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Cube Cutting Example

Cube Cutting Example
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2021-05-18 18:14
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates a cube's cut. Key mathematical concepts include solid geometry. Using GeoGebra commands such as Line, OrthogonalLine, Point, Segment, Polygon, Prism, Intersect, Plane, etc., a cube and its cutting faces can be constructed. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(A, a, space) → b
  3. OrthogonalLine(A, a, space) → c
  4. OrthogonalLine(B, a, space) → d
  5. OrthogonalLine(D, a, space) → e
  6. Line(B, e) → f
  7. Point(f) → C
  8. Segment(D, A) → h
  9. Segment(A, B) → i
  10. Segment(B, C) → j
  11. Segment(C, D) → k
  12. Polygon(A, B, C, D) → poly1, a_1, b_1, d_1, c_1
  13. Prism(poly1, 5) → l, A_1, edgeAE, edgeBF, edgeDG, edgeCH, edgeEF, edgeFG, edgeGH, edgeEH, B_1, C_1, D_1, faceABFE, faceBDGF, faceCDGH, faceACHE, faceEFGH
  14. Point(a_1) → I
  15. Point(edgeAE) → J
  16. Point(edgeGH) → K
  17. Line(J, I) → g
  18. Line(B_1, A_1) → m
  19. Point(m) → L
  20. Line(K, L) → n
  21. Line(B_1, C_1) → p
  22. Line(B_1, B) → q
  23. Intersect(p, n) → M
  24. Point(g) → N
  25. Line(M, N) → r
  26. Point(edgeEH) → P
  27. Point(r) → Q
  28. Point(b_1) → R
  29. Segment(I, R) → s
  30. Segment(K, Q) → t
  31. Segment(J, P) → e_1
  32. Segment(J, I) → f_1
  33. Segment(I, R) → g_1
  34. Segment(R, Q) → h_1
  35. Segment(Q, K) → i_1
  36. Segment(K, P) → j_1
  37. Segment(P, J) → k_1
  38. Point(p) → E
  39. Plane(J, I, R) → o
  40. Polygon(I, R, Q, K, P, J) → poly2, i_2, r_1, q_1, k_2, p_1, j_2

AI Drawing Prompt Reference

Draw a cube and demonstrate its cutting process. First, construct the edges and vertices of the cube. Then, create lines orthogonal to the cube's edges to define the cutting planes. Identify key intersection points using these orthogonal lines and connect them to form the cutting planes. Finally, combine the cutting planes with the cube to show the立体效果 of the cube being cut, highlighting the shape and position of the cutting planes.
The prompt above was compiled from the original drawing commands and is for reference only.