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Cube Animation

Cube Animation
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2017-06-04 22:35
Solid GeometryGeometric Construction
This example demonstrates the dynamic rotation of a cube. It involves core mathematical concepts such as solid geometry, geometric transformations, and the representation of three-dimensional shapes. Key construction elements include commands/objects like Point, Polygon, Cube, Rotate, OrthogonalLine, Line, Circle, and Intersect from GeoGebra. Suitable for high school and above students studying solid geometry, geometric constructions, and 3D visualization.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(yAxis) → B
  3. Polygon(A, B, 4) → poly1, g, h, i, j, C, D
  4. Point(Circle[D, Distance[C, D], Segment[C, D]]) → E
  5. Cube(C, D, E) → a_1, F, faceEFJI, faceGHIJ, arêteCF, arêteCD, arêteDE, arêteEF, arêteCG, arêteFJ, arêteGJ, arêteGH, G, arêteDH, arêteHI, arêteEI, arêteIJ, H, I, J, faceCDEF, faceCFJG, faceCDHG, faceDEIH
  6. Rotate(faceCFJG, (a * π / 2), arêteCF) → faceCFJG'
  7. Rotate(G, (a * π / 2), arêteCF) → G'
  8. Rotate(faceCFJG, (a * π / 2), arêteCF) → faceCFJG'_1
  9. Rotate(J, (a * π / 2), arêteCF) → J'
  10. OrthogonalLine(G', faceCFJG'_1) → k
  11. OrthogonalLine(J', faceCFJG'_1) → l
  12. Line(J', G') → m
  13. Circle(m, C) → c
  14. Circle(m, B) → d
  15. Intersect(k, c) → K, L
  16. Intersect(l, d) → M, N
  17. Polygon(J', M, K, G') → poly2, j', m_1, k_1, g'
  18. Circle(m, G') → p
  19. Circle(m, G') → q
  20. Line(J', F) → r
  21. Circle(m, F) → s
  22. Intersect(l, s) → O, P
  23. Polygon(J', O, K, G') → poly3, j'_1, o, k_2, g'_1
  24. Rotate(poly3, (a * π / 2), m) → poly3'
  25. Rotate(faceCDHG, (a * π / 2), arêteCD) → faceCDHG'
  26. Rotate(faceDEIH, (-(((-a) * π / 2))), arêteDE) → faceDEIH'
  27. Rotate(faceEFJI, (-(((-a) * π / 2))), arêteEF) → faceEFJI'

AI Drawing Prompt Reference

Draw an animated cube to demonstrate its three-dimensional geometry and transformations. Start by constructing a quadrilateral base, then form the cube from this base. Use rotation commands to make the cube rotate around a specific edge. During the rotation, draw auxiliary lines, circles, and intersection points to accurately depict the changes on the cube's surface, ultimately presenting an animated rotating cube effect.
The prompt above was compiled from the original drawing commands and is for reference only.