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Mathematical statements and physics equations often are named after a person (like Pythagoras theorem or Newton's second law). Reading from different authors with different origins one may sometimes find a common statement with a different name. I have usually seen this in French and Russian sources, where Snell's law became Descartes' law and Gauss' theorem became Ostrogradsky's theorem respectively.

Is there a law/theorem well known for having many different names/authors depending on the language/region? I am looking for more than 2 names/languages/regions.

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I think that what you asking for is not so rare, for example the "Rouché-Capelli theorem" is

  1. Rouché–Capelli theorem in English speaking countries, Italy, Brazil and Japan;
  2. Kronecker–Capelli theorem in Austria, Poland, Romania and Russia;
  3. Rouché–Fontené theorem in France;
  4. Rouché–Frobenius theorem in Spain and many countries in Latin America;
  5. Frobenius theorem in the Czech Republic and in Slovakia.

Another example, certainly less conspicuous, is the "law of cosines" that in France is the théorème d'Al-Kashi (but also loi des cosinus is common), and "generalized Pythagorean theorem" in many countries where the two names coexist (in France again, but also in Italy).

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The richest example in this regard according to me is the WKB approximation. WKB approximation, which is technically not a theorem but a recipe for obtaining approximate solutions to the time-independent Schrodinger equation, is named after Wentzel, Kramers and Brillouin. However, the technique is called by different names by/at different people/places:

  1. In Holland, it is called the KWB.
  2. In France, it is called the BWK.
  3. In England, it is called the JWKB with 'J' standing for Jeffreys.
  4. In the scientific community it is also known by the name LG or Liouville–Green method.
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  • $\begingroup$ I've also seen BKW, and suspect that all 6 permutations of W,K,B are used. Plus a J in front or in the back. $\endgroup$ Feb 17 at 20:53
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Cauchy, Schwarz and Bunyakovski names are used in French, Russian and English speaking countries, along with various combinations of these names.

The names Weierstrass, Casorati and Sochocki are variously associated with one theorem (which was really stated for the first time by Briot and Bouquet).

Another theorem of Sochoski is variousuly credited to Plemelj or to Kramers and Kronig. (Only Russian speakers call it correctly).

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The Ludolphian number (as it is known in Germany—at least it was up to 100 years ago) is called $\pi$ in English-language texts. It was called the Ludolphian number recognizing that Ludolph Van Ceulen calculated it to 35 decimal places in the sixteenth century.

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    $\begingroup$ The question is about things that have at least three names. $\endgroup$
    – Mauricio
    Feb 18 at 14:59
  • $\begingroup$ $\pi$ is also called "Archimedes's constant" (see), so we have three names for it... $\endgroup$
    – user6530
    Feb 18 at 17:28
  • $\begingroup$ That's for the moment not in your answer also in which language is it called that aside from English? $\endgroup$
    – Mauricio
    Feb 18 at 17:54
  • $\begingroup$ I'm not sure this is a good example in the way it is written now, as π is the symbol and "Ludolphian number" the (antiquated) name. All constants have both a name and a symbol (Euler's number = e) which don't even have to be based in a person (imaginary unit = i, Gravity constant = G etc.). $\endgroup$ Feb 19 at 9:49
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    $\begingroup$ It's now generally called "Kreiszahl" ("circle number") or "Kreiszahl Pi" in German, so it does have alternative