MathPlotAI Logo MathPlotAI

Spinning Top with 3D Surfaces

Spinning Top with 3D Surfaces
Loading the math board and drawing, please wait…
2020-05-16 15:06
SequenceSolid GeometryParametric EquationGraphing
① This GeoGebra example demonstrates a spinning top constructed from multiple 3D surfaces, including cylinders and parametric surfaces, with dynamic rotation to visualize the solid shape. ② Core mathematical concepts include 3D surface equations, parametric curves (e.g., sine curves), and solids of revolution, along with the use of sequences and element operations to generate repeated geometric components. ③ Construction highlights: from the summary, commands such as Circle, CurveCartesian, Cylinder, Surface, Sequence, and Element are used to define base geometries, while Color and multiple named objects (A1–A16, B1–B5) assemble the final top. ④ Suitable for high school or early college students learning solid geometry, parametric surfaces, and GeoGebra 3D graphing, as well as for demonstrating rotational solids or volume concepts.

GeoGebra Commands & Parameters

  1. Circle((0, 0, 0), d / 2, zAxis) → f
  2. CurveCartesian((sin(t)^(r) * d / 4), (cos(t) * d / 4) + d / 4, ((h * t / π) * d / 2), t, (-π), π) → a
  3. CurveCartesian((sin(t)^(0.1) * b / 4), (cos(t) * b / 4) + b / 4, ((h * t / π) * b / 2), t, (-π), π) → c
  4. Circle(A, 0.5, zAxis) → k
  5. Cylinder(k, 1.5) → i, i_2, i_3
  6. Surface(a, l, zAxis) → e
  7. Sequence(Rotate[e, i, zAxis], i, 0, (2 * π), (2 * π / n)) → l1
  8. Surface(c, 0 + l + l + l + l + l + l + l + l + l, zAxis) → j
  9. Element(l1, A1) → B1
  10. Element(l1, A2) → B2
  11. Element(l1, A3) → B3
  12. Element(l1, A4) → B4
  13. Element(l1, A5) → B5
  14. Element(l1, A6) → B6
  15. Element(l1, A7) → B7
  16. Element(l1, A8) → B8
  17. Element(l1, A9) → B9
  18. Element(l1, A10) → Surface(c, 0 + l + l + l + l + l + l + l + l + l, axeZ)
  19. Element(l1, A11) → B11
  20. Element(l1, A12) → B12
  21. Element(l1, A13) → B13
  22. Element(l1, A14) → B14
  23. Element(l1, A15) → B15
  24. Element(l1, A16) → B16
  25. Surface(c, (2 * π), zAxis) → g
  26. CurveCartesian((sin(t)^(10) * d / 4), (cos(t) * d / 4) + d / 4, ((h * t / π) * d / 2), t, (-π), π) → m
  27. Surface(m, (2 * π), zAxis) → o

AI Drawing Prompt Reference

Create a spinning top made of multiple 3D surfaces, including cylinders and parametric surfaces. Start by drawing a base circle, then plot two parametric curves to form the side and top of the top. Rotate these curves around the z-axis to generate multiple repeated geometric components. Finally, use colors and element operations to assemble these components into a complete spinning top.
The prompt above was compiled from the original drawing commands and is for reference only.