Crossed Torus
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This example demonstrates the geometric construction and dynamic variation of a crossed torus (Tore Croisé). It involves core mathematical concepts such as parametric equations, symmetry, stochastic processes, and the application of bar charts in geometry. The construction utilizes GeoGebra's Sequence command combined with list objects (listeb, listea) and variables (a, b) for parametric control. Suitable for high school and above mathematics learners to understand the parametric representation and dynamic demonstration of spatial geometric bodies.
GeoGebra Commands & Parameters
Sequence(CurveCartesian[cos(u + v) / (sqrt(2) + cos(v - u)), sin(u + v) / (sqrt(2) + cos(v - u)), sin(v - u) / (sqrt(2) + cos(v - u)), v, 0, 6.283185307179586], u, 0, 3.141592653589793, π / n) → listebSequence(CurveCartesian[cos(u + v) / (sqrt(2) + cos(v - u)), sin(u + v) / (sqrt(2) + cos(v - u)), sin(v - u) / (sqrt(2) + cos(v - u)), u, 0, 3.141592653589793], v, 0, 6.28319, π / n) → listea
AI Drawing Prompt Reference
Create a 3D parametric surface of a crossed torus. The surface is formed by two families of intertwined curves: one set runs along one direction of the torus, the other set runs perpendicularly, crossing each other to form a grid-like structure. The shape is based on trigonometric parametric equations, exhibiting a symmetric toroidal form with periodic undulations. Use dynamic parameters to control the density of the curves, allowing the grid spacing to vary. The graphic should highlight the crossed, intertwined nature of the torus and show how parameter changes affect the surface morphology.
The prompt above was compiled from the original drawing commands and is for reference only.