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Sixth Egg Shape Surface

Sixth Egg Shape Surface
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2020-04-12 16:11
Coordinate GeometryParametric Equation
In collections Eggs
This example demonstrates the construction of the sixth egg shape surface. It involves the geometric properties of ellipses and circles. Using commands like Circle, Sphere, Sequence, and Surface, the shape and size of the surface can be dynamically adjusted. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. Circle(O, R, xOyPlane) → c
  2. Sphere(O, R - 0.05) → d
  3. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) + ((R + h) * sin(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, π, π / n) → liste1
  4. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) - ((R + h) * sin(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, π, π / n) → liste2
  5. Sequence(CurveCartesian[x(O) + (R * sin(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) + (((R + h) * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, π, π / n) → liste4
  6. Sequence(CurveCartesian[x(O) - (R * sin(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) + (((R + h) * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, π, π / n) → liste5
  7. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) + (R * sin(i - (π / ((2 * n)) * ff((m * t))))), z(O) + (((R + h) * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, π, π / n) → liste6
  8. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) - (R * sin(i - (π / ((2 * n)) * ff((m * t))))), z(O) + (((R + h) * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, π, π / n) → liste7
  9. Surface(x(O) + ((R * cos(i)) * cos(j)), y(O) + ((R * cos(i)) * sin(j)), z(O) + ((R + h) * sin(i)), i, 0, (2 * π), j, 0, (2 * π)) → e

AI Drawing Prompt Reference

Draw a sixth egg shape surface by first creating a circle centered at the origin, then drawing a slightly smaller sphere, and using a series of parametric curves to generate the surface parts, finally using a parametric surface command to create the entire sixth egg shape surface.
The prompt above was compiled from the original drawing commands and is for reference only.