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Golden Prism Volume =? Surface Area Demo

Golden Prism Volume =? Surface Area Demo
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2016-10-02 23:28
Solid GeometryGeometric Construction
In collections Geo&Alg:Area Volume Pythagorean Th.
This example demonstrates the relationship between volume and surface area of a golden prism. Key math concepts include solid geometry, golden ratio, volume, and surface area calculations. Construction involves GeoGebra commands like Segment, Polygon, Midpoint, Ray, Circle, Intersect, OrthogonalLine, and Prism. Suitable for high school students and educators for geometric exploration and teaching.

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. Point(GoldenPrism) → Pointd

AI Drawing Prompt Reference

Draw a golden prism to demonstrate the relationship between its volume and surface area. Start by constructing a quadrilateral, find its midpoint, draw a circle and a ray, determine a golden rectangle through intersections and perpendicular lines, then extrude the rectangle vertically to form the prism, highlighting key points and faces.
The prompt above was compiled from the original drawing commands and is for reference only.