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Cutting a Prism with an Interactive Plane

Cutting a Prism with an Interactive Plane
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2020-04-13 20:13
Solid GeometryTransformationGeometric Construction
In collections Cutting solids by a plane
This example demonstrates how to cut a prism with an interactive plane. Key mathematical concepts include the intersection of a plane and a prism in solid geometry. Using GeoGebra commands such as Point, Cube, Line, Intersect, etc., the various faces of the prism and the intersection lines after cutting can be constructed. Suitable for high school geometry education or self-study.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, arêteAD, arêteAB, arêteBC, arêteCD, arêteAE, arêteDH, arêteEH, arêteEF, E, arêteBF, arêteFG, arêteCG, arêteGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Midpoint(C, A) → I
  4. Midpoint(F, H) → J
  5. Line(J, I) → f
  6. Circle(I, Distance[A, B], f) → c
  7. Point(c) → K
  8. Midpoint(F, C) → M
  9. Mirror(K, I) → K'
  10. Line(K', K) → g
  11. Circle(I, (1.2 * Distance[A, B]), g) → d
  12. Point(d) → L
  13. Plane(L, K, K') → p
  14. Circle(K', L, K) → e
  15. Center(e) → N
  16. OrthogonalLine(N, p) → h
  17. Point(h) → O
  18. Vector(I, O) → u
  19. Translate(p, u) → p'
  20. Segment(K', K) → b
  21. Line(L, b) → f_1
  22. Point(arêteEF) → D_1
  23. OrthogonalLine(K, p) → h_1
  24. Plane(K', h_1) → p_1
  25. OrthogonalLine(K, p_1) → k_1
  26. Line(K', k_1) → l_1
  27. Intersect(f_1, l_1) → E_1
  28. Intersect(k_1, f_1) → F_1
  29. Mirror(F_1, K) → G_1
  30. Mirror(E_1, K') → H_1
  31. Polygon(F_1, E_1, H_1, G_1) → q2, m_1, e_1, n_1, q_1
  32. Translate(q2, u) → q2'
  33. Circle(I, Distance[I, A], f) → q
  34. Point(f) → S
  35. Segment(A, I) → i
  36. Segment(I, S) → j
  37. Sequence(Rotate[A, i, f], i, 0, (2 * π), (2 * π / Sides)) → l1
  38. Polygon(l1) → poly1
  39. Sequence(Rotate[A + (0, 0, Distance[I, S]), i, f], i, 0, (2 * π), (2 * π / Sides)) → l1b
  40. Prism(poly1, (-Distance[I, S])) → o, R_2, face45, face46, face47, face48, face43, face49, arête42, arête43, arête44, arête45, S_2, arête46, arête47, arête48, arête49, arête51, arête52, arête53, arête54, arête55, arête50, T_2, U_2, V_2, W_2, Z_2, face42, face44
  41. IntersectPath(p', o) → poly2, P, l, m, n, r, s, t, c_1, Q, R, T, Z, A_1, B_1, P_1, k
  42. Sequence(Segment[Element[l1, i], Element[l1b, i]], i, 1, Length[l1]) → l3
  43. Polygon(l1) → poly3
  44. Polygon(l1b) → poly4

AI Drawing Prompt Reference

Draw a cube and then cut it with a movable plane to show the intersection lines and new polygonal faces. First, create the cube's faces and edges, then define a plane and move it to cut the cube, and finally display the intersection lines and new polygonal faces.
The prompt above was compiled from the original drawing commands and is for reference only.