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Archimedian Approximation of Pi

Archimedian Approximation of Pi
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2020-03-11 21:45
CirclePolygonTrigonometryCalculusGeometric Construction
This example demonstrates Archimedes' method of approximating pi by inscribing and circumscribing polygons around a circle. Key math concepts include circles, polygons, area calculations, and the concept of limits. GeoGebra commands used in construction are Circle, Intersect, Sequence, Polygon, Zip, and Segment. Suitable for high school and above students to understand the limit concept and the calculation of pi.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 1) → c
  2. Intersect(c, xAxis, 2) → A
  3. Sequence(Rotate[A, ((2 * π / n) * ii)], ii, 1, n) → l1
  4. Polygon(l1) → inpoly
  5. Zip(Tangent[AA, c], AA, l1) → l2
  6. Zip(Intersect[ll, pp], ll, l2, pp, Join[{Last[l2, n - 1], First[l2]}]) → l3
  7. Polygon(l3) → outpoly
  8. Segment((0, 0), A) → f

AI Drawing Prompt Reference

Draw a circle and inscribe and circumscribe polygons around it to demonstrate Archimedes' method of approximating pi. Rotate a line segment from the center to the circle's edge to generate vertices for the inscribed polygon, connect the vertices. For the circumscribed polygon, draw tangents from the vertices to the circle and connect the intersection points. Display the relationship between the inscribed and circumscribed polygons and the circle.
The prompt above was compiled from the original drawing commands and is for reference only.