MathPlotAI Logo MathPlotAI

Annulus Area Dissection Demo

Annulus Area Dissection Demo
Loading the math board and drawing, please wait…
2019-08-14 04:04
CircleGeometric Construction
This example demonstrates the calculation of an annulus' area through geometric dissection. It involves core concepts like circle area, geometric partitioning, and polygon assembly. GeoGebra commands and objects used in construction include Midpoint, Sequence, Segment, and Angle. Suitable for high school mathematics education to understand the derivation of the annulus area formula and geometric intuition.

GeoGebra Commands & Parameters

  1. Midpoint(B, Rotate[B, (-2 * π / n)]) → E
  2. Sequence(Rotate[Segment[A, Rotate[A, (2 * π / n)]], ((2 * π) * k / n)], k, 1, n) → l1
  3. Sequence(Rotate[Segment[B, Rotate[B, (2 * π / n)]], ((2 * π) * k / n)], k, 1, n) → l2
  4. Sequence(Polygon[Rotate[A, ((2 * π) * k / n)], Rotate[E, ((2 * π) * k / n)], Rotate[B, ((2 * π) * k / n)], Rotate[D, ((2 * π) * k / n)]], k, 1, n) → l3
  5. Sequence(Rotate[Polygon[Rotate[E, ((-t) * π), E], Rotate[C, ((-t) * π), E], Rotate[B, ((-t) * π), E]], ((2 * π) * k / n)], k, 1, n) → l4
  6. Segment(O, A) → f
  7. Segment(A, B) → g
  8. Segment(O, B) → h
  9. Angle(B, A, O) → α