Geometric Curiosities on a Sphere
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This example demonstrates geometric shapes on a sphere, particularly isosceles triangles. By adjusting parameters, one can observe the changes in isosceles triangles on the sphere. The core mathematical concepts include spherical geometry and triangles. The construction uses Surface and CurveCartesian commands. Suitable for high school and above students to learn about spherical geometry and triangle-related knowledge.
GeoGebra Commands & Parameters
Surface((cos(u) * sin(v)), (sin(u) * sin(v)), cos(v), u, 0, (2 * π), v, 0, (2 * π)) → aSurface(a(t, cos(t) + k), k, n, n + 1, t, 0, (2 * π)) → cCurveCartesian(a(t, cos(t) + n), t, 0, (2 * π)) → bCurveCartesian(a(t, cos(t) + n + 1), t, 0, (2 * π)) → d