Net of a Cylinder by Norm Prokup

Net of a Cylinder by Norm Prokup
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2017-11-01 06:35
① This GeoGebra example dynamically demonstrates the unfolding of a cylinder's surface into a plane net, showing how the lateral surface becomes a rectangle and the top/bottom bases become circles. ② Core mathematical concepts include solid geometry of cylinders, nets, surface area calculation, and basic geometric elements such as circles, rectangles, and coordinate transformations. ③ Construction highlights: using GeoGebra commands like Line, Surface, Circle, Rotate, and CurveCartesian to build the cylinder and its unfolding process, involving objects such as height h, base radius g, rotation angle θ_max, a button (button1) to control animation, and auxiliary points (O, O_1, O_2) and curves (f, a, v, c, d, etc.) to achieve dynamic rotation and curve drawing. ④ Suitable for middle and high school geometry classes, this resource helps students understand the derivation of the cylinder's surface area formula and supports exploratory learning in mathematics labs.

GeoGebra Commands & Parameters

  1. Line((0, 0, h), Vector[(0, 1, 0)]) → g
  2. Line(O_2, Q) → f
  3. Surface(x(Q) - (tanT * cos(u)), y(Q) + (tanT * sin(u)), z(Q) + z, u, (-θ_{max}), θ_{max}, z, 0, h) → a
  4. Circle((1, 0, h), (0, 0, h), v) → c
  5. Circle((1, 0, 0), (0, 0, 0), v) → d
  6. Rotate(c, (-2 * T) + π / 2, g) → c'
  7. Line((0, 0, 0), Vector[(0, 1, 0)]) → g_1
  8. Rotate(d, (2 * T) - π / 2, g_1) → d'
  9. CurveCartesian(x(Q) - (tanT * cos(θ_{max})), y(Q) + (tanT * sin(θ_{max})), z(Q) + z, z, 0, h) → b
  10. CurveCartesian(x(Q) - (tanT * cos((-θ_{max}))), y(Q) + (tanT * sin((-θ_{max}))), z(Q) + z, z, 0, h) → b_1
  11. CurveCartesian(x(Q) - (tanT * cos(u)), y(Q) + (tanT * sin(u)), z(Q), u, (-θ_{max}), θ_{max}) → e
  12. CurveCartesian(x(Q) - (tanT * cos(u)), y(Q) + (tanT * sin(u)), z(O_2), u, (-θ_{max}), θ_{max}) → e_1
  13. Rotate((1, 0, h), (-2 * T) + π / 2, g) → O_1
  14. Rotate((1, 0, 0), (2 * T) - π / 2, g_1) → O