Sections of Cones by Anthony OR 柯志明

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2014-11-04 00:25

In collections Area, Surface Area, Volume, Cross Section, 3D 3D Geometry & Cross Sections Geometry - Areas and Volumes Sections of 3D Shapes Cross sections Cross Sections

This example demonstrates different sections of a cone using GeoGebra, highlighting geometric and calculus concepts. Key mathematical ideas include solid geometry, coordinate geometry, and integral calculus. Construction involves commands like Polygon, PointIn, Translate, Rotate, Cone, Plane, IntersectPath, and others. Suitable for high school students or college freshmen learning geometry and calculus fundamentals.

GeoGebra Commands & Parameters

Polygon(B + (-2, -2), B + (2, -2), B + (2, 2), B + (-2, 2)) → poly3, e, f, g, i
PointIn(poly3) → C
Translate((0, 0, 0), Vector[B, C]) → A
Polygon(A + (-4, -4), A + (4, -4), A + (4, 4), A + (-4, 4)) → poly1, a, b, c, d
Rotate(Rotate[Translate[poly1, Vector[A, A + (0, 0, h)]], (90° * s), A + (0, 0, h), yAxis], (90° * t), A, zAxis) → poly2
Rotate(D, 120°, (0, 0, 0)) → E
Cone((0, 0, 0), (0, 0, 4), 2) → m, e_1, o
Polygon(D, E, 3, xOyPlane) → poly4, j, k, l, F
PointIn(poly2) → G
PointIn(poly2) → H
PointIn(poly2) → I
Plane(G, I, H) → n
IntersectPath(n, m) → poly6
OrthogonalLine(A, n) → d_1
Ends(m) → g_1, g_1_1

AI Drawing Prompt Reference

Draw a geometric figure formed by the intersection of a cone and a plane. The cone has its vertex at the origin, a base radius of 2, and a height of 4. The plane intersects the cone's side and base, creating a cross-section. The figure includes the cone, the plane, the intersecting path, and related points. The construction order starts with the cone, then the plane, and finally the intersecting section.

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