Exploring Inside the Torus
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This example demonstrates how to visualize the internal structure of a torus using parametric equations and 3D graphing techniques. Key math concepts include complex number operations, analytical geometry, parametric equations, and solid geometry. Construction highlights involve commands like Sequence for generating sequences, points A and B, image1 for image processing, R and r for defining torus size, n and p for parameters, and liste1 and liste2 for data storage. Suitable for high school and above learners to understand parametric surfaces and the application of complex numbers in 3D space.
GeoGebra Commands & Parameters
Sequence(Surface[((R - (r * cos(u))) * cos((p * u) + v)), ((R - (r * cos(u))) * sin((p * u) + v)), (r * sin(u)), u, 0, (2 * π), v, i + π / n, i + (2 * π / n)], i, 0, (2 * π), (2 * π / n)) → liste1Sequence(Surface[((R - (r * cos(u))) * cos((p * u) + v)), ((R - (r * cos(u))) * sin((p * u) + v)), (r * sin(u)), u, 0, (2 * π), v, i, i + π / n], i, 0, (2 * π), (2 * π / n)) → liste2