and K on the z-axis. Then create point M at the intersection of the y-axis and z-axis. Use these points to construct multiple polygons from poly1 to poly23, forming the shape of the difference between the two cubes.
The prompt above was compiled from the original drawing commands and is for reference only.