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Prism Model Demonstration

Prism Model Demonstration
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2020-02-05 16:04
Solid GeometryCalculusIntegral
This example demonstrates the 3D geometric construction and properties of a prism. It involves core math concepts like solid geometry, integral calculus, root calculations, arithmetic operations, cuboids, and conic sections. The construction uses GeoGebra commands and objects such as points, polygons, orthogonal lines, lines, angles, segments, conditional statements, rotations, rays, and intersections. Suitable for high school students and math enthusiasts learning solid geometry and integral calculus.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Polygon(A, B, C) → t1, c, a, b
  3. Point(t1) → D
  4. OrthogonalLine(D, a) → f
  5. Line(source, D) → g
  6. Point(f) → F
  7. Angle(F, D, source) → α
  8. Point(f) → G
  9. Segment(source, D) → ray1
  10. If(0 ≤ α ≤ 90, asin(sin(α) / n_p), (-asin(sin(α) / n_p))) → β
  11. Rotate(G, β, D) → G'
  12. Angle(G, D, G') → γ
  13. Ray(D, G') → ray_{inside}
  14. Intersect(b, ray_{inside}) → H
  15. OrthogonalLine(H, b) → j
  16. Intersect(ray_{inside}, c) → I
  17. OrthogonalLine(I, c) → k
  18. Intersect(ray_{inside}, c) → J
  19. Segment(D, H) → ray_{2visible}
  20. Point(j) → E
  21. Angle(D, H, E) → δ
  22. If(δ ≤ θ_{c}, asin((n_p * sin(δ))), π - δ) → ε
  23. Point(j) → K
  24. Rotate(K, (-ε), H) → K'
  25. Angle(K', H, K) → ζ
  26. Ray(H, K') → h