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Parallelepiped Section

Parallelepiped Section
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2016-07-09 03:01
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the section of a parallelepiped. Key mathematical concepts include the properties of sections in solid geometry. Using GeoGebra commands such as RotateText, Mirror, Rotate, etc., the construction of a parallelepiped and its section is achieved. Suitable for high school students studying solid geometry.

GeoGebra Commands & Parameters

  1. RotateText("uStas\;\&\,Т.С.", 90°) → надпись01
  2. Mirror(A, Q) → C
  3. Rotate(A, 90°, Q) → B
  4. Mirror(B, Q) → D
  5. Polygon(A, B, C, D) → ABCD, a, b, c, d
  6. PointIn(z = (h * m) + zQ) → A_1
  7. Prism(ABCD, A_1) → Π, B_1, BB1, CC1, DD1, a_1, b_1, c_1, d_1, C_1, D_1, g_1, g_2, g_3, g_4, ABCD1, AA1
  8. Point(d_1) → L
  9. Point(CC1) → N
  10. Point(sp1) → K
  11. PathParameter(K) → k
  12. Plane(K, L, N) → α
  13. IntersectPath(α, Π) → ss1, E, j, l, n, F, G, H, I, J, f, g, i
  14. Line(K, N) → KN
  15. Line(K, L) → KL
  16. Intersect(KN, Line[B, C]) → P1
  17. Intersect(KN, Line[B, B_1]) → P2
  18. Intersect(KN, Line[C_1, B_1]) → P3
  19. If(Distance[P1, B] < Distance[P1, C], Segment[P1, B], Segment[P1, C]) → p1
  20. If(Distance[P2, B] < Distance[P2, B_1], Segment[P2, B], Segment[P2, B_1]) → p2
  21. If(Distance[P3, B_1] < Distance[P3, C_1], Segment[P3, B_1], Segment[P3, C_1]) → p3
  22. If(Distance[P1, K] < Distance[P1, N], Segment[P1, K], Segment[P1, N]) → p_1
  23. Segment(P2, K) → p_2
  24. If(Distance[P3, K] < Distance[P3, N], Segment[P3, K], Segment[P3, N]) → p_3
  25. Intersect(KN, Line[D, C]) → Q1
  26. Intersect(KN, Line[D, D_1]) → Q2
  27. Intersect(KN, Line[C_1, D_1]) → Q3
  28. If(Distance[Q1, C] < Distance[Q1, D], Segment[Q1, C], Segment[Q1, D]) → q1
  29. If(Distance[Q2, D] < Distance[Q2, D_1], Segment[Q2, D], Segment[Q2, D_1]) → q2
  30. If(Distance[Q3, C_1] < Distance[Q3, D_1], Segment[Q3, C_1], Segment[Q3, D_1]) → q3
  31. If(Distance[Q1, K] < Distance[Q1, N], Segment[Q1, K], Segment[Q1, N]) → q_1
  32. Segment(Q2, K) → q_2
  33. If(Distance[Q3, K] < Distance[Q3, N], Segment[Q3, K], Segment[Q3, N]) → q_3
  34. Intersect(KL, Line[D, A]) → R1
  35. Intersect(KL, Line[A_1, A]) → R2
  36. Intersect(KL, Line[D_1, D]) → R3
  37. If(Distance[R1, A] < Distance[R1, D], Segment[R1, A], Segment[R1, D]) → r1
  38. If(Distance[R2, A] < Distance[R2, A_1], Segment[R2, A], Segment[R2, A_1]) → r2
  39. If(Distance[R3, D] < Distance[R3, D_1], Segment[R3, D], Segment[R3, D_1]) → r3
  40. If(Distance[R1, K] < Distance[R1, L], Segment[R1, K], Segment[R1, L]) → r_1
  41. If(Distance[R2, K] < Distance[R2, L], Segment[R2, K], Segment[R2, L]) → r_2
  42. If(Distance[R3, K] < Distance[R3, L], Segment[R3, K], Segment[R3, L]) → r_3
  43. Intersect(KL, Line[A_1, B_1]) → S1
  44. Intersect(KL, Line[C_1, B_1]) → S2
  45. Intersect(KL, Line[C_1, D_1]) → S3
  46. If(Distance[S1, A_1] < Distance[S1, B_1], Segment[S1, A_1], Segment[S1, B_1]) → s1
  47. If(Distance[S2, C_1] < Distance[S2, B_1], Segment[S2, C_1], Segment[S2, B_1]) → s2
  48. If(Distance[S3, C_1] < Distance[S3, D_1], Segment[S3, C_1], Segment[S3, D_1]) → s3
  49. If(Distance[S1, K] < Distance[S1, L], Segment[S1, K], Segment[S1, L]) → s_1
  50. If(Distance[S2, K] < Distance[S2, L], Segment[S2, K], Segment[S2, L]) → s_2
  51. If(Distance[S3, K] < Distance[S3, L], Segment[S3, K], Segment[S3, L]) → s_3

AI Drawing Prompt Reference

Draw a parallelepiped with a square base, whose vertices are obtained by rotation and reflection. Choose a point above the base to form the prism. Select three points on the edges of the prism to define a cutting plane. This plane intersects the edges of the prism, forming a cross-section polygon. At the intersection points, based on distance comparisons, draw segments between the section and the prism edges, as well as internal segments of the section, clearly showing the shape of the cross-section of the parallelepiped cut by the plane.
The prompt above was compiled from the original drawing commands and is for reference only.