Monday Morning Math: 𝝅

Tomorrow, March 14, is 3/14 [in month/year form] and so we celebrate Pi Day!  And since I’m teaching History of Math for the first time in rather a lot of years, I’m thinking that the perfect topic is the history of the symbol.

But first, what is 𝝅?  The idea is that no matter how big or small a circle, the circumference is always a little more than 3 times as large as the diameter:  that ratio is about 3.14 in decimal terms.  Because it’s a ratio, the first symbols were also written as ratios:  William Oughtred called it 𝝅/δ in 1647, and while he didn’t explain what either of the terms meant, since 𝝅 is the Greek p it likely stood for periphery (according to my source, though I think of perimeter myself when I see it); likewise, δ is the Greek d and likely stood for diameter.  Several other mathematicians adopted this notation.

The first person to use a single symbol to represent this ratio was Johann Christoph Sturm, who in 1689 referred to it with the letter e.  Wait, what?  (Double check.)  Well that is something I didn’t know before.  Cool!  But using e didn’t catch on, and less than twenty years later, in 1706, William Jones used the symbol 𝝅 for this same ratio. No explanation as to why, and also no consistency – he used the same symbol to mean other things earlier in the same book.  This use of 𝝅 also didn’t catch on: other mathematicians continued to use other symbols for the ratio of a circumference to the diameter, and 𝝅 itself continued to be used for different mathematical numbers.  But eventually, over the 1700s, its use caught on and so we have the well known symbol today.

Source:  A History of Mathematical Notations by Florian Cajori

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