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Cross Sections of Solids Demo

Cross Sections of Solids Demo
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2017-01-09 20:05
Solid GeometryTransformationGeometric Construction
This example demonstrates the process of creating cross-sectional shapes by intersecting various solids (e.g., pyramids) with planes. It involves core concepts in solid geometry and section geometry, along with geometric transformations. GeoGebra commands and objects used include Pyramid, IntersectPath, Midpoint, Rotate, Segment, Polygon, RemoveUndefined, and Sequence. Suitable for high school geometry education to visually understand the relationship between cross-sections and original solids.

GeoGebra Commands & Parameters

  1. Pyramid((2, 2, 0), (-2, 2, 0), (-2, -2, 0), (2, -2, 0), (0, 0, 5)) → a, face5, edge3, edge5, edge7, edge8, face1, face3, face4, face2, edge1, edge4, edge6, edge2
  2. IntersectPath(b, a) → poly1, A, B, C, D, f, g, h, i
  3. Midpoint(A, D) → E
  4. Midpoint(B, C) → F
  5. Rotate(b, (-α), Segment[E, F]) → b'
  6. Rotate(b', β, zAxis) → b''
  7. IntersectPath(b'', a) → poly2, G, s, H, I, J, K, j, k, l, m
  8. Segment((0, 0, zz), (0, 0, 5)) → n
  9. Rotate(n, α) → n'
  10. Rotate(Rotate[n, (-α), Segment[E, F]], β, zAxis) → p
  11. Rotate(Rotate[(0, 0, 5), (-α), Segment[E, F]], β, zAxis) → L
  12. Rotate(Line[E, F], β) → q
  13. Rotate(Rotate[{J, K, G, H, I}, α, q] - (0, 0, zz), (-β), zAxis) → list1
  14. Polygon(list1) → poly3
  15. RemoveUndefined(list1) → list3
  16. Sequence(Segment[Element[list3, Mod[i, Length[list3]] + 1], Element[list3, Mod[i + 1, Length[list3]] + 1]], i, 1, Length[list3]) → list2
  17. Polygon(list3) → poly4

AI Drawing Prompt Reference

Draw the intersection lines between a square-based pyramid and multiple planes to demonstrate the formation of various cross-sectional shapes. Start by creating a pyramid with a square base, then sequentially intersect it with planes at different angles to observe the changes in cross-sectional shapes. Rotate and move the cross-sections to show their relationship with the original pyramid, finally presenting a collection of cross-sectional shapes.
The prompt above was compiled from the original drawing commands and is for reference only.