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Wobbling Wall

Wobbling Wall
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2020-07-17 00:29
VectorTrigonometrySolid GeometryDerivativeGeometric Construction
In collections Action Modular Origami
This example demonstrates an animated model folded from paper, sourced from the book 'Action Modular Origami'. It involves core mathematical concepts such as triangles, quadratic equations, derivatives, and rational numbers. The construction utilizes GeoGebra commands like Intersect, Point, If, Cube, Translate, Midpoint, OrthogonalLine, Rotate, Sequence, Vector, Plane, and Mirror, along with objects like ff, A, B, α, C, a, D, E, F, G, H, and various faces, edges, and cubes. It is suitable for high school and above, focusing on solid geometry, geometric construction, and calculus.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xAxis) → A
  2. Point(xAxis) → B
  3. If(ff > 0, 90° + (ff * 180°), 90° - (ff * 180°)) → α
  4. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  5. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  6. Translate({faceABCD, faceABFE, faceADHE, faceBCGF, faceCDHG, faceEFGH}, Vector[(0, 0, 0)]) → cube0
  7. Midpoint(A, C) → I
  8. OrthogonalLine(I, xOyPlane) → f
  9. Rotate(cube0, (-α), edgeCG) → cube0'
  10. Sequence(Rotate[cube0', (n * 90°), f], n, 0, 3) → listPolySideCubes
  11. Rotate(B, α, C) → B'
  12. Vector(B, B') → u
  13. Translate(cube0, u) → cube0'_1
  14. Sequence(Rotate[cube0'_1, (n * 90°), f], n, 0, 3) → listPolyCornerCubes
  15. Plane(D, F, H) → b
  16. Mirror({listPolyCornerCubes, listPolySideCubes}, b) → listReflect

AI Drawing Prompt Reference

Create an animated model folded from paper, demonstrating a wobbling effect. The structure consists of multiple cubes centered around a triangle, formed by rotations and reflections. Begin with a base cube, then replicate it by rotating around an axis, followed by vector translation and mirroring to expand the shape, resulting in a complex polyhedron with distinct faces and edges, showcasing mathematical concepts like trigonometry, quadratic equations, and vectors.
The prompt above was compiled from the original drawing commands and is for reference only.