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Angle between Two Planes in a Square Pyramid

Angle between Two Planes in a Square Pyramid
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2018-05-22 10:35
VectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the calculation and visualization of the angle between two planes in a square pyramid, such as a lateral face and the base. Key math concepts include plane equations in solid geometry, vector cross product for angle calculation, and matrix operations. GeoGebra commands like Point, Polygon, Pyramid, Midpoint, Circle, Intersect, Rotate, Segment, and Angle are used to construct the geometry and measure the angle. Suitable for high school students and teachers exploring spatial geometry and linear algebra applications in 3D shapes.

GeoGebra Commands & Parameters

  1. If(t < 1, 0, t < 2, t - 1, 1) → t_2
  2. Point(Segment[(sqrt(2), 0, 0), (sqrt(50), 0, 0)]) → B
  3. Polygon(B, C, D, A) → q1, a, b, c, d
  4. Point(Segment[(0, 0, 1), (0, 0, 9)]) → V
  5. Pyramid(q1, V) → e, faceABE, faceBCE, faceCDE, faceADE, edgeAE, edgeBE, edgeCE, edgeDE
  6. If(t ≤ 1, t, 1) → t_1
  7. If(t < 2, 0, t - 2) → t_3
  8. Midpoint(A, B) → E
  9. Circle(d, V) → k
  10. Intersect(xOyPlane, k) → F, G
  11. Rotate(V, ((t_1 - t_3) * Angle[V, E, G]), d) → V'
  12. Polygon(V', A, B) → t2, b_1, v', a_2
  13. Midpoint(C, D) → H
  14. Segment(G, I) → i
  15. Intersect(d, i) → M
  16. Segment(V', M) → l
  17. Segment(M, I) → m
  18. Angle(I, M, A) → δ
  19. Angle(V', M, B) → ε
  20. Angle(V', M, I) → ζ