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A Plane Intersecting a Triangular Pyramid

A Plane Intersecting a Triangular Pyramid
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2017-08-03 05:48
VectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the intersection of a plane with a triangular pyramid, visually showing how the cross-section changes. Key math concepts include solid geometry, vector operations, parametric equations, and coordinate geometry. GeoGebra commands used in construction are Vector, OrthogonalLine, Translate, Line, Polygon, Midpoint, Segment, etc. Suitable for high school students and math enthusiasts to understand spatial geometry and transformations.

GeoGebra Commands & Parameters

  1. Vector(B_1, X) → u_1
  2. Vector(B_1, Z) → w_1
  3. OrthogonalLine(Uchwyt, yAxis) → a
  4. OrthogonalLine(Uchwyt, xAxis) → b
  5. Vector(B_1, Y) → v_1
  6. Translate(O, w_1) → G
  7. Line(O, G) → e
  8. Translate(O, u_1) → K
  9. Translate(O, v_1) → N
  10. Vector(O, G) → v
  11. Vector(O, K) → u
  12. Vector(O, N) → w
  13. Translate(N, u) → Z1
  14. If(m < 2 / 3, ((1 - (1.5 * m)) * A1) + ((1.5 * m) * S), ((1 - (3 * n)) * S) + ((3 * n) * A3)) → B3
  15. If(m < 2 / 3, ((1 - (1.5 * m)) * A1) + ((1.5 * m) * S), ((1 - (3 * n)) * S) + ((3 * n) * A2)) → B4
  16. Polygon(B2, B1, B4, B3) → poly1, b2, b1, b4, b3
  17. Polygon(E4, E1, E2, E3) → poly2, e4, e1, e2, e3
  18. Midpoint(A2, A3) → A
  19. Segment(A, A1) → p
  20. Odcinek3D(S, A2, A1, A3) → d, f
  21. Odcinek3D(S, A3, A2, A1) → h, i
  22. Odcinek3D(S, A1, A3, A2) → j, l
  23. Odcinek3D(A1, A2, A3, S) → q, r
  24. Odcinek3D(A1, A3, S, A2) → s, t
  25. Odcinek3D(A2, A3, A1, S) → a_1, b_1

AI Drawing Prompt Reference

Draw a triangular pyramid and intersect it with a plane to show how the cross-section changes. First, establish a coordinate system and define the pyramid's vertices and base. Then, create a plane and adjust its position to observe the changes in the cross-section. Key objects include the pyramid's vertices, base, the intersecting plane, and the lines of intersection.
The prompt above was compiled from the original drawing commands and is for reference only.