3 (Position 288165) #pi

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Leonardo Pisano (c.1170–after 1240), dubbed ‘Fibonacci’, thought that Archimedes' proof that π was between $3\frac{10}{71}$ and $3\frac{1}{7}$ was beautiful [pulcra].

Archimedes' proof proceeds by calculating approximate ratios of the perimeters of 96-gons circumscribed about and inscribed in a circle to the diameter of that circle, implicitly starting with dodecagons and repeatedly bisecting edges to obtain 24-, 48-, and then 96-gons (see attached image).

Fibonacci’s judgement seems to be the earliest extant description of a *proof* as beautiful in the European tradition. [Al-Nasawī (fl. 1029–44) had earlier described a proof as beautiful.]

But there is a twist in the story...

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#MathematicalBeauty #BeautifulProof #HistMath #Fibonacci #Archimedes #Pi

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Happy #pi-day! i shall go to sleep.

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