Pi - Ximera

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We think about a common ratio.

After discussing our Great Theorem, Dunham goes on to other works of Archimedes that could equally well have been chosen as the highlight of the chapter. We have already seen Archimedes’ famous approximation of $\pi$ , which we still sometimes use today. But Archimedes isn’t quite finished with this constant, and neither are mathematicians. Our second reading will be a history of this constant throughout history. People are still studying $\pi$ today! For more information about modern estimations of $\pi$ , see the third reading. The optional fourth reading has more detail than the second one.

In case you are curious: as of June 2022, the record for digits of $\pi$ computed is 100 trillion. Look up “Chronology of computation of $\pi$ ” on Wikipedia (and its linked sources) for an overview.

Readings

First reading: Dunham, Chapter 4, pages 99 - 112

Second reading: A History of Pi

Third reading: Pi in the Sky: Calculating a record-breaking 31.4 trillion digits of Archimedes’ constant on Google Cloud

Questions

How many days (start-to-end time) did the calculation of 31.4 trillion digits of $\pi$ take? $\answer [given]{121.1}$ days

Which of the following had the most accurate estimation for $\pi$ ?

Archimedes Ptolemy Zu Chongzhi al-Khwarizmi