Thomas Guettler <zopestol...@thomas-guettler.de> writes: > Hi!
> I need to compute the third square root:
> Example: > sqrt3(27) --> 3
> I use Allegro 3.0.2 on win32
> I searched in the documentation, but I didn't find > an answer.
You should search in your old math books first. What is "the third square root" supposed to be? From your example I suppose you're looking for the third root of x instead which is the same as x to the power of 1/3th:
[CMUCL 18d]
* (expt 27 1/3) 3.0
Some implementations might even yield exact results in some cases (see the notes at the end of the CLHS page for EXPT):
* Will Deakin wrote: > Really? are you sure? Where in England. I have lived, studied and > worked all my life in the UK I have never encountered this phrase.
Me too. Fourth and up root is common, but I've never come across third root.
>n...@spam.thanks wrote: >> It's quite common in England. >Really? are you sure? Where in England. I have lived, studied and >worked all my life in the UK I have never encountered this phrase.
Just based on my school and college experience. Admittedly 'cube' root is more common. I cannot cite a reference but "third power" and "third root" go together as well as "cube" and "cube root".
Peter Ward wrote: > Just based on my school and college experience.
Hmmm. Where?
(I have experience of school and college in Bristol, Powys, Birmingham, Stoke, Stafford, Sheffield, Leeds and Manchester and as I currently live and work in Yorkshire and I still have yet to encounter "third root" except in the context of enumerating the roots of polynomial equations: e.g. to refering to the third root of the quartic[1] (+ (* (+ (* (+ (* (+ x a) x) b) x) c) x) d) [2]...)
:)w
[1] ...or bi-quadratic... [2] or in infix notation x^4 + ax^3 +bx^2 + cx + d ;)
In article <ey3y9a6npg0....@cley.com>, Tim Bradshaw <t...@cley.com> wrote:
> * Will Deakin wrote: > > Really? are you sure? Where in England. I have lived, studied and > > worked all my life in the UK I have never encountered this phrase.
> Me too. Fourth and up root is common, but I've never come across > third root.
I was commenting more about grammar than about frequency of use. I certainly agree that "cube root" is far more commonly heard than "third root", but I wouldn't expect anyone to have any trouble understanding what is meant by "third root". "third square root", on the other hand, is quite dissonant to the ear.
It's pretty easy to find uses of "third root". e.g.
>Peter Ward wrote: >> Just based on my school and college experience. >Hmmm. Where?
>(I have experience of school and college in Bristol, Powys, >Birmingham, Stoke, Stafford, Sheffield, Leeds and Manchester and as I >currently live and work in Yorkshire and I still have yet to encounter >"third root" except in the context of enumerating the roots of >polynomial equations: e.g. to refering to the third root of the >quartic[1] (+ (* (+ (* (+ (* (+ x a) x) b) x) c) x) d) [2]...)
I defer to your greater mobility. I went to school only in Ramsgate and college in Cambridge. I work in London, but not with Lisp. So I could claim it was commonly used in the Isle of Thanet, but I won't.
In article <ey3y9a6npg0....@cley.com>, Tim Bradshaw <t...@cley.com> wrote: >* Will Deakin wrote: >> Really? are you sure? Where in England. I have lived, studied and >> worked all my life in the UK I have never encountered this phrase.
>Me too. Fourth and up root is common, but I've never come across >third root.
Ditto for me, born, raised, and currently living in the US.
I assume this convention exists to minimize the length of (English) utterances: "square" and "cube" are monosyllabic, whereas quartic, quintic, and the like are polysyllablic.
* none wrote: > I assume this convention exists to minimize the length of > (English) utterances: "square" and "cube" are monosyllabic, > whereas quartic, quintic, and the like are polysyllablic.
No, I don't think so. I think it's because of the relation between nth-order expressions and n-dimensional spaces. I think it stops after `cube' because people tend not to have experience of (and therefore words for) spaces of dimension greater than 3.
* Bruce Hoult | Erik perhaps could have mentioned that "third root" is also perfectly | acceptable English.
