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Semi-rigid Cube

Semi-rigid Cube
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2022-03-08 18:43
FunctionTrigonometrySolid GeometryGeometric Construction
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This example demonstrates the construction and motion properties of a semi-rigid cube. It involves core mathematical concepts such as geometric construction, solid geometry, quadratic equations, and conditional probability. The construction uses GeoGebra commands and objects like Point, IntersectConic, PointIn, and If. Suitable for high school students and math enthusiasts studying geometric constructions and mechanical structures.

GeoGebra Commands & Parameters

  1. Point(Circle[O, 1, zAxis]) → E
  2. IntersectConic(Sphere[U, sqrt(2)], Sphere[E, sqrt(2)]) → cUE2
  3. PointIn(Sphere[O, 1]) → A
  4. IntersectConic(Sphere[U, sqrt(2)], Sphere[A, sqrt(2)]) → cUA2
  5. PointIn(Sphere[U, sqrt(2)]) → J1
  6. Point(cUA2) → J2
  7. Point(cUE2) → J3
  8. If(E ≟ U ∧ A ≟ U, J1, E ≟ U ∨ A ≟ E, J2, A ≟ U, J3, J0) → J
  9. IntersectConic(Sphere[E, 1], Sphere[J, 1]) → cEJ
  10. IntersectConic(Sphere[U, 1], Sphere[J, 1]) → cUJ
  11. Point(cUJ) → B3
  12. Point(cUJ) → F2
  13. If(E ≟ U, F2, F0) → F
  14. If(A ≟ U, B3, B0) → B
  15. Point(cEJ) → D2
  16. If(A ≟ E, D2, D0) → D

AI Drawing Prompt Reference

Draw a semi-rigid cube by first drawing a sphere with radius 1 centered at point O, then selecting points A and E on this sphere. Draw two spheres with radius sqrt(2) that intersect with the original sphere to get circles cUA2 and cUE2. Select points J1, J2, and J3 on these circles. Choose the appropriate point J based on conditions. Draw two spheres with radius 1 centered at points E and J, intersecting to get circle cEJ, and at points U and J to get circle cUJ. Select points B3 and F2 from circle cUJ, choose the appropriate points F and B based on conditions. Finally, draw two spheres with radius 1 centered at points E and J, U and J, intersecting to get circles cEJ and cUJ, and select point D2 from circle cEJ, choosing the appropriate point D based on conditions.
The prompt above was compiled from the original drawing commands and is for reference only.