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Squares on Sphere

Squares on Sphere
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2020-05-19 01:39
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates squares on a sphere. It involves spherical geometry and the properties of squares. Using GeoGebra commands such as Join, Length, and Sphere, dynamic squares on a sphere can be constructed. Suitable for high school and above students to learn about spherical geometry and the properties of squares.

GeoGebra Commands & Parameters

  1. Join(Sequence[Sequence[(x(O) + ((cos(j° + b) * R) * sin(i)^(r)), y(O) + ((R * sin(j° + b)) * sin(i)^(r)), z(O) + (R * cos(i))), j, 0, 360, nn], i, tt, t, π / ((2 * n))]) → liste3
  2. Length(liste3) → dire
  3. Sphere(O, R - 0.01) → c
  4. Surface(x(O) + (((R - 0.081) * cos(i)) * cos(j)), y(O) + (((R - 0.081) * sin(i)) * cos(j)), z(O) + ((R - 0.081) * sin(j)), i, 0, 6.28319, j, 0.2, (2 * t)) → d
  5. Sequence(Polygon[Element[liste3, i], Element[liste3, i + 1], Element[liste3, i + 1 + e], Element[liste3, i + e]], i, 1, Length[liste3], h) → liste4
  6. Sequence(Prism[Element[liste4, i], p], i, 1, Length[liste4]) → l1

AI Drawing Prompt Reference

Draw a sphere and construct a series of squares on its surface. First, create a series of points that form the vertices of squares on the sphere. Then, connect these points to form squares and calculate their side lengths. Next, create a slightly smaller sphere as a background. Finally, use these squares to construct prisms, showing the arrangement of squares on the sphere.
The prompt above was compiled from the original drawing commands and is for reference only.