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Longest Rod in a Rectangular Prism Geometry Construction

Longest Rod in a Rectangular Prism Geometry Construction
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2017-10-03 22:24
Coordinate GeometrySolid GeometryOptimizationGeometric Construction
This example demonstrates finding the longest rigid rod fitting inside a rectangular prism, representing the space diagonal. Core concepts involve solid geometry, Pythagorean theorem, and spatial distance formulas. Construction utilizes GeoGebra commands like Point, Line, Prism, and Segment to build the 3D structure and highlight the diagonal. OrthogonalLine and Intersect ensure vertex precision. Suitable for high school geometry classes or self-exploration of spatial optimization and distance maximization in 3D space.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Line(A, B) → f
  4. OrthogonalLine(A, f) → h
  5. Line(B, h) → g
  6. Point(g) → C
  7. Line(C, f) → i
  8. Intersect(h, i) → D
  9. Polygon(D, A, B, C) → q1, d, a, b, c
  10. Point(zAxis) → E
  11. Line(E, yAxis) → j
  12. OrthogonalLine(B, q1) → k
  13. OrthogonalLine(C, q1) → l
  14. OrthogonalLine(A, q1) → m
  15. OrthogonalLine(D, q1) → n
  16. Line(E, a) → p
  17. Point(p) → F
  18. Intersect(n, j) → G
  19. Line(G, c) → q
  20. Intersect(k, p) → H
  21. Line(F, b) → r
  22. Prism(A, B, C, D, E) → e, I, edgeAB, edgeBC, edgeCD, edgeAD, edgeAE, edgeBI, edgeCJ, edgeDK, edgeEI, edgeIJ, J, edgeJK, edgeEK, K, faceABCD, faceABIE, faceBCJI, faceCDKJ, faceADKE, faceEIJK
  23. Intersect(edgeAE, edgeAB) → L
  24. Intersect(edgeCJ, edgeBC) → M
  25. Segment(L, M) → s
  26. Segment(C, E) → t
  27. Segment(E, L) → f_1