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Rotating Box Demonstration

Rotating Box Demonstration
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2018-01-24 23:45
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the process of a rectangular box rotating around an axis to form a geometric solid. Core math concepts include rotation, solid geometry, trigonometry, and inequalities. Construction highlights involve commands like Sequence, Join, and Polygon from GeoGebra. Suitable for high school and above students to learn spatial geometry and rotation solids.

GeoGebra Commands & Parameters

  1. Sequence(Element[L_1, i] + (0, 0, h), i, 1, 4) → L_2
  2. Join({L_1, L_2}) → L_P
  3. Sequence(hom[Element[L_P, i]], i, 1, 8) → L_h
  4. Sequence((T * Element[L_h, i]), i, 1, 8) → L_T
  5. Sequence(((D * Element[L_T, i, 1, 1] / Element[L_T, i, 3, 1]), (D * Element[L_T, i, 2, 1] / Element[L_T, i, 3, 1])), i, 1, 8) → L_{Prj}
  6. Polygon(Element[L_{Prj}, 1], Element[L_{Prj}, 2], Element[L_{Prj}, 6], Element[L_{Prj}, 5]) → P_3, q, r, s, t
  7. Polygon(Element[L_{Prj}, 5], Element[L_{Prj}, 6], Element[L_{Prj}, 7], Element[L_{Prj}, 8]) → P_2, k, m, n, p
  8. Polygon(Element[L_{Prj}, 2], Element[L_{Prj}, 3], Element[L_{Prj}, 7], Element[L_{Prj}, 6]) → P_4, a, b, c, d
  9. Polygon(Element[L_{Prj}, 3], Element[L_{Prj}, 4], Element[L_{Prj}, 8], Element[L_{Prj}, 7]) → P_5, e, f_1, g_1, h_1
  10. Polygon(Element[L_{Prj}, 1], Element[L_{Prj}, 4], Element[L_{Prj}, 8], Element[L_{Prj}, 5]) → P_6, i_1, j_1, k_1, l_1
  11. Polygon(Element[L_{Prj}, 1], Element[L_{Prj}, 2], Element[L_{Prj}, 3], Element[L_{Prj}, 4]) → P_1, f, g, i, j
  12. Sequence(A - Element[PInPoly, i], i, 1, 6) → σList
  13. Sequence((Element[NList, i] * Element[σList, i]), i, 1, 6) → visibleL