Am 18.05.2016 um 23:51 schrieb Anthony D. Baye:
> Because I know you're both a camera guy and a math guy.
> 
> I was perusing this site:
> http://davetrott.com/inventions/double-arm-barn-door-drive/
> 
> and came across a funny (read: strange) computation: 3 + 2**1/3 which google
> tells me is the same as 3 + 2^(1/3), except that the website (referencing a
> magazine article from almost 30 years ago) says is equal to 6.464, which is
> blatantly wrong unless they're doing something completely different with that
> double asterisk.

Neither the double asterisk (**) nor the caret (^) are mathematical
symbols (well, at least not in this context); they are merely
ASCII-conformant kludges to write mathematical formulae for which ASCII
lacks proper necessary symbols, and different "schools" exist.

The school currently dominant in prose texts uses the caret to denote
superscript in general, or exponentiation in particular, with x^y
therefore denoting "x raised to the y-th power" (e.g. x^2 denoting "x
squared").

This is quite independent of the use in computer languages: While some
do use the caret as an exponentiation operator, others use it for a
bitwise-or. Most notably, all the old-school programming languages like
Ada, COBOL and FORTRAN used the double asterisk instead.

Thus there is indeed reason to assume that the 30 year-old expression "3
+ 2**1/3" is meant to denote "3 plus the one-third power of 2" or, in
other words, "3 plus the cubic root of 2". This is far from certain
though; most notably, in virtually all programming languages that use
the double-asterisk notation for exponentiation, the expression would be
interpreted as "3+((2**1)/3)", which doesn't make much sense because the
exponentiation would be redundant.

Another thing that really doesn't fit is that this expression seems to
be related to straightforward geometry, and you rarely get a cubic root
there; what you usually get is plenty of square roots.

As a matter of fact, the alleged result, 6.464, happens to be
suspiciously close to 3+2*sqrt(3), or 3+2*3**(1/2), which has all of the
ingredients of the expression in question, albeit arranged differently
and with an additional factor of 2 thrown in. Since this expression may
easily arise from a geometric problem, my guess is that the original
author seriously screwed up the formula when trying to express it in
ASCII, but that the numeric result is legit.

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