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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.
This is why I'm going to have a LaTeX script on my website, when I finally get
around to working on it seriously...
anyway, I was hoping you might be able to unravel this conundrum for me. Not
that I'm likely to be building one of these things, as I haven't got anything
resembling a workshop.
Rather unfortunate, as I have an interest in astrophotography.
Regards,
A.D.B.
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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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Am 19.05.2016 um 02:55 schrieb clipka:
> 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.
BTW, there _is_ a mathematical notation that looks pretty similar to the
caret "notation":
https://en.wikipedia.org/wiki/Knuth's_up-arrow_notation
If you substitute the caret for the up-arrow, x^y would indeed denote "x
to the y-th power".
Given Knuth's connection to computer science, there may have well been
some influence between the use of the caret to denote exponentiation in
some computer languages and/or ASCII text, and Knuth's up-arrow
notation, though it is not clear to me which one was first.
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clipka <ano### [at] anonymous org> wrote:
> 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.
something tells me they might have been trying to express the equation in terms
of fractional exponents to make up for a lack of radical notation, but it's
still screwy. And it could be a source error, but considering their result was
verified independently by others, I'm assuming it's a transcription or OCR
error.
Regards,
A.D.B.
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