MathPlotAI Logo MathPlotAI

Pear Curves

Pear Curves
Loading the math board and drawing, please wait…
2020-05-17 01:18
TrigonometrySolid GeometryParametric EquationGeometric Construction
This example demonstrates the construction and 3D visualization of pear curves. It involves core mathematical concepts such as quadratic equations, cosine functions, rotation, symmetry, and solid geometry. Key GeoGebra commands and objects used in the construction include Spline, Rotate, Surface, Circle, Cylinder, Sequence, Mirror, Point, Segment, PointIn, Line, and CircumcircleArc. It is suitable for high school students and mathematics enthusiasts exploring complex curves and 3D shapes.

GeoGebra Commands & Parameters

  1. Spline(l1, 3) → a
  2. Rotate(a, 90°, xAxis) → a'
  3. Surface(a', (2 * π), zAxis) → b
  4. Rotate(A, 90°, xAxis) → A'
  5. Circle(A' - (0, 0, 0.2), 0.1, zAxis) → c
  6. Cylinder(c, 0.7665838069903629) → d, e, f
  7. Rotate(J, 90°, xAxis) → J'
  8. Sequence(Rotate[J' + (0.4, 0, 0.05), i, zAxis], i, 0, (2 * π), (2 * π / 6)) → l2
  9. Sequence(Rotate[J' + (0.02, 0, 0.05), i, zAxis], i, 0, (2 * π), (2 * π / 12)) → l3
  10. Sequence(Polygon[Element[l3, i], Element[l3, i + 1], Element[l2, i]], i, 1, Length[l3]) → l4
  11. Mirror(a, yAxis) → a'_1
  12. Point(yAxis) → K
  13. Segment(A, K) → g
  14. PointIn(f) → L
  15. Segment(L, M) → h
  16. Point(h) → N
  17. Line(N, yAxis) → i
  18. Point(i) → O
  19. CircumcircleArc(L, O, M) → k
  20. Mirror(k, h) → k'