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Cross Sections of a Cube by nandrews (2)

Cross Sections of a Cube by nandrews (2)
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2015-05-01 20:19
PolygonSolid GeometryCalculus
In collections Cross Sections of Prisms
This example demonstrates the geometric transformations of a cube's cross-sections from various angles, highlighting polygonal shapes, integral and differential calculus, and trigonometric functions. It constructs the model using commands like Polygon, Prism, Point, OrthogonalLine, Intersect, Plane, IntersectPath, Segment, and Midpoint in GeoGebra. Ideal for high school students and math enthusiasts exploring solid geometry and calculus.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Prism(poly1, 4) → e, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  3. Point(edgeFG) → I
  4. OrthogonalLine(I, edgeEH, space) → f
  5. OrthogonalLine(I, b, space) → g
  6. Intersect(b, g) → J
  7. OrthogonalLine(J, d, space) → h
  8. Intersect(edgeEH, f) → K
  9. Intersect(h, faceADHE) → L
  10. Polygon(I, K, L, J) → poly2, i, k, l, j
  11. Point(edgeCG) → M
  12. OrthogonalLine(M, edgeBF, space) → n
  13. OrthogonalLine(M, edgeDH, space) → p
  14. Intersect(p, edgeDH) → N
  15. OrthogonalLine(N, edgeAE, space) → q
  16. Point(q) → O
  17. Point(n) → P
  18. Polygon(M, N, O, P) → poly3, m_1, n_1, o, p_1
  19. Point(edgeEH) → Q
  20. Intersect(edgeCG, edgeGH) → R
  21. Point(edgeDH) → S
  22. Plane(Q, R, S) → s
  23. IntersectPath(s, e) → poly4, T, U, V, W, t, a_1, b_1, c_1
  24. Intersect(edgeGH, edgeDH) → Z
  25. Intersect(edgeDH, d) → C_1
  26. Intersect(edgeGH, edgeEH) → A_1
  27. Intersect(edgeFG, edgeBF) → B_1
  28. Segment(A_1, B_1) → d_1
  29. Intersect(edgeBF, a) → D_1
  30. Segment(C_1, D_1) → e_1
  31. Point(d_1) → E_1
  32. Intersect(edgeCG, edgeFG) → F_1
  33. Intersect(edgeEH, edgeAE) → G_1
  34. Segment(G_1, C_1) → f_1
  35. Segment(F_1, C_1) → g_1
  36. Midpoint(g_1) → I_1
  37. Midpoint(f_1) → J_1
  38. Plane(E_1, J_1, I_1) → v
  39. IntersectPath(v, e) → poly5, K_1, l_1, L_1, M_1, N_1, O_1, h_1, i_1, j_1, k_1

AI Drawing Prompt Reference

Draw a cube and display its cross-sections from various angles. First, construct the cube, then select several points on the cube and draw polygonal cross-sections through these points. Use orthogonal lines and intersection points to determine the shapes of the cross-sections, including quadrilaterals and triangles. Finally, combine all the cross-sections with the cube to show the relationship between the cross-sections and the cube, as well as the changes in the cross-sections at different angles.
The prompt above was compiled from the original drawing commands and is for reference only.