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Surprising Annulus Area Result

Surprising Annulus Area Result
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2018-08-12 03:14
CircleFunctionOptimizationGeometric ConstructionSlider Animation
This example demonstrates the dynamic construction and surprising results of calculating the area of an annulus, involving core math concepts like circles, area calculation, linear functions, optimization problems, hyperbolas, and complex numbers. Key GeoGebra commands/objects used include Segment, Midpoint, OrthogonalLine, Point, Circle, and Angle for geometric construction. Suitable for high school and above learners to explore geometric optimization and function applications.

GeoGebra Commands & Parameters

  1. Segment(D, E) → f
  2. Midpoint(f) → H
  3. OrthogonalLine(H, f) → k
  4. Point(k) → P
  5. Circle(P, H) → p
  6. Circle(P, D) → q
  7. Segment(P, D) → l
  8. Segment(P, H) → m
  9. Segment(H, D) → n
  10. Angle(D, H, P) → β