MathPlotAI Logo MathPlotAI

Granville Egg Parametric Curve Demo

Granville Egg Parametric Curve Demo
Loading the math board and drawing, please wait…
2016-02-08 06:54
PolygonFunctionParametric Equation
In collections surface 3D surface 3D
This example demonstrates how to draw complex curves using parametric equations, involving core mathematical concepts such as parametric curves, polygons, exponent functions, linear functions, and line segments. Construction highlights include the use of GeoGebra's If and Surface commands, along with objects e, m, a, b, r, d, m3, m2, m7, m6, m5, m4, U, oe2, oe3, oe4, oe5, oe6, oe7, oe1, op. Suitable for high school and above students to explore the applications of parametric equations.

GeoGebra Commands & Parameters

  1. If(m < 1, 0, If[m < 2, (e * (m - 1)), e]) → m3
  2. If(m < 1, (e * m), e) → m2
  3. If(m < 5, 0, If[m < 6, (e * (m - 5)), e]) → m7
  4. If(m < 4, 0, If[m < 5, (e * (m - 4)), e]) → m6
  5. If(m < 3, 0, If[m < 4, (e * (m - 3)), e]) → m5
  6. If(m < 2, 0, If[m < 3, (e * (m - 2)), e]) → m4
  7. Surface((((a * (r + d)) * sin(t)) * cos(u) / (b + ((r + d) * cos(t)))), (((a * (r + d)) * sin(t)) * sin(u) / (b + ((r + d) * cos(t)))), ((r + d) * cos(t)), t, m7, π, u, (-π), U) → oe2
  8. Surface((((a * (r + (2 * d))) * sin(t)) * cos(u) / (b + ((r + (2 * d)) * cos(t)))), (((a * (r + (2 * d))) * sin(t)) * sin(u) / (b + ((r + (2 * d)) * cos(t)))), ((r + (2 * d)) * cos(t)), t, m6, π, u, (-π), U) → oe3
  9. Surface((((a * (r + (3 * d))) * sin(t)) * cos(u) / (b + ((r + (3 * d)) * cos(t)))), (((a * (r + (3 * d))) * sin(t)) * sin(u) / (b + ((r + (3 * d)) * cos(t)))), ((r + (3 * d)) * cos(t)), t, m5, π, u, (-π), U) → oe4
  10. Surface((((a * (r + (4 * d))) * sin(t)) * cos(u) / (b + ((r + (4 * d)) * cos(t)))), (((a * (r + (4 * d))) * sin(t)) * sin(u) / (b + ((r + (4 * d)) * cos(t)))), ((r + (4 * d)) * cos(t)), t, m4, π, u, (-π), U) → oe5
  11. Surface((((a * (r + (5 * d))) * sin(t)) * cos(u) / (b + ((r + (5 * d)) * cos(t)))), (((a * (r + (5 * d))) * sin(t)) * sin(u) / (b + ((r + (5 * d)) * cos(t)))), ((r + (5 * d)) * cos(t)), t, m3, π, u, (-π), U) → oe6
  12. Surface((((a * (r + (6 * d))) * sin(t)) * cos(u) / (b + ((r + (6 * d)) * cos(t)))), (((a * (r + (6 * d))) * sin(t)) * sin(u) / (b + ((r + (6 * d)) * cos(t)))), ((r + (6 * d)) * cos(t)), t, m2, π, u, (-π), U) → oe7
  13. Surface((((a * r) * sin(t)) * cos(u) / (b + (r * cos(t)))), (((a * r) * sin(t)) * sin(u) / (b + (r * cos(t)))), (r * cos(t)), t, 0, π, u, (-π), π) → oe1