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Section of Sphere and Cone

Section of Sphere and Cone
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2020-03-29 16:01
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric construction of a sphere, a cone, and their sections. Key mathematical concepts include solid geometry and coordinate geometry. By using the Sequence command to generate a series of sections and the Sphere command to create the sphere, it illustrates how to construct complex geometric shapes using GeoGebra. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(Point[e, i], i, 0, 1, 1 / n) → liste1
  2. Sphere((x_0, y_0, z_0), r) → a
  3. RemoveUndefined(Sequence[If[(x(Element[liste1, i])^(2) * (1 + 1 / c^(2))) - ((2 * x_0) * x(Element[liste1, i])) + (y(Element[liste1, i])^(2) * (1 + 1 / c^(2))) - ((2 * y_0) * y(Element[liste1, i])) + x_0^(2) + y_0^(2) + z_0^(2) - r^(2) ≟ ((2 * z_0 / c) * sqrt(x(Element[liste1, i])^(2) + y(Element[liste1, i])^(2))), Element[liste1, i]], i, 1, n]) → liste3
  4. Sequence((x(Element[liste3, i]), y(Element[liste3, i]), g(x(Element[liste3, i]), y(Element[liste3, i]))), i, 1, Length[liste3]) → liste30