Tuesday, 25 August 2009

More About One Letter Math Words

I questioned Craig Conley for an oversight in missing the letter m for slope in my last blog, but I have to give him credit for catching an oversight of mine.

I write a lot about the history of math and math words and symbols, and I thought I pretty well knew the History of &pi, so I was a little surprised to see a note that he had that said that the first person to use a single symbol for the ratio of the circumference to diameter of a circle was J. Christoph Sturm, who used the letter e for the value 3.14159.. Sturm, was considered the leading experimental physicist in Germany of his time.

Cajori writes that "perhaps the earliest use of a single letter to represent the ratio of the length of a circle to its diameter" occurs in 1689 in Mathesis enucleata by J. Christoph Sturm, who used e for 3.14159....

si diameter alicuius circuli ponatur a, circumferentiam appellari posse ea (quaecumque enim inter eas fuerit ratio, illius nomen potest designari littera e).

Cajori cites a note by A. Krazer in Euleri opera omnia as a reference for the above.

The first known use of the symbol π for its present purposes was in 1706 by William Jones, an English mathematician, although it was the use of the symbol by Euler that brought it its permanency. Euler, of course, is the one who popularized the use of e for 2.71828..., the base of the natural logarithms.

I had earlier mistakenly thought that Euler was the discoverer of the value, but in fact the number was published in Edward Wright's English translation of Napier's work on logarithms in 1618, almost 100 years before Euler's birth. The number represented by e is approximately 2.718281828459045... Euler actually computed the number to eight more decimal places. This was done in 1727, and would seem almost impossible accuracy for anyone else, but of Euler it was said, "Euler calculates as other men breathe."

There has been lots of speculation about why he might have chosen e, since it is almost sure that is was not for his initial. My favorite supposition is that e is the first letter in the German for one, eins as he was studying the value of x for which the area under the hyperbolic curve y= 1/x from x=1 to this value would equal one. Well, that's my story and I'm sticking to it.
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