Spherical Stack of Prisms: Visualizing 3D Geometry and Differential Equations
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① This example demonstrates how a series of prisms are stacked along a spherical direction, forming a spherical-like structure composed of multiple prisms, offering an intuitive visualization of geometric stacking in 3D space. ② Core mathematical concepts include prisms, spheres, right triangles, polygons, inequalities, and differential equations, bridging solid geometry and calculus. ③ Construction highlights: using GeoGebra commands such as Join, Sequence, Intersect, Sphere, and Surface, combined with sliders (Speed, b) and buttons (Bouton1, Bouton2) to control parameters, and objects like a, h, d, n, R, O to build the dynamic model, with auxiliary objects l1, l2, l3, l4 for precise geometric construction. ④ Suitable for high school to university-level mathematics education, especially for teaching solid geometry, introductory calculus, and dynamic mathematical experiments, helping students understand 3D structure generation and parametric modeling.
GeoGebra Commands & Parameters
Join(Sequence[Sequence[(x(O) + ((R * cos(t)) * sin(s)), y(O) + ((R * sin(t)) * sin(s)), z(O) + (R * cos(s))), t, 0, 6.28319, (2 * π / n)], s, 0, 6.28319, (2 * π / n)]) → l1Sequence(Polygon[Element[l1, i], Element[l1, i + 1], Element[l1, i + 1 + d], Element[l1, i + d]], i, 1, Length[l1], h) → l2Sequence(Prism[Element[l2, i], 1], i, 1, Length[l2]) → l3Intersect(xAxis, yAxis) → O_1Sphere(O, R) → bSurface(x(O) + ((R * cos(k)) * cos(j)), y(O) + ((R * cos(k)) * sin(j)), z(O) + (R * sin(k)), k, 0, (2 * π), j, 0, (2 * π)) → eSequence(Prism[Element[l2, i], 1], i, 1, Length[l2]) → l4