No, I could not. /You/ could have mentioned this, which is contrary to an amazing array of reference works, both online and offline. Unless, of course, you refer to something else entierely, such as in "go, go, go!" where the last "go" would be the third root.
-- Erik Naggum, Oslo, Norway
Act from reason, and failure makes you rethink and study harder. Act from faith, and failure makes you blame someone and push harder.
Tim Bradshaw <t...@cley.com> writes: > * none wrote:
> > I assume this convention exists to minimize the length of > > (English) utterances: "square" and "cube" are monosyllabic, > > whereas quartic, quintic, and the like are polysyllablic.
> No, I don't think so. I think it's because of the relation between > nth-order expressions and n-dimensional spaces. I think it stops > after `cube' because people tend not to have experience of (and > therefore words for) spaces of dimension greater than 3.
I don't know about that. With that logic we would have developed the term "hypercube root".
In article <3240919023488...@naggum.no>, Erik Naggum <e...@naggum.no> wrote:
>* Bruce Hoult >| Erik perhaps could have mentioned that "third root" is also perfectly >| acceptable English.
> No, I could not. /You/ could have mentioned this, which is contrary to an > amazing array of reference works, both online and offline.
Although the term "cube root" is the common one, I think "third root" would be well understood. There's no special term for all the other roots, they're all just known by their ordinal numbers: fourth root (this could be called "tesseract root", but AFAIK it's not), fifth root, etc. "Third root" fits into this pattern, so I can't imagine any confusion over it.
"Third square root" on the other hand, is definitely confusing. When I first saw that subject, my first thought was "the first square root of 4 is 2, the second one is -2, I wonder what he's thinking the third one would be?"
-- Barry Margolin, bar...@genuity.net Genuity, Woburn, MA *** DON'T SEND TECHNICAL QUESTIONS DIRECTLY TO ME, post them to newsgroups. Please DON'T copy followups to me -- I'll assume it wasn't posted to the group.
In article <ey3k7lp7qqo....@cley.com>, Tim Bradshaw <t...@cley.com> wrote:
>* Duane Rettig wrote:
>> I don't know about that. With that logic we would have developed the >> term "hypercube root".
>I don't think so, because hypercube (to me, anyway) means a `cube' in >a space of dimension > 3, so hypercube root is too vague...
Like I said in my last post, the term would be "tesseract root".
-- Barry Margolin, bar...@genuity.net Genuity, Woburn, MA *** DON'T SEND TECHNICAL QUESTIONS DIRECTLY TO ME, post them to newsgroups. Please DON'T copy followups to me -- I'll assume it wasn't posted to the group.
In article <ey3bs72neq4....@cley.com>, Tim Bradshaw <t...@cley.com> wrote: >* none wrote:
>> I assume this convention exists to minimize the length of >> (English) utterances: "square" and "cube" are monosyllabic, >> whereas quartic, quintic, and the like are polysyllablic.
>No, I don't think so. I think it's because of the relation between >nth-order expressions and n-dimensional spaces. I think it stops >after `cube' because people tend not to have experience of (and >therefore words for) spaces of dimension greater than 3.
Interesting hypothesis.
When I think of roots and multidimensional spaces, I think of the Minkowski distance metric. We say "distance" and "Euclidean distance" for the special cases of N=1 and N=2, respectively, but use the general form of the metric when N>=3.
I don't know is this is relevant or a non-sequitir...
* none wrote: > When I think of roots and multidimensional spaces, I think of the > Minkowski distance metric. We say "distance" and "Euclidean > distance" for the special cases of N=1 and N=2, respectively, but > use the general form of the metric when N>=3.
I think for a physicist that (a) the minkowski metric would actually something with signature (+,+,+,-) (or (-,-,-,+)), or in general with n-1 +s and a - or vice-versa. And obviously it isn't actually a metric, but... And (b) `Euclidian' can be used for any number of dimensions (`Euclidian n-space'). Euclidean can *certainly* be used in physics for n=3.
> I don't know is this is relevant or a non-sequitir...
No, me neither. more interesting than some other current threads though.
