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Difference of Cubes - Part 2

Difference of Cubes - Part 2
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2016-03-19 06:55
FunctionCoordinate GeometryTransformation
This example demonstrates the geometric meaning of the difference of cubes formula. By constructing the cutting of a cube, it illustrates the difference of cubes formula. Key mathematical concepts include cubes and geometric transformations. GeoGebra commands used include Intersect, Point, Polygon, etc. Suitable for high school mathematics education, helping students understand the geometric background of the difference of cubes formula.

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(L, J, N, O) → poly9, l_2, j_2, n_2, o_2
  17. Polygon(Q, P, L, O) → poly10, q, p, l_3, o_3
  18. Polygon(O, N, R, Q) → poly11, o_4, n_3, r, q_1
  19. Polygon(P, K, R, Q) → poly12, p_1, k, r_1, q_2
  20. Polygon(K, J, N, R) → poly13, k_1, j_3, n_4, r_2
  21. Polygon(K, J, L, P) → poly14, k_2, j_4, l_4, p_2
  22. Polygon(S, E, D, P) → poly15, s, e_1, d_4, p_3
  23. Polygon(E, H, V, S) → poly16, e_2, h_2, v, s_1
  24. Polygon(V, Q, P, S) → poly17, v_1, q_3, p_4, s_2
  25. Polygon(H, V, T, I) → poly18, h_3, v_2, t, i_1
  26. Polygon(T, W, G, I) → poly19, t_1, w, g_2, i_2
  27. Polygon(Q, W, T, V) → poly20, q_4, w_1, t_2, v_3
  28. Polygon(W, U, R, Q) → poly21, w_2, u, r_3, q_5
  29. Polygon(U, C, G, W) → poly22, u_1, c_1, g_3, w_3
  30. Polygon(U, R, B, C) → poly23, u_2, r_4, b_4, c_2

AI Drawing Prompt Reference

Draw a geometric representation of the difference of cubes formula. Start by drawing the x-axis, y-axis, and z-axis. Then, mark points B and C on the y-axis, D and E on the x-axis, J and K on the z-axis. Next, draw a polygon with points B, C, and G; a polygon with D, F, G, and H; a polygon with E, D, F, and H; a polygon with D, L, J, and A; a polygon with J, N, B, and A; a polygon with L, O, F, and D; a polygon with O, N, B, and F; a polygon with L, J, N, and O; a polygon with Q, P, L, and O; a polygon with O, N, R, and Q; a polygon with P, K, R, and Q; a polygon with K, J, N, and R; a polygon with K, J, L, and P; a polygon with S, E, D, and P; a polygon with E, H, V, and S; a polygon with V, Q, P, and S; a polygon with H, V, T, and I; a polygon with T, W, G, and I; a polygon with Q, W, T, and V; a polygon with W, U, R, and Q; a polygon with U, C, G, and W; a polygon with U, R, B, and C.
The prompt above was compiled from the original drawing commands and is for reference only.