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Net of a Cone by Christopher Lim

Net of a Cone by Christopher Lim
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2018-07-10 08:58
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the net of a cone. It involves solid geometry and geometric construction. Using GeoGebra commands such as OrthogonalLine, Circle, Point, Intersect, etc., the net of a cone can be constructed. Suitable for middle school and above students or teachers.

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. Start by drawing a circle centered at the origin, then take a point on the circle as the cone's apex and another point as the center of the base circle. Rotate the apex and draw the corresponding line segments and arcs. Finally, construct the curved surface and straight segments of the net based on these elements.
The prompt above was compiled from the original drawing commands and is for reference only.