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Golden Prism: Volume = TSA?

Golden Prism: Volume = TSA?
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2016-10-02 22:14
FunctionSolid GeometryGeometric Construction
This example demonstrates a golden prism and explores whether its volume equals its surface area. Key mathematical concepts include the calculation of volume and surface area in solid geometry. Using GeoGebra commands such as Segment, Polygon, Prism, etc., the faces and edges of the golden prism can be constructed. Suitable for high school mathematics education or research.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Polygon(A, B, 4) → poly1, g, h, i, j, C, D
  3. Midpoint(h) → E
  4. Segment(E, D) → k
  5. Ray(B, C) → l
  6. Circle(E, k) → c
  7. Intersect(c, l) → F,
  8. OrthogonalLine(F, l) → m
  9. Ray(A, D) → n
  10. Intersect(m, n) → G
  11. Polygon(A, G, F, B) → GoldenRectangle, a, g_1, f_1, w
  12. Prism(GoldenRectangle, a) → GoldenPrism, H, edgeAH, edgeGI, edgeFJ, edgeBK, edgeHI, edgeIJ, edgeJK, edgeHK, I, J, K, faceAGIH, faceFGIJ, faceBFJK, faceABKH, faceHIJK
  13. Volume(GoldenPrism) → volumed
  14. Point(GoldenPrism) → Pointd