Superegg

Loading the math board and drawing, please wait…

2015-07-21 22:48

In collections surface 3D surface 3D

This example demonstrates the construction of a superegg, a shape that combines the properties of an ellipse and a circle. By adjusting parameters, various shapes can be generated. The construction uses commands like If, Surface, and Sequence, suitable for high school mathematics education.

GeoGebra Commands & Parameters

If(n ≟ (2 * floor(n / 2)) + 1, V, 0) → VV
Surface((v * cos(u)), (v * sin(u)), (b * (1 - sqrt((((v * cos(u)))^(2) + ((v * sin(u)))^(2)) / a^(2))^(n))^(1 / n)), u, 0, U, v, 0, a + VV) → c
Surface((v * cos(u)), (v * sin(u)), ((-b) * (1 - sqrt((((v * cos(u)))^(2) + ((v * sin(u)))^(2)) / a^(2))^(n))^(1 / n)), u, 0, U, v, 0, a + VV) → d
Surface((v * cos(u)), (v * sin(u)), (b * (1 - sqrt((((v * cos(u)))^(2) + ((v * sin(u)))^(2)) / a^(2))^(n))^(1 / n)), u, 0.01, U, v, 0, a + VV) → f
Surface((v * cos(u)), (v * sin(u)), ((-b) * (1 - sqrt((((v * cos(u)))^(2) + ((v * sin(u)))^(2)) / a^(2))^(n))^(1 / n)), u, 0, U, v, 0.01, a + VV) → g
Sequence(CurveCartesian[(v * cos(u)), (v * sin(u)), (b * (1 - sqrt((((v * cos(u)))^(2) + ((v * sin(u)))^(2)) / a^(2))^(n))^(1 / n)), v, 0, a + VV], u, 0, U, U / nbl) → liste1
Sequence(CurveCartesian[(v * cos(u)), (v * sin(u)), (b * (1 - sqrt((((v * cos(u)))^(2) + ((v * sin(u)))^(2)) / a^(2))^(n))^(1 / n)), u, 0, U], v, 0, a + VV, ((a + VV) * 2 / nbl)) → liste2
Surface(((a * cos(u)) * cos(v)), ((a * sin(u)) * cos(v)), (a * sin(v)), u, 0, 6.28319, v, -1.5708, 0) → desp

AI Drawing Prompt Reference

Draw a superegg, which combines the properties of an ellipse and a circle. Start by defining a parameter n, then use the Surface command to draw the upper and lower parts, adjusting n changes the shape. Next, use the Sequence command to generate a series of curves, and finally, draw the base.

The prompt above was compiled from the original drawing commands and is for reference only.