Comments on: Need a definite answer for approximately equal

Question: Need a definite answer for approximately equal

font_snob — Thu, 28 Aug 2008 11:14:16 -0800

Here's the deal: I've exhausted my neurons looking for some kind of answer to a mathematical symbol stumper. I'd love to know who invented, originated, or was the first individual to use the double-tilde (≈) as a means of expressing/denoting "approximately equal" in mathematics. I know that Robert-Recorde is supposed to have introduced the "equals" sign (=) in 1557. Any and all assistance is greatly appreciated. I await enlightenment.

By: wittgenstein

wittgenstein — Thu, 28 Aug 2008 12:05:13 -0800

I have a copy of this book at home. I will check later to see if it is mentioned.

By: jedicus

jedicus — Thu, 28 Aug 2008 12:13:02 -0800

The use of the single tilde for geometrical similarity and the tilde & horizontal line for congruence is due to Leibniz (See also here).

But for a more definitive answer, A History of Mathematical Notations by Florian Cajori says that Greenhill first used the parallel wavy lines in 1892 (Google Books link; hopefully it works for others). You can see the Greenhill work via Google Books. The citations given in Cajori are correct, though Greenhill does not explain his notation that I can see, so he may not have actually been the first.

By: wavering

wavering — Thu, 28 Aug 2008 13:16:14 -0800

I haven't found approximation yet in this list but its long and covers a lot.

There are some references to the first uses of the word approximation, so that may lead you down the correct path.

By: languagehat

languagehat — Thu, 28 Aug 2008 13:48:44 -0800

Greenhill first used the parallel wavy lines in 1892

Except that those are not wavy lines, they're jagged; check out page 303 (near the bottom). Interesting question!

By: wittgenstein

wittgenstein — Fri, 29 Aug 2008 09:12:52 -0800

oops; Beaten to it!