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Drawing a Cube's Section

Drawing a Cube's Section
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2014-12-05 04:16
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to use GeoGebra to draw a section of a cube. Key mathematical concepts include solid geometry and geometric construction. Commands such as Line, OrthogonalLine, Point, Segment, Polygon, Prism, Intersect, and Plane are used to construct the cube and its section. Suitable for middle school and above students or teachers.

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 its section. Start by constructing the edges and vertices of the cube, then use orthogonal lines to determine the section's position. Connect the section vertices with line segments to form a polygon, refining the shape with intersections of edges and section points. Finally, combine the section with the cube to clearly show its internal structure.
The prompt above was compiled from the original drawing commands and is for reference only.