MathPlotAI Logo MathPlotAI

Orange Wedges Geometry Demo

Orange Wedges Geometry Demo
Loading the math board and drawing, please wait…
2020-01-14 23:10
TrigonometryCoordinate GeometrySolid GeometryCalculusGeometric Construction
This example dynamically demonstrates the relationship between a sphere and its cross-sectional circle through orange slices. It involves core math concepts like fractions, sphere, secant line, multiplication, isosceles triangles, differential equations, and median value. GeoGebra commands used include Circle, Segment, Vector, Sequence, Surface, CurveCartesian, Translate, and Join. Suitable for high school mathematics teaching, focusing on solid geometry and analytical geometry visualization.

GeoGebra Commands & Parameters

  1. Circle(O, R, xOyPlane) → d
  2. Segment(B, A) → j
  3. Vector(O, C) → z
  4. Sequence(CurveCartesian[x(C) + ((R * cos(i)) * cos(j)), y(C) + ((R * sin(i)) * cos(j)), z(C) + (R * sin(j)), i, 0, Angle], j, -1.5708, 1.5708, (2 * π / Part)) → liste1
  5. Sequence(CurveCartesian[x(C) + ((R * cos(i)) * cos(j)), y(C) + ((R * cos(i)) * sin(j)), z(C) + (R * sin(i)), i, -1.5708, 1.5708], j, 0, Angle, (2 * π / Part)) → liste2
  6. Sequence(CurveCartesian[x(C) + ((R * cos(i)) * cos(j)), y(C) + ((R * cos(i)) * sin(j)), z(C) + (R * sin(i)), i, -1.5708, 1.5708], j, 0, Angle, π / Part) → liste6
  7. Surface(x(O) + ((R * cos(i)) * cos(j)), y(O) + ((R * sin(i)) * cos(j)), z(O) + (R * sin(j)), i, Angle, 6.28319, j, -1.5708, 1.5708) → a
  8. Surface(x(C) + ((R * cos(i)) * cos(j)), y(C) + ((R * sin(i)) * cos(j)), z(C) + (R * sin(j)), i, 0, Angle, j, -1.5708, 1.5708) → k
  9. CurveCartesian(x(O) + ((R * cos(i)) * cos(Angle)), y(O) + ((R * cos(i)) * sin(Angle)), z(O) + (R * sin(i)), i, -1.5708, 1.5708) → o
  10. CurveCartesian(x(O) + (R * cos(i)), y(O) + ((R * cos(i)) * 0), z(O) + (R * sin(i)), i, -1.5708, 1.5708) → p
  11. CurveCartesian(x(C) + ((R * cos(i)) * cos(Angle)), y(C) + ((R * cos(i)) * sin(Angle)), z(C) + (R * sin(i)), i, -1.5708, 1.5708) → q
  12. CurveCartesian(x(C) + (R * cos(i)), y(C) + ((R * cos(i)) * 0), z(C) + (R * sin(i)), i, -1.5708, 1.5708) → r
  13. CurveCartesian(x(C) + ((R * cos(i)) * cos(Angle)), y(C) + ((R * cos(i)) * sin(Angle)), z(C) + (R * sin(i)), i, -1.5708, 1.5708) → e
  14. Surface(x(O) + ((R * cos(i)) * cos(j)), y(O) + ((R * sin(i)) * cos(j)), z(O) + (R * sin(j)), i, Angle, 6.28319, j, -1.5708, 1.5708) → m
  15. CurveCartesian(x(C) + (R * cos(i)), y(C) + ((R * cos(i)) * 0), z(C) + (R * sin(i)), i, -1.5708, 1.5708) → f
  16. CurveCartesian(x(O) + (R * cos(i)), y(O) + ((R * cos(i)) * 0), z(O) + (R * sin(i)), i, -1.5708, 1.5708) → i
  17. Translate(B, Vector[(Extend * u)]) → B'
  18. Translate(A, Vector[(Extend * u)]) → A'
  19. Segment(B', A') → j'
  20. Join(Sequence[Sequence[(x(O) + ((R * cos(j)) * sin(i)), y(O) - ((R * sin(j)) * sin(i)), z(O) - (R * cos(i))), j, Angle, 6.28319, π / n], i, Angle, 6.28319, π / n]) → liste3
  21. Sequence(CurveCartesian[x(C) + ((k * cos(i)) * cos(Angle)), y(C) + ((k * cos(i)) * sin(Angle)), z(C) + (k * sin(i)), i, -1.5708, 1.5708], k, R - 0.25, R - 0.025, 0.025) → liste4
  22. Sequence(CurveCartesian[x(O) + ((k * cos(i)) * cos(Angle)), y(O) + ((k * cos(i)) * sin(Angle)), z(O) + (k * sin(i)), i, -1.5708, 1.5708], k, R - 0.25, R - 0.025, 0.025) → liste7
  23. Sequence(CurveCartesian[x(O) + (k * cos(i)), y(O) + ((k * cos(i)) * 0), z(O) + (k * sin(i)), i, -1.5708, 1.5708], k, R - 0.25, R - 0.025, 0.025) → liste8
  24. Sequence((x(C) + (((R - 0.26) * cos(i)) * cos(Angle)), y(C) + (((R - 0.26) * cos(i)) * sin(Angle)), z(C) + ((R - 0.26) * sin(i))), i, -1.5708, 1.5708, π / b) → liste9
  25. Sequence(CurveCartesian[x(C) + (k * cos(i)), y(C) + ((k * cos(i)) * 0), z(C) + (k * sin(i)), i, -1.5708, 1.5708], k, R - 0.25, R - 0.035, 0.025) → liste5
  26. Sequence(Polygon[Element[liste9, i], Element[liste9, i + 1], C], i, 1, Length[liste9]) → liste10
  27. Sequence((x(C) + ((R - 0.26) * cos(i)), y(C) + (((R - 0.26) * cos(i)) * 0), z(C) + ((R - 0.26) * sin(i))), i, -1.5708, 1.5708, π / b) → liste11
  28. Sequence(Polygon[Element[liste11, i], Element[liste11, i + 1], C], i, 1, Length[liste11]) → liste12
  29. Sequence((x(O) + (((R - 0.26) * cos(i)) * cos(Angle)), y(O) + (((R - 0.26) * cos(i)) * sin(Angle)), z(O) + ((R - 0.26) * sin(i))), i, -1.5708, 1.5708, π / b) → liste13
  30. Sequence((x(O) + ((R - 0.26) * cos(i)), y(O) + (((R - 0.26) * cos(i)) * 0), z(O) + ((R - 0.26) * sin(i))), i, -1.5708, 1.5708, π / b) → liste14
  31. Sequence(Polygon[Element[liste13, i], Element[liste13, i + 1], O], i, 1, Length[liste13]) → liste15
  32. Sequence(Polygon[Element[liste14, i], Element[liste14, i + 1], O], i, 1, Length[liste14]) → liste16
  33. Sequence(Segment[Element[liste9, i], C], i, 1, Length[liste9], 4) → liste17
  34. Sequence(Segment[Element[liste11, i], C], i, 1, Length[liste11], 4) → liste18
  35. Sequence(Segment[Element[liste13, i], O], i, 1, Length[liste13], 4) → liste19
  36. Sequence(Segment[Element[liste14, i], O], i, 1, Length[liste14], 4) → liste20