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Cylinder Area Paradox Demonstration

Cylinder Area Paradox Demonstration
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2015-06-16 00:34
Solid GeometryCalculusInequalityGeometric Construction
This example demonstrates the relationship and calculation process between the lateral surface area of a cylinder and the surface area of a sphere, involving core math concepts like cylinder lateral area, sphere surface area, inequalities, and rational numbers. It uses GeoGebra commands and objects such as Point, Line, Cylinder, Sequence, Rotate, Flatten, VerticalText. Suitable for high school students and math enthusiasts to understand solid geometry and calculus-related area calculations and paradox phenomena.

GeoGebra Commands & Parameters

  1. Point(zAxis) → D
  2. Line(D, V) → f
  3. Cylinder(D, V, 3) → a, c, d, b
  4. Sequence(Sequence[((3 * cos(((2 * π) * k / n))), (3 * sin(((2 * π) * k / n))), (5 * h / m)), k, 0, n], h, 0, m) → punti
  5. Rotate(punti, (180 * ° / n), f) → punti'
  6. Flatten(Sequence[Sequence[Polygon[Element[punti, h, k], Element[punti', h + 1, k], Element[punti, h, k + 1]], k, 1, n], h, 1, m]) → listaA
  7. Flatten(Sequence[Sequence[Polygon[Element[punti', h + 1, k], Element[punti, h, k + 1], Element[punti', h + 1, k + 1]], k, 1, n], h, 1, m]) → listaB
  8. VerticalText(text1) → text3
  9. VerticalText(text2) → text4