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Cross Section Pyramid

Cross Section Pyramid
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2018-04-05 20:22
Solid GeometryOptimizationGeometric Construction
This example dynamically visualizes the 3D shape of a pyramid and its cross-section by calculating intersection points. It involves core math concepts like solid geometry, cross-section analysis, linear programming, derivatives, integrals, and probability statistics (Poisson & Normal distributions). Construction uses commands like Point, Pyramid, Plane, IntersectPath, and Intersect. Suitable for high school and above mathematics education and geometric visualization research.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → C
  3. Point(zAxis) → E
  4. Pyramid(A, B, C, D, E) → a, faceABCD, edgeAE, edgeBE, edgeCE, edgeDE, faceABE, faceBCE, faceCDE, faceADE, edgeAB, edgeBC, edgeCD, edgeAD
  5. Point(edgeDE) → F
  6. Point(edgeAE) → G
  7. Point(edgeCE) → H
  8. Plane(F, G, H) → b
  9. IntersectPath(b, faceCDE) → f
  10. Intersect(b, faceCDE) → I, J
  11. Segment(F, G) → g
  12. Intersect(edgeBE, b) → K
  13. Segment(H, K) → h
  14. Segment(K, G) → i

AI Drawing Prompt Reference

Draw a 3D pyramid with a quadrilateral base and an apex above the center. Pick two points on two lateral edges and one point on a base edge, then define a plane through these three points. This plane cuts obliquely through the pyramid, intersecting one side face to form a cross-section path and meeting another lateral edge at a point. Connect the key points of the section with line segments to clearly show the shape and position of the cross-section, while keeping the pyramid's edges and faces visible for spatial understanding.
The prompt above was compiled from the original drawing commands and is for reference only.