Sphere and Cone Section Demonstration by Patrick Clément

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2015-11-01 22:04

In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve

This example demonstrates the intersection shapes formed by a sphere and a cone. It involves core mathematical concepts such as solid geometry, cross-section analysis, natural numbers, exponentiation, and vectors. Construction highlights include using commands like Sequence, Sphere, and RemoveUndefined, along with objects like r, c, z_0, x_0, y_0 in GeoGebra. Suitable for high school and above, helping students understand cross-section forms and parameter variations in solid and analytical geometry.

GeoGebra Commands & Parameters

Sequence(Point[e, i], i, 0, 1, 1 / n) → liste1
Sphere((x_0, y_0, z_0), r) → a
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
Sequence((x(Element[liste3, i]), y(Element[liste3, i]), g(x(Element[liste3, i]), y(Element[liste3, i]))), i, 1, Length[liste3]) → liste30