Euler's Constant (was: Re: Character for e, 2.71828...)

From: Kenneth Whistler (
Date: Mon Apr 08 2002 - 15:11:20 EDT

Elliotte Rusty Harold also asked:

> While hunting down the candidates I noticed that 0x2107, a Latin
> capital letter open E, is named the "EULER CONSTANT". However a quick
> Google search seems to indicate that the Euler constant is
> 0.577215... generated from a different series and is normally
> represented with a lower case gamma, not an e of any kind. Is this a
> mistake in the Unicode data?

Well, conceivably the name is a misnomer. The source for this
character is XCCS 353/046 "Euler's". That Xerox standard didn't
say Euler's *what*, however. And the character committees just
added "CONSTANT" to it. If it represents an old, possibly German
usage for the particular constant more commonly known as
"Euler's Number", i.e., the base for natural logarithms, then
I can see why people might get confused between that and 'e'.

But this is another illustration of why encoding *constants* in
Unicode would be wrong -- as opposed to encoding characters which
may be used to represent constants.

You should have done a longer Google search.

"The Euler-Mascheroni constant is denoted <ital>gamma</ital> (or
sometimes <ital>C</ital> and has the numerical value..."

So here we have gamma or 'C' (both italic, of course, as is
usual for math) representing the Euler-Mascheroni constant.

And we have 'e' or italic e or double-struck italic e or a
probable old blackletter epsilon all representing Euler's Number.
(And I've also seen 'E', since 'e' may follow capitalization
rules when put in lists of constants.)

So Unicode just encodes a bunch of characters. And mathematical
and physical constants may get referred to by any number of
different characters, depending on typographical usage and
orthographical traditions. There is no close one-to-one
relationship here, nor should there be.


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