Cone & Cylinder from Revolution by Panayiotis Panayiotou

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2013-06-11 01:13

This example demonstrates the creation of solids of revolution, specifically cones and cylinders, by rotating 2D shapes. Key math concepts include solids of revolution, integral calculus, and spatial geometry. GeoGebra commands used in construction are Vector, Polygon, Sequence, and CurveCartesian. Suitable for high school students and above learning solid geometry and calculus, or for educational purposes.

GeoGebra Commands & Parameters

Vector(1.1 * d * W_x) → u
Vector(1.1 * d * W_y) → v
Vector(1.1 * d * W_z) → w
Polygon(1.1 * d * (W_x + W_y), 1.1 * d * (-W_x + W_y), 1.1 * d * (-W_x - W_y), 1.1 * d * (W_x - W_y)) → poly1, g, i, j, l
Sequence(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y, i, 0, p) → list1
Sequence(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y + k * W_z, i, 0, p) → list3
CurveCartesian(x(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y), y(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y), i, 0, p) → e_1
CurveCartesian(x(r * cos(0.125 * t) * W_x + r * sin(0.125 * t) * W_y + k * W_z), y(r * cos(0.125 * t) * W_x + r * sin(0.125 * t) * W_y + k * W_z), t, 0, p) → e_2
Sequence(Segment[A, Element[list1, i]], i, 1, p + 1) → list2
Sequence(Segment[Element[list1, i], Element[list3, i]], i, 1, p + 1) → list4
Sequence(Segment[(0, 0) + k * W_z, Element[list3, i]], i, 1, p + 1) → list5

AI Drawing Prompt Reference

Draw a cone and a cylinder by first creating three vectors u, v, and w, then constructing a quadrilateral with these vectors. Next, rotate this quadrilateral to generate the outlines of the cone and cylinder, and finally use these outlines to create the surfaces of the cone and cylinder.

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