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Net of a Cone by Anthony OR 柯志明

Net of a Cone by Anthony OR 柯志明
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2014-12-30 17:26
CircleAngleFunctionSolid GeometryGeometric Construction
In collections Area, Surface Area, Volume, Cross Section, 3D 3D Geometry & Cross Sections Surface Area and Volume Geometry: Surface Area & Volume Geometry: Surface Area & Volume Geometry: Surface Area & Volume GA Chapter 11: Surface Area and Volume Nets of 3D Figures 立體圖形的摺紙圖樣 Nets of Solids Parametric Surfaces
This example demonstrates the net of a cone, illustrating how a three-dimensional cone unfolds into a two-dimensional sector. It involves core mathematical concepts such as solid geometry, angles, circles, functions, and transformations. The construction utilizes GeoGebra commands/objects like OrthogonalLine, Circle, Point, Intersect, Cone, Segment, Distance, Angle, Rotate, CircumcircleArc, Surface, and CurveCartesian. It is suitable for high school and above students learning about geometric properties and calculations related to cones.

GeoGebra Commands & Parameters

  1. OrthogonalLine((1, 0, 0), xOyPlane) → a
  2. Circle(a, (0, 0, 0)) → c
  3. Point(a) → A
  4. Intersect(xAxis, a) → B
  5. Cone(B, A, 1) → b, d, e
  6. Intersect(yAxis, xAxis) → C
  7. Segment(C, A) → l
  8. Distance(B, C) → r
  9. Angle(A, C, B) → α
  10. Rotate(A, (t * α), yAxis) → A'
  11. OrthogonalLine(A', xOyPlane) → f
  12. Intersect(f, xOyPlane) → B'
  13. Rotate(C, β / 2, f) → C'
  14. Rotate(C, ((-β)) / 2, f) → C'_1
  15. CircumcircleArc(C', C, C'_1) → g
  16. Distance(A', B') → h
  17. Distance(B', C') → r'
  18. Surface(((k - ((v * r') * cos((u * β / 2)))) * cos(ϕ)) - (((1 - v) * h) * sin(ϕ)), ((v * r') * sin((u * β / 2))), (((1 - v) * h) * cos(ϕ)) + ((k - ((v * r') * cos((u * β / 2)))) * sin(ϕ)), u, -1, 1, v, 0, 1) → j
  19. CurveCartesian(((k - (r' * cos((u * β / 2)))) * cos(ϕ)), (r' * sin((u * β / 2))), ((k - (r' * cos((u * β / 2)))) * sin(ϕ)), u, -1, 1) → m
  20. Segment(E, F) → n
  21. Segment(D, F) → p

AI Drawing Prompt Reference

Draw the net of a cone. First, create a cone. Then, unfold it into a sector. The sector's angle relates to the cone's slant height. Ensure the sector matches the cone's lateral surface. Construct by determining the cone's vertex, base circle, and slant line. Then calculate the sector's dimensions. Finally, compare the sector with the cone's lateral surface to verify correctness.
The prompt above was compiled from the original drawing commands and is for reference only.