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Net of a Cone by Norm Prokup (2)

Net of a Cone by Norm Prokup (2)
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2017-11-08 13:11
Solid GeometryTransformationGeometric Construction
This example demonstrates the net of a cone, involving basic geometric concepts such as the base radius, slant height, and side unfolding. Using GeoGebra commands like CurveCartesian, Segment, Line, and Rotate, the process of unfolding the cone is visually illustrated. Suitable for middle and high school students studying solid geometry.

GeoGebra Commands & Parameters

  1. CurveCartesian(((4 * cos(t)) * sin(t)), 0, ((4 * cos(t)) * cos(t)), t, 0.01, (0.4 * π)) → a
  2. Segment(A, C) → f
  3. Line(A, C) → g
  4. Segment(C, B) → r
  5. Segment(B, D) → rr
  6. Rotate(B, (-θ), g) → B_2
  7. Rotate(B, θ, g) → B_1
  8. Vector(C, B) → u
  9. Rotate(u, 90°, g) → u'
  10. Surface(((1 - t) * x(A)) + (t * (x(C) + (x(u) * cos(s)) + (x(u') * sin(s)))), ((1 - t) * y(A)) + (t * (y(C) + (y(u) * cos(s)) + (y(u') * sin(s)))), ((1 - t) * z(A)) + (t * (z(C) + (z(u) * cos(s)) + (z(u') * sin(s)))), s, (-θ), θ, t, 0, 1) → b
  11. Segment(A, B_1) → h
  12. Segment(B_2, A) → i
  13. Circle(D, abs(B - D), Vector[D, A]) → c
  14. Angle(F, B, D) → α
  15. Rotate(c, (d * (π / 2 + β)), yAxis) → c'
  16. Rotate(D, (d * (π / 2 + β)), yAxis) → D'
  17. CurveCartesian(x(C) + (x(u) * cos(s)) + (x(u') * sin(s)), y(C) + (y(u) * cos(s)) + (y(u') * sin(s)), z(C) + (z(u) * cos(s)) + (z(u') * sin(s)), s, (-θ), θ) → e
  18. Vector(D, D - (sqrt(3), 0, 1)) → v
  19. Rotate(c, (d * (π / 2 + β)), yAxis) → c''