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Cross Section of a Cuboid

Cross Section of a Cuboid
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2017-10-22 18:13
Solid GeometryTransformationGeometric Construction
This example demonstrates the dynamic visualization of cross-sections of a cuboid through interactive manipulation. Key math concepts include solid geometry, cross-sectional geometry, and geometric transformations. Construction highlights involve commands like Prism, Translate, IntersectPath, Rotate, Segment, utilizing objects such as EE, DD, CC, etc. Suitable for high school and university students learning solid geometry, cross-section analysis, and geometric modeling.

GeoGebra Commands & Parameters

  1. Prism(Polygon[AA, BB, CC, DD], EE) → p, O, edgeBBO, edgeCCP, edgeDDQ, edgeEEO, edgeOP, edgePQ, edgeEEQ, P, Q, faceAABBOEE, faceBBCCPO, faceCCDDQP, faceAADDQEE, faceEEOPQ, edgeAAEE
  2. Translate(Rotate[Rotate[Plane[xAxis, yAxis], tt, xAxis], rr, zAxis], Vector[(0, 0, ud)]) → b
  3. IntersectPath(b, p) → poly3, R, S, T, U, l, m, n, q
  4. Rotate(Rotate[Translate[poly3, Vector[(0, 0, (-ud))]], (-rr), zAxis], (-tt), xAxis) → poly2
  5. Segment(AA, BB) → edgeAABB
  6. Segment(BB, CC) → edgeBBCC
  7. Segment(CC, DD) → edgeCCDD
  8. Segment(DD, AA) → edgeDDAA

AI Drawing Prompt Reference

Draw a cuboid and dynamically show its cross-sections at different planes. First, draw a cuboid with a quadrilateral base. Then, generate different angle cross-sections through rotation and translation. Use the IntersectPath command to find the intersection lines between the cross-section and the cuboid. Finally, rotate and translate the cross-section back to its initial position.
The prompt above was compiled from the original drawing commands and is for reference only.