Quadriken: Geometric Transformation and Optimization

Loading the math board and drawing, please wait…

2022-12-13 19:24

In collections intersection: surface-surface, curve-curve

Quadriken is a mathematical example demonstrating geometric transformations and optimization. It uses GeoGebra commands to construct a three-dimensional figure, illustrating concepts like similarity and linear optimization. The construction involves commands such as Surface and objects like a, b, c, u, v, w, along with transformation parameters gl1, gl2, gl3. This example is suitable for high school students or college students learning about geometric transformations and optimization problems.

GeoGebra Commands & Parameters

Surface(((sqrt(abs(w + a)) * sin(s)) * cos(t)), ((sqrt(abs(w + b)) * sin(s)) * sin(t)), (sqrt(abs(w + c)) * cos(s)), s, 0, pi, t, 0, (2 * pi)) → O_3
Surface(((-sqrt(abs(u + a))) * s), ((sqrt(abs(u + b)) * sqrt(s^(2) - 1)) * cos(t)), ((sqrt(abs(u + c)) * sqrt(s^(2) - 1)) * sin(t)), s, (-pi), pi, t, 0, (2 * pi)) → O_1
Surface(((sqrt(abs(v + a)) * cosh(s)) * cos(t)), ((sqrt(abs(v + b)) * cosh(s)) * sin(t)), (sqrt(abs(v + c)) * sinh(s)), s, (-pi), pi, t, 0, (2 * pi)) → O_2

AI Drawing Prompt Reference

Create a 3D figure with three surfaces O_1, O_2, and O_3, controlled by parameters w, u, and v. O_1 is a rotational surface, O_2 is a hyperbolic surface, and O_3 is an ellipsoid. Use parameters a, b, and c to demonstrate similarity and linear optimization through transformations gl1, gl2, and gl3.

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