# 16,000 and a Square

I reached my 16,000th page view, sometime on Thursday. That’s a tiny bit slower than I projected based on May’s readership statistics, but May was a busy month and I’ve had a little less time to write stuff this month, so I’m not feeling bad about that.

Meanwhile, while looking for something else, I ran across a bit about mathematical notation in Florian Cajori’s A History of Mathematical Notation which has left me with a grin since. The book is very good about telling the stories of just what the title suggests. It’s a book well worth dipping into because everything you see written down is the result of a long process of experimentation and fiddling about to find the right balance of “expressing an idea clearly” and “expressing an idea concisely” and “expressing an idea so it’s not too hard to work with”.

The idea here is the square of a variable, which these days we’d normally write as $a^2$. According to Cajori (section 304), René Descartes “preferred the notation $aa$ to $a^2$.” Cajori notes that Carl Gauss had this same preference and defended it on the grounds that doubling the symbol didn’t take any more (or less) space than the superscript 2 did. Cajori lists other great mathematicians who preferred doubling the letter for squaring, including Christiaan Huygens, Edmond Halley, Leonhard Euler, and Isaac Newton. Among mathematicians who preferred $a^2$ were Blaise Pascal, David Gregory (who was big in infinite series), and Wilhelm Leibniz.

Well of course Newton and Leibniz would be on opposite sides of the $aa$ versus $a^2$ debate. How could the universe be sensible otherwise?

## Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

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