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theorems on sums of squares

Defines: 
Hurwitz theorem, Pfister's theorem, Hilbert's 17th Problem
Synonym: 
Pfister theorem
Type of Math Object: 
Theorem
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

12D15 no label found16D60 no label found15A63 no label found11E25 no label found

Comments

Hello everybody!

I have posted a message a while ago, but no one replied on it, may be because it was exteremely busy time, so I decided to post it again:

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Is there any rule which says what is right

"Planck's constant" or "Planck constant" (the same with Euler)
"Green's function" or "Green function"
"Poincare's inequality" or "Poincare inequality"
and so on...

I saw in some places with "'s" in some places without. May be both variants are acceptable, but may be variants with "'s" mean something different then without?

It would be nice to have some clear explanation. Thanks in advance :)
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The reason to post it here (near this entry), is that there are two names:

Hurwitz theorem, Pfister's theorem

one with 's and one without, and thus the question has applied nature: why "Hurwitz thrm" is without 's and "Pfister's thrm" is with 's?????

Thanks in advance!
Serg.

-------------------------------
knowledge can become a science
only with a help of mathematics

It should link correctly either way. I'd suggest going with whatever you think the most common usage is. My guess is that this will usually be the possessive form.

apk

I have seen that Hurwitz theorem is used most often, instead of Hurwitz's theorem. Perhaps it is because the z at the end of the name is similar sounding to s. On the other hand, I have never seen Pfister's theorem being stated as Pfister theorem.

Chi

It's impossible to pronounce the genitive marker "s" in the names ending in a sibilant phoneme as in Hurwitz, Weierstrass, Bush. Therefore the "s" letter must not be written in such names, but if one wants to denote the genitive of them then write e.g. Hurwitz' theorem. Otherwise the "s" letter may be written if it's an established, standard procedure.

Jussi

Thanks for replies!

I would like then to ask: does possesiveness affect the meaning of the notion? Originally I submitted a correction to the entry "Simmon's line" for forgetting 's in the phrase like "the line *** is a Simson line for triangle ***"

http://planetmath.org/?op=getobj&from=corrections&id=5786

and I got a reply like 'a' makes it possible to write "Simson line" without 's. So, is it really true that the absence of 's make the notion more general meaning...

I am not sure, but it seems to me now that things like "Simson line", or "Green function", or "Prandtl number" are NOT some fixed 'line', 'function', 'number' and they just have the names of Simson, Green and Prandtl. And that's why one shouldn't use posseive case here.

On the other hand "Fermat's theorem", "Zorn's lemma", "Planck's constant" are some concrete "theorem", "lemma" and "constant" and they actually BELONG to the persons who invented them and thus possesive case should be used here.

What do you think about this?

-------------------------------
knowledge can become a science
only with a help of mathematics

ok I think I misunderstood your correction then, I'm sorry
I thought you were complaining about the "THE"
as in "THE line", because there are many of them, not a single one, that's why I changed it to "A" and closed the correction.

Again, It was me who misunderstood the correction
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

> ok I think I misunderstood your correction then
Wait, wait! I am not so sure that you misunderstood it ;).

For everyone to understand what we are talking about here is the original sentence which I thought has some problems:

"In the picture, the line passing through $U,V,W$ is the Simson line for $\triangle ABC$."

So, as already said "Simson line" is NOT some fixed line but rather a line determined by some things (see the entry). Thus "the Simson line for triangle..." sounds like triangle has ONE Simson line, which is not the case, so it is better to use "a Simson line".

But what we are talking about now, is another thing: when to use 's? According to what I wrote in the previous post "Simson line" should be written everywhere WITHOUT 's. The big question is of cource, whether what I wrote is actually correct ;). Have you really seen the expression "Simson's line"?
-------------------------------
knowledge can become a science
only with a help of mathematics

yes
THAT was the line
yet when you submited your correction I saw:

You probably forgot 's in "line passing through $U,V,W$ is a Simson line for $\triangle ABC$".

So I noticed you had changed THE by A in the text of your correction
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

ok I think you had two points to mak in the correction, yet I failed to see one of them, I truly never understood that you were talking about posesives
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

But anyway, let's forget about that correction ;) and return to the issue of this post. So, once more: have you seen in some quite reliable source (I mean say, written by native speaker ;) "Simson's line" really WITH 's?

And what do you think about the following rule (retyped from previous posts):

-------------
It seems that things like "Simson line", or "Green function", or "Prandtl number" are NOT some fixed 'line', 'function', 'number' and they just have the names of Simson, Green and Prandtl. And that's why one shouldn't use posseive case here.

On the other hand "Fermat's theorem", "Zorn's lemma", "Planck's constant" are some concrete "theorem", "lemma" and "constant" and they actually BELONG to the persons who invented them and thus possesive case should be used here.
-------------

-------------------------------
knowledge can become a science
only with a help of mathematics

I did some research about this a long time ago, then I discovered I'm not supposed to write
Pythagoras's theorem but Pythagoras' theorem, but this was already pointed on this thread, otherwise I'm of not much help, but I got a few books behind me and this are some random checks. When nothing else is stated, they were taken from the subject index:

From: Interpolation and Approximation by polynomials (George M. Phillips)
Pappu's theorem
Pascal identities
Euler-Mclaurin formula
Gauss-Legendre rule
Hermite-Féjer operator
Gregory's formula
Kronecker delta
Lagrange interpolation
Minkoski's inequality (ALSO checked on the text, not on index)
Legendre polynomial (checked on the text, not on index)
Chebyshev polynomial (checked on the text, not on index)
Bernoulli numbers (checked on the text, not on index)

From: Concrete Mathematics (Graham, Knuth and Patashnik)
Stirling numbers
Pascal's triangle
Stirling's numbers (as listed on the List o f tables)
Lagrange's identity (checked on the text, not on index)
Wilson's theorem (checked on the text, not on index)

Complex analysis (Lang )
All named theorems in text use 's
but he also uses
Bernoulli polynomial,
Green function
Euler product
Picard-Borel theorem
Dirac family
Poisson family
Poisson kernel
Poisson integral

it seems that when lang refers to a mathematical entity, he doens't uses 's (since mathematicians do not "own" math objects) but when refering to statements, lemmas and theorems, he does use 's

That convention makes sense to me, so I would say
"By the Simson's theorem on Simson lines..."
I'll do more checks soon...
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

> it seems that when refering to a mathematical entity,
> [one] doens't uses 's (since mathematicians do not "own" math objects)
> but when refering to statements, lemmas and theorems,
> [one] does use 's

> That convention makes sense to me, so I would say
> "By the Simson's theorem on Simson lines..."

Well, it is something similar to what I said. It would be interesting to find some place where some rule is explicitly stated ;)

> I'll do more checks soon...

I'll also be looking for...
-------------------------------
knowledge can become a science
only with a help of mathematics

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