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Orange Slice

Orange Slice
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2017-04-24 01:03
Coordinate GeometrySolid GeometryTransformation
This GeoGebra example demonstrates a wedge section of a sphere. It involves parametric curves and rotation transformations. Using commands like RotateText, Surface, Arc, Rotate, Sequence, Vector, CurveCartesian, Point, Translate, a dynamic wedge shape is constructed. Suitable for high school geometry and transformation learning.

GeoGebra Commands & Parameters

  1. RotateText("uStas\;\&\;T.C.", 90°) → надпись01
  2. SelectedElement(sp1) → n
  3. Surface(((scaLe * cos(k)) * cos(t)), ((scaLe * cos(k)) * sin(t)), zQ + (scaLe * sin(k)), k, ((-π)) / 2, π / 2, t, 0, π / n) → c1
  4. Arc(Circle[Q, scaLe, yAxis], (0, 0, zQ + scaLe), (0, 0, zQ - scaLe)) → ψ
  5. Rotate(ψ, π / n, zAxis) → ω
  6. Sequence(Rotate[c1, (t * π / n), zAxis], t, 1, (2 * n) - 1) → sp2
  7. Sequence(Rotate[ψ, (t * π / n), zAxis], t, 2, (2 * n) - 1) → ψ2
  8. Vector(Q, Q + ((scaLe * cos(π / ((2 * n)))), (scaLe * sin(π / ((2 * n)))), 0)) → v1
  9. CurveCartesian((x(v1) * t), (y(v1) * t), zQ, t, 0, 1) → a
  10. Point(a) → A
  11. Vector(Q, A) → v2
  12. Translate(c1, v2) → c2
  13. Translate(ψ, v2) → ψ1
  14. Translate(ω, v2) → ω1
  15. Sequence(Rotate[c2, (t * π / n), zAxis], t, 1, (2 * n) - 1) → sp3
  16. Sequence(Rotate[ψ1, (t * π / n), zAxis], t, 1, (2 * n) - 1) → ψ3
  17. Sequence(Rotate[ω1, (t * π / n), zAxis], t, 1, (2 * n) - 1) → ω3