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Net of a Cylinder by Anthony OR 柯志明

Net of a Cylinder by Anthony OR 柯志明
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2014-12-29 19:08
Solid Geometry
In collections 3D Geometry & Cross Sections Surface Area and Volume Nets of 3D Figures 立體圖形的摺紙圖樣 Parametric Surfaces
This example demonstrates the net of a cylinder. It involves the geometric construction and unfolding principle of a cylinder. Using GeoGebra commands such as Point, Circle, Cylinder, Intersect, Line, etc., the side unfolding process of the cylinder can be dynamically displayed. Suitable for students at junior high school level and above to learn solid geometry.

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, start by drawing two circles with their centers on the y-axis. Then, use these circles as the bases to form a cylinder. Next, unfold the cylinder along its axis to create a rectangle, where the two longer sides correspond to the circumferences of the two base circles, and the shorter side corresponds to the height of the cylinder. Finally, draw the circles and rectangle in the net, and mark the key points and segments.
The prompt above was compiled from the original drawing commands and is for reference only.