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Pyramid Geometric Construction with Trigonometric Functions

Pyramid Geometric Construction with Trigonometric Functions
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2024-07-15 21:53
CirclePolygonAngleTrigonometrySolid Geometry
In collections Simplifying Radicals: Geometric Thin Slice
This GeoGebra example demonstrates how to construct a 3D pyramid geometry combined with circles and polygons to illustrate geometric relationships. The core mathematical concepts include cosine theorem, geometric mean, and parametric curve equations. Construction key points: Use Polygon command to draw the polygonal base, Circle command to construct auxiliary circles, Angle command to measure and label vertex angles α, β, γ, Rotate command for rotation operations, Intersect to find intersection points, and RotateText for angle annotations. Suitable for upper middle school and lower undergraduate students learning solid geometry fundamentals, understanding polyhedron construction methods, or for teaching the visualization of parametric equations combined with trigonometric functions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. OrthogonalLine(C, b) → f
  3. Circle(C, 1) → d
  4. Intersect(d, f, 1) → D
  5. Segment(A, D) → g
  6. OrthogonalLine(D, g) → h
  7. Circle(D, 1) → e
  8. Intersect(e, h, 2) → E
  9. Segment(A, E) → i
  10. OrthogonalLine(E, i) → j
  11. Circle(E, 1) → k
  12. Segment(C, D) → m_2
  13. Segment(D, E) → n_2
  14. Angle(C, B, A) → α
  15. Angle(D, C, A) → β
  16. Angle(E, D, A) → γ
  17. Segment(A, B) → l_3
  18. Segment(C, B) → m_3
  19. Segment(C, A) → n_3
  20. RotateText(text1_{1}, atand(Slope[n_3])) → text2
  21. RotateText(text3, atand(Slope[g])) → text4
  22. Rotate(D, If[0 < o ≤ 1, ((-o) * pi / 3), ((-pi)) / 3], E) → D'
  23. Rotate(E, If[0 < o ≤ 1, ((-o) * pi / 3), ((-pi)) / 3], E) → E'
  24. Segment(D', E') → p_3
  25. Rotate(D', If[1 < o ≤ 2, ((-(o - 1)) * pi), (-pi)], D') → D''
  26. Rotate(E', If[1 < o ≤ 2, ((-(o - 1)) * pi), pi], D') → E''
  27. Segment(D'', E'') → q_3
  28. Polygon(A, B, C) → t2, c_4, a_4, b_4
  29. Polygon(A, C, D) → t3, d_4, a_5, c_5
  30. Polygon(A, D, E) → t4, e_4, a_6, d_5
  31. Circle(A, Distance[A, C]) → k_4

AI Drawing Prompt Reference

Draw a triangular pyramid with base triangle ABC and side triangles ACD and ADE. Use circles and polygons to assist in construction, find key points D and E through rotation and intersection. Measure and label the vertex angles α, β, and γ, and finally annotate the angles with rotated text.
The prompt above was compiled from the original drawing commands and is for reference only.