3D Spirals Sequence and Parametric Surfaces
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① This example demonstrates generating multiple 3D spiral curves using the Sequence command, potentially combined with parametric surfaces to visualize helical structures in space. ② Core mathematical concepts include parametric curves, 3D spiral motion, sequence generation, and connections to surfaces, perimeter, rectangles, cubes, as well as binomial distribution and exponent. ③ Construction highlights: using GeoGebra's Sequence command with parameters n, k, Tmax, V, d, h to create a list (liste1), and a text object (texte1) for dynamic display; involves parametric curves, surfaces, rectangles, and cubes. ④ Suitable for high school to undergraduate mathematics education, helping students intuitively understand 3D parametric equations, iterative sequences, and interdisciplinary links between geometry and probability, ideal for math labs or inquiry-based learning.
GeoGebra Commands & Parameters
Sequence(Surface[((((t * cos(t)) * cos(i)) - ((sin(i) * t) * sin(t))) * (1 - v)) + (v * ((((t - d) * cos(t - d)) * cos(i + (2 * π / n))) - ((sin(i + (2 * π / n)) * (t - d)) * sin(t - d)))), ((((t * cos(t)) * sin(i)) + ((cos(i) * t) * sin(t))) * (1 - v)) + (v * ((((t - d) * cos(t - d)) * sin(i + (2 * π / n))) + ((cos(i + (2 * π / n)) * (t - d)) * sin(t - d)))), (h * (Tmax - t)) + ((t * k / 2) * sqrt(1 - ((2 * v) - 1)^(2))), v, 0, V, t, d, Tmax], i, 0, ((2 * π) * (1 - 1 / n)), (2 * π / n)) → liste1