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We all have to write and rewrite the equations that have been known for thousands of years. Is there any repository where, say, the Pythagorean's theorem can be fetched as $a^2 + b^2 = c^2$?

Update: By 'repository' I mean a browsable/downloadable database, where if you type "Pythagorean theorem", you get the string $a^2 + b^2 = c^2$ (or the several well-known ways of representing it).

Note: Springer's database is clearly not that kind of repository.

Sebastiano
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nightcod3r
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    Wikipedia would likely be a nice resource. Just hit edit the source code of an article with math formulae, to access the LaTeX source. – marsupilam Mar 27 '17 at 16:18
  • Do you really have the need to rewrite the classic equations with the same letters? In actual cases it seems that you don't need the a^2+b^2=c^2 but something like a^2+(r-x)^2=l^2 for which the standard repository would be not that usable... – Džuris Mar 27 '17 at 21:50
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    @marsupilam Since Wikipedia generates the equations in such a way that the LaTeX syntax is in the alt (aka hover) text, you can actually just select the equation you want to copy and then drag&drop it into your TeX editor. – Wojciech Morawiec Mar 27 '17 at 23:08
  • @Džuris You're right, that's because it is specified in the question "or the several well-known ways of representing it". We can't cover all needs, but there could be a, say, JSON-based repository that provides a solution for most demands. – nightcod3r Mar 28 '17 at 02:23

4 Answers4

19

Yes, there is! In some sense, at least for mathematics.

The NIST Digital Library of Mathematical Functions allows you to download for each equation its LaTeX representation. Click on the information symbol on the right of any equation and then click on the "TeX encoding": it will download the LaTeX form.

For instance, for the equation 5.10.1, it reports

\[\mathop{\mathrm{Ln}\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(z\right)+z-%
\left(z-\tfrac{1}{2}\right)\mathop{\ln\/}\nolimits z-\tfrac{1}{2}\mathop{\ln\/%
}\nolimits\!\left(2\pi\right)=\cfrac{a_{0}}{z+\cfrac{a_{1}}{z+\cfrac{a_{2}}{z+%
\cfrac{a_{3}}{z+\cfrac{a_{4}}{z+\cfrac{a_{5}}{z+}}}}}}\cdots,\]
Massimo Ortolano
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    While this is the closest concept, there is a manual process involved (clicking here and there), plus you really can't find basic stuff, like, for example, the mentioned Pythagorean theorem. – nightcod3r Mar 27 '17 at 19:44
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    This is unusable: the code includes many redundant pieces, for example \nolimits, \left, \!, %. It includes LaTeX specific sequences like \mathrm, \tfrac. If I need to write such equation then I do this: $\def\dst#1{\displaystyle{\strut#1}} {\rm Ln}\,\Gamma(z) + z - (z- {1\over2})\ln z - {1\over2}\ln(2\pi) = \dst{a_0\over z+ \dst{a_1\over z+ \dst{a_2\over z + \dst{a_3\over z+\dst{a_4\over z+\dst{a_5\over z+}}}}}}\cdots,$ – wipet Mar 28 '17 at 10:01
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    @wipet "It includes LaTeX specific sequences": in fact, as I wrote, it's LaTeX. – Massimo Ortolano Mar 28 '17 at 10:07
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    Well, this uses \tfrac which is not part of standard tex or latex - but is defined by amsmath. Given that amsmath is required, it is very strange the rest of the encoding is so archaic. – Andrew Swann Mar 29 '17 at 08:36
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    I don't complain -- just thanks for sharing! :) – Dr. Manuel Kuehner Mar 29 '17 at 16:50
10

There seems to be three options:

Community
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Clément
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  • Basic search queries such as central limit theorem Riemann sum total probability eigenvector or integration by parts tend to prove rather disappointing at latexsearch – marsupilam Mar 27 '17 at 16:16
  • Well, their search-engine is weird, since you're supposed to make queries using… latex code. I'm not sure what is the exact use of that, but that's the only search engine I know of that would remotely meet @op's needs. – Clément Mar 27 '17 at 16:18
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    In order to find the statement for the Pythagorean theorem, should OP search for a^2 or for c^2 ? – marsupilam Mar 27 '17 at 16:20
  • Now that I think of it, I genuinely don't know what is the use of that search engine. I edited my original answer to reflect that, mentioning your idea of looking at wikipedia, which is possibly the best answer, actually. Do you want me to turn my question into community wiki? – Clément Mar 27 '17 at 16:22
  • If I were to guess, the point of this search engine is probably : "because we can" ! Community wiki ? er... sure (never really understood what they're for, really !) – marsupilam Mar 27 '17 at 16:30
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    There's a post for that ;-) https://meta.stackexchange.com/a/11741/262759 Now you can freely upgrade and update my answer, and, actually, everybody (well, anybody over 100 point) can! – Clément Mar 27 '17 at 16:40
  • @marsupilam Correct, this is what I would expect: you enter keywords, and get a formula. – nightcod3r Mar 27 '17 at 19:33
  • https://proofwiki.org might be a better source than Wikipedia itself. – nightcod3r Mar 28 '17 at 08:19
3

I think that mathran.org can help you. In this site, if you select "Search" it shows "Find formulas" and you type, for example, "Schrodinger" and you obtain the registers in the database made by users: http://www.mathtran.org/formulas/search/?q=Schrodinger&tags=&users=

Roberto
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    This looks pretty much as the right thing, problem is that is being shutdown: "Notice of decomission We would like to thank you for using this site but would like to tell you it is going to be decommissioned following the completion of the Mathtran project. Please Note: The final date this site will be open is the (24th March 2017). After this date the site will no longer be available." – nightcod3r Mar 28 '17 at 08:09
2

Sangaku provides a unified context for maths in secondary education and first courses of technical studies. Searching for circumference general equation you can access a page containing it, right-clicking on it you get the TeX commands.

Not really the kind of repository the question asks for, but it can help.

Note: Right-cliking on an equation you can also select Math Settigns > Math Renderer > Plain Source, so that the page displays the original TeX equations.

nightcod3r
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