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Cylinder - Illusion

Cylinder - Illusion
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2017-01-14 00:52
CircleFunctionSolid Geometry
This example demonstrates the geometric construction and visual illusion of a cylinder. Key mathematical concepts include cylinder, circle, and piecewise-defined functions. Using GeoGebra commands such as Surface, Point, Polygon, Line, etc., the various faces and edges of the cylinder can be constructed. Suitable for high school geometry and solid geometry education.

GeoGebra Commands & Parameters

  1. Surface((2 * cos(u)), sin(u), v, u, 0, (2 * π), v, -4, 4) → a
  2. Point(zAxis) → A
  3. Point(xAxis) → B
  4. Point(zAxis) → C
  5. Point(xAxis) → D
  6. Polygon(B, A, D, C) → Vieleck1, b, a_1, d, c
  7. Line(B, yAxis) → f
  8. Point(yAxis) → E
  9. OrthogonalPlane(E, yAxis) → e
  10. Intersect(f, e) → F
  11. Mirror(F, B) → F'
  12. Prism(Vieleck1, F) → g, G, KanteAG, KanteDH, KanteCI, KanteFG, KanteGH, KanteHI, KanteFI, H, I, FlächeABFG, FlächeADHG, FlächeCDHI, FlächeBCIF, FlächeFGHI, KanteBF
  13. Prism(Vieleck1, F') → h, J, KanteAJ, KanteDK, KanteCL, KanteF'J, KanteJK, KanteKL, KanteF'L, K, L, FlächeABF'J, FlächeADKJ, FlächeCDKL, FlächeBCLF', FlächeF'JKL, KanteBF'
  14. CurveCartesian((2 * cos(t)), sin(t), 1 - cos(t), t, (-π) / 2, 0) → k_1
  15. CurveCartesian((2 * cos(t)), sin(t), -1 + cos(t), t, 0, π / 2) → k_2
  16. CurveCartesian((-2 * cos(t)), sin(t), -1 + cos(t), t, 0, π / 2) → k_3
  17. CurveCartesian((-2 * cos(t)), sin(t), 1 - cos(t), t, (-π) / 2, 0) → k_4

AI Drawing Prompt Reference

Draw the geometric construction and visual illusion of a cylinder, showcasing the mathematical concepts of cylinder, circle, and piecewise-defined functions. Start by creating a rotating surface, then construct the top and bottom faces and the side surface of the cylinder. Use points on the axis and planes orthogonal to it to form the side surface, and represent the edges with curves to complete the 3D shape.
The prompt above was compiled from the original drawing commands and is for reference only.