Intersection of Cone and Sphere

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2016-08-29 17:53

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 curve of a cone and a sphere. Key mathematical concepts include solid geometry, similar triangles, and tangents. Using GeoGebra commands such as Sequence and CurveCartesian, the intersection curve can be dynamically displayed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

LaTeX(c, false, false) → text7
LaTeX(b, false, false) → text8
Sequence(CurveCartesian[(i * sqrt(R^(2) - t^(2) - fy_z(t)^(2))), fy_z(t), t, t, -15, 15], i, -1, 1, 2) → l
CurveCartesian(x0, fy_z(t), t, t, -15, 15) → lx
Sequence(CurveCartesian[(i * sqrt(R^(2) - t^(2) - fy_z(t)^(2))), y0, t, t, -15, 15], i, -1, 1, 2) → ly
Sequence(CurveCartesian[(i * sqrt(R^(2) - t^(2) - fy_z(t)^(2))), fy_z(t), z0, t, -15, 15], i, -1, 1, 2) → lz
Textfield(x0) → InputBox1
Textfield(y0) → InputBox2
Textfield(z0) → InputBox3

AI Drawing Prompt Reference

Draw the intersection curve of a cone and a sphere. The sphere is centered at the origin with a fixed radius. The cone has its apex outside the sphere, with its axis vertical. The intersection consists of two symmetric closed spatial curves on the sphere's surface, one above and one below. Also show three auxiliary curves: a vertical line on the cone surface, a horizontal ring, and a horizontal circle on the sphere. Three adjustable numeric parameters control the cone apex's x, y, and z coordinates, dynamically changing the intersection shape. This illustrates the spatial intersection of a cone and a sphere in solid geometry.

The prompt above was compiled from the original drawing commands and is for reference only.