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Area Under Archimedes' Spiral

Area Under Archimedes' Spiral
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2016-02-11 23:42
FunctionCalculusIntegral
This example demonstrates how to calculate the area under Archimedes' spiral. It involves the concept of area in polar coordinates and basic calculus. Using GeoGebra commands such as Point, Intersect, Segment, Sequence, Circle, and CurveCartesian, the construction of Archimedes' spiral and the calculation of the area under it are shown. Suitable for high school mathematics education and calculus students.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. Segment(A, B) → a
  4. Sequence(Sector[Circle[B, (a * i / n)], ((2 * π) * (i - 1) / n), ((2 * π) * i / n)], i, 1, n) → list1
  5. Circle(B, a) → c
  6. CurveCartesian(((a / ((2 * π)) * t) * cos(t)), ((a / ((2 * π)) * t) * sin(t)), t, 0, 6.28319) → b