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Pythagorean Square Pyramid

Pythagorean Square Pyramid
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2018-11-20 11:05
TrigonometrySolid GeometryGeometric Construction
This example demonstrates a geometric model of a square-based pyramid constructed based on the Pythagorean theorem. It involves core mathematical concepts such as solid geometry, the Pythagorean theorem, polygon area, and angle calculations. The construction uses GeoGebra commands/objects like Line, OrthogonalLine, Circle, Point, Plane, Intersect, Segment, Pyramid, Angle, and Polygon. Suitable for high school mathematics teaching or exploration by geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. OrthogonalLine(B, xOyPlane) → g
  3. Circle(g, A) → c
  4. OrthogonalLine(A, xOyPlane) → i
  5. Point(g) → C
  6. Plane(A, B, C) → b
  7. OrthogonalLine(A, b) → h
  8. OrthogonalLine(B, b) → j
  9. Circle(i, B) → d
  10. Intersect(h, d) → D, E
  11. Intersect(j, c) → F, G
  12. Segment(B, E) → k
  13. Segment(A, G) → l
  14. Intersect(l, k) → H
  15. OrthogonalLine(H, xOyPlane) → m
  16. Point(m) → I
  17. Pyramid(B, G, E, A, I) → a, faceABGE, edgeBI, edgeGI, edgeEI, edgeAI, faceBGI, faceEGI, faceAEI, faceABI, edgeBG, edgeEG, edgeAE, edgeAB
  18. Segment(H, I) → n
  19. Angle(A, H, B) → α
  20. Angle(I, H, B) → β
  21. Angle(A, H, E) → γ
  22. Angle(G, H, E) → δ
  23. Angle(B, H, G) → ε
  24. Angle(I, H, A) → ζ
  25. Angle(I, H, G) → η
  26. Angle(I, H, E) → θ
  27. Polygon(I, H, A) → t1, a_1, i_1, h_1
  28. Polygon(A, H, B) → t2, b_1, a_2, h_2