MathPlotAI Logo MathPlotAI

Cylinder Net by Mrs. Simon

Cylinder Net by Mrs. Simon
Loading the math board and drawing, please wait…
2018-02-12 10:34
CirclePolygonSolid GeometryGeometric Construction
This example demonstrates the process of unfolding a cylinder into a flat net, involving core math concepts like solid geometry, circles, polygons, angles, and vectors. It utilizes GeoGebra commands and objects such as Point, Circle, Cylinder, Intersect, Line, OrthogonalLine, Rotate, If, Segment as outlined in the construction summary. Ideal for high school students learning about solid geometry, helping them understand the principles and calculations behind cylinder surface展开.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(yAxis) → B
  3. Circle(A, B) → c
  4. Cylinder(c, 3) → b, e, f
  5. Intersect(zAxis, e) → C,
  6. Line(C, xAxis) → a
  7. OrthogonalLine(D, xOyPlane) → g
  8. Circle(g, C) → k
  9. Rotate(Rotate[e, ϕ, a], ϕ, xAxis) → e'
  10. Rotate(Rotate[e, ϕ, a], ϕ, xAxis) → d
  11. Circle(A, B) → h
  12. If(t < 1, ((r * sin((-θ))), ((r * (1 - cos((-θ)))) * cos(ϕ)) - (3 * sin(ϕ)), (3 * cos(ϕ)) + ((r * (1 - cos((-θ)))) * sin(ϕ))), ((-π), ((-3) * sin(ϕ)), (3 * cos(ϕ)))) → E
  13. If(t < 1, ((r * sin(θ)), ((r * (1 - cos(θ))) * cos(ϕ)) - (3 * sin(ϕ)), (3 * cos(ϕ)) + ((r * (1 - cos(θ))) * sin(ϕ))), (π, ((-3) * sin(ϕ)), (3 * cos(ϕ)))) → F
  14. If(t < 1, ((r * sin((-θ))), ((r * (1 - cos((-θ)))) * cos(ϕ)), ((r * (1 - cos((-θ)))) * sin(ϕ))), (-3.141592653589793, 0, 0)) → G
  15. If(t < 1, ((r * sin(θ)), ((r * (1 - cos(θ))) * cos(ϕ)), ((r * (1 - cos(θ))) * sin(ϕ))), (3.141592653589793, 0, 0)) → H
  16. Segment(E, G) → m
  17. Segment(F, H) → n
  18. Line((0, 1, 0), zAxis) → p
  19. Circle(p, B) → q
  20. Circle(p, B) → s
  21. If(t < 1, Surface[(r * sin((u * θ))), ((r * (1 - cos((u * θ)))) * cos(ϕ)) - (v * sin(ϕ)), (v * cos(ϕ)) + ((r * (1 - cos((u * θ)))) * sin(ϕ)), u, -1, 1, v, 0, 3], Surface[(π * u), ((-v) * sin(ϕ)), (v * cos(ϕ)), u, -1, 1, v, 0, 3]) → i
  22. If(t < 1, CurveCartesian[(r * sin((u * θ))), ((r * (1 - cos((u * θ)))) * cos(ϕ)), ((r * (1 - cos((u * θ)))) * sin(ϕ)), u, -1, 1], CurveCartesian[(π * u), 0, 0, u, -1, 1]) → l
  23. If(t < 1, CurveCartesian[(r * sin((u * θ))), ((r * (1 - cos((u * θ)))) * cos(ϕ)) - (3 * sin(ϕ)), (3 * cos(ϕ)) + ((r * (1 - cos((u * θ)))) * sin(ϕ)), u, -1, 1], CurveCartesian[(π * u), (-3 * sin(ϕ)), (3 * cos(ϕ)), u, -1, 1]) → j

AI Drawing Prompt Reference

Draw the net of a cylinder, showing how the cylinder unfolds into a flat shape. Start by drawing a circle, then create a cylinder using this circle as the base. Extract key points from the cylinder to draw the rectangular side and circular base of the unfolded shape, ensuring geometric accuracy. Finally, combine the unfolded parts to clearly illustrate the process of unfolding the cylinder.
The prompt above was compiled from the original drawing commands and is for reference only.