The Computation of π by Archimedes

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The Computation of π by Archimedes. Bill McKeeman Dartmouth College 2012.02.15. Abstract. - PowerPoint PPT Presentation

Transcript of The Computation of π by Archimedes

The Computation of by Archimedes

The Computation of by ArchimedesBill McKeemanDartmouth College2012.02.15AbstractIt is famously known that Archimedes approximatedby computing the perimeters of many-sided regular polygons, one polygon inside the circle and one outside. This presentation recapitulates Archimedes' computation, using MATLAB instead of hand, ink and papyrus. The surprise to me was how many "tweaks" Archimedes applied at various stages of an otherwise systematic approach.

follow along

MATLAB publication is a sort of self-checking paper. This URL takes you to the MATLAB version of the talk. Grey background is the MATLAB code; typeset material is MATLAB comments, everything else is MATLAB output. Earlier that 200BCE

Archimedes lived in Sicily, Euclid in Egypt, Pythagoras in Turkey and ItalyArchimedes did other things

Syracuse was often under attack. Archimedes invented weapons to defend his city. This iron ship-dumper may be a myth. Other weapons such as fireballs were not.When a Roman sneak attack finally conquered Syracuse, Archimedes was considered by the commanding general as the most important catch. Unfortunately a Roman soldier killed old Archimedes for not being instantly obedient. Too bad for the Roman soldier.RA polygon inside the circle and a polygon outside the circle.

The perimeters of the polygons bound the circumference of the circle which (by definition) is 2R.

The inner hexagon has perimeter 6R which implies 6R