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Angle MAX on the Diagonal of a Cube

Angle MAX on the Diagonal of a Cube
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2018-03-19 15:34
AngleSolid GeometryGeometric Construction
This example demonstrates the angle MAX on the diagonal of a cube. Key mathematical concepts include solid geometry angles. Using GeoGebra commands such as Derivative, Intersect, Point, etc., as listed in the construction summary, a cube and its diagonal can be constructed. Suitable for high school mathematics education or students learning solid geometry.

GeoGebra Commands & Parameters

  1. Derivative(q) → q'
  2. Intersect(q', xAxis, (0.666666666374032, 4.561722849665948E-9)) → N
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, E_1, faceCEIH, faceFGHI, arêteAE, arêteAB, arêteBC, arêteCE, arêteAF, arêteEI, arêteFI, arêteFG, E, arêteBG, arêteGH, arêteCH, arêteHI, F, G, H, faceABCE, faceAEIF, faceABGF, faceBCHG
  5. Segment(D, F) → f
  6. Point(f) → M
  7. Vector(D, M) → u
  8. Segment(E, M) → g
  9. Segment(M, B) → h
  10. Angle(E, M, B) → α
  11. Vector(D, F) → v
  12. Intersect(yAxis, xAxis) → O
  13. Point(yAxis) → I
  14. Point(xAxis) → J
  15. Outil1(I, O, P) → i
  16. Outil1(J, O, P) → j
  17. Intersect(i, yAxis) → K
  18. Intersect(j, xAxis) → L
  19. Intersect(q, yAxis, (0, 1.0471975511965979)) → Q
  20. Derivative(cx) → cx'