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Prisms and Cylinders Geometric Demo

Prisms and Cylinders Geometric Demo
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2022-08-30 16:27
VectorTrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric construction and properties of prisms and cylinders. It involves core mathematical concepts such as solid geometry, vectors, trigonometric functions, and median values. GeoGebra commands and objects used include Sequence, Insert, Div, Segment, Polygon, and Centroid. Suitable for high school and above students for learning 3D geometry and understanding three-dimensional shapes.

GeoGebra Commands & Parameters

  1. Sequence({{cos(((k * a) * t)), (-sin(((k * a) * t))), 0}, {sin(((k * a) * t)), cos(((k * a) * t)), 0}, {0, 0, 1}}, k, 0, N) → LiRa
  2. Sequence({{cos((k * a)), sin((k * a)), 0}, {(-sin((k * a))), cos((k * a)), 0}, {0, 0, 1}}, k, 0, N) → LiR
  3. Sequence(Element[({{l, 0, 0}} * Element[LiR, k]), 1], k, 1, N + 1) → V_0
  4. Sequence(Element[Element[RV_0, k], 1], k, 1, N + 1) → RV_x
  5. Sequence(Element[Element[RV_0, k], 2], k, 1, N + 1) → RV_y
  6. Sequence({Sum[RV_x, k], Sum[RV_y, k], 0}, k, 1, N + 1) → SumRV
  7. Sequence(Element[({Element[V_0, k]} * Element[LiRa, k]), 1], k, 1, N) → VQ
  8. Sequence(Element[Element[VQ, k], 1], k, 1, N) → VQ_x
  9. Sequence(Element[Element[VQ, k], 2], k, 1, N) → VQ_y
  10. Sequence({Sum[VQ_x, k], Sum[VQ_y, k], 0}, k, 1, N) → SumVQ
  11. Sequence(Element[SumVQ, k] + {0, 0, (-1 * altezza)}, k, 1, N) → R
  12. Sequence(Element[Element[V_0, k], 2], k, 1, N + 1) → V_{0y}
  13. Sequence(Element[Element[V_0, k], 1], k, 1, N + 1) → V_{0x}
  14. Sequence({Sum[V_{0x}, k], Sum[V_{0y}, k], 0}, k, 1, N + 1) → SumV_0
  15. Sequence(Element[SumV_0, k], k, 1, N + 1) → P
  16. Insert({Element[P, N]}, SumVQ, 1) → Q
  17. Div(N, 2) → M
  18. Insert({Element[P, N] + {0, 0, (-1 * altezza)}}, R, 1) → R1
  19. Sequence((Element[Element[(Q * Cav), k], 1], Element[Element[(Q * Cav), k], 2]), k, 1, N + 1) → PQ
  20. Sequence((Element[Element[(RP * Cav), k], 1], Element[Element[(RP * Cav), k], 2]), k, 1, N + 1) → PP
  21. Sequence(Element[R, N] + Element[S_R, k], k, 1, N + 1) → S
  22. Sequence((Element[Element[(R1 * Cav), k], 1], Element[Element[(R1 * Cav), k], 2]), k, 1, N + 1) → PR
  23. Sequence((Element[Element[(S * Cav), k], 1], Element[Element[(S * Cav), k], 2]), k, 1, N + 1) → PS
  24. Sequence(Segment[Element[PS, k], Element[PS, k + 1]], k, 1, N) → SpigoliSotto
  25. Sequence(Segment[Element[PP, k], Element[PP, k + 1]], k, 1, N) → SpigoliSopra
  26. Sequence(Polygon[Element[PQ, k], Element[PQ, k + 1], Element[PR, k + 1], Element[PR, k]], k, 1, N) → FacceLat
  27. Sequence(Segment[Element[PQ, k], Element[PR, k]], k, 1, N + 1) → SpigoliLat
  28. Sequence(Segment[Element[PS, k], Element[PS, k + 1]], k, 1, N) → p_{base}
  29. Sequence(Segment[Element[PR, k], Element[PR, k + 1]], k, 1, N + 1) → SpigoliLatSotto
  30. Segment(Element[PQ, 1], Element[PR, 1]) → h
  31. Polygon(PS) → poly2
  32. Centroid(poly2) → D
  33. Polygon(PP) → poly1
  34. Centroid(poly1) → A

AI Drawing Prompt Reference

Draw a 3D prism. The prism has a polygonal base and a top face that are parallel and congruent. The lateral faces are rectangles perpendicular to the base. The construction order: first draw the base polygon, then the top polygon, then draw vertical lines connecting them, and finally draw all rectangular side faces. The figure should clearly show the geometric structure of the prism, including the base, top, and sides.
The prompt above was compiled from the original drawing commands and is for reference only.