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Cube Cross Section Demo

Cube Cross Section Demo
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2016-06-23 23:47
Solid GeometryGeometric Construction
This example demonstrates the formation of various cross-section shapes of a cube by moving three points. It involves core math concepts like solid geometry, cross-section transformation, and spatial visualization. Construction highlights the use of GeoGebra commands: Segment, Point, Plane, Intersect, Prism, IntersectPath. Suitable for high school students and learners needing spatial geometry practice.

GeoGebra Commands & Parameters

  1. Segment(G, H) → GH
  2. Segment(F, G) → FG
  3. Segment(H, E) → HE
  4. Segment(E, F) → EF
  5. Segment(C, G) → CG
  6. Segment(D, H) → DH
  7. Segment(C, D) → CD
  8. Segment(B, F) → BF
  9. Segment(B, C) → BC
  10. Segment(A, E) → AE
  11. Segment(D, A) → DA
  12. Segment(A, B) → AB
  13. Point(list1) → I
  14. Point(list1) → J
  15. Point(list1) → K
  16. Plane(I, J, K) → P
  17. Intersect(HE, EF) → L
  18. Intersect(EF, BF) → M
  19. Intersect(GH, FG) → N
  20. Point(GH) → O
  21. Intersect(CD, DA) → T
  22. Prism(H, E, F, G, D) → BoundingPrism, Q, edgeEH, edgeEF, edgeFG, edgeGH, edgeDH, edgeEQ, edgeFR, edgeGS, edgeDQ, edgeQR, R, edgeRS, edgeDS, S, faceEFGH, faceDHEQ, faceEFRQ, faceFGSR, faceDHGS, faceDQRS
  23. IntersectPath(P, BoundingPrism) → BoundedPolygon_1, U, d, e, f, V, W, Z, A_1, B_1, a, b, c

AI Drawing Prompt Reference

Draw a cube and demonstrate the formation of various cross-section shapes by moving three points. The cube is composed of multiple line segments connecting eight vertices. Inside the cube, three movable points define a plane that intersects the edges of the cube, forming a cross-sectional polygon. The shape of the polygon changes as the positions of the three points vary, ranging from a triangle to a pentagon. Start by drawing the edges and vertices of the cube, then add the three points and the operation to define the plane, and finally show the cross-sectional polygon and its changes as the points move.
The prompt above was compiled from the original drawing commands and is for reference only.