MathPlotAI Logo MathPlotAI

Truncated Cone Created from Revolution

Truncated Cone Created from Revolution
Loading the math board and drawing, please wait…
2013-06-11 01:22
VectorSolid GeometryGeometric Construction
This example demonstrates how to create a truncated cone through revolution. Key mathematical concepts include cones, geometric construction, and solid geometry. It utilizes commands such as Vector, Polygon, Sequence, and CurveCartesian in GeoGebra. Suitable for high school geometry and solid geometry lessons.

GeoGebra Commands & Parameters

  1. Vector(1.1 * d * W_x) → u
  2. Vector(1.1 * d * W_y) → v
  3. Vector(1.1 * d * W_z) → w
  4. 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
  5. Sequence(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y + h * W_z, i, 0, p) → list3
  6. Sequence((r + 1.5) * cos(0.125 * i) * W_x + (r + 1.5) * sin(0.125 * i) * W_y, i, 0, p) → list1
  7. Sequence(Segment[Element[list1, i], Element[list3, i]], i, 1, p + 1) → list4
  8. Sequence(Segment[(0, 0), Element[list1, i]], i, 1, p + 1) → list2
  9. CurveCartesian(x((r + 1.5) * cos(0.125 * i) * W_x + (r + 1.5) * sin(0.125 * i) * W_y), y((r + 1.5) * cos(0.125 * i) * W_x + (r + 1.5) * sin(0.125 * i) * W_y), i, 0, p) → e_1
  10. Sequence(Segment[(0, 0) + h * W_z, Element[list3, i]], i, 1, p + 1) → list5
  11. CurveCartesian(x(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y + h * W_z), y(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y + h * W_z), i, 0, p) → h_1

AI Drawing Prompt Reference

Draw a truncated cone by first creating three direction vectors u, v, and w, then forming a quadrilateral as the base using these vectors. Next, generate a series of arcs through rotation to form the side surface of the truncated cone. Finally, connect the apex to the arcs of the base to complete the truncated cone.
The prompt above was compiled from the original drawing commands and is for reference only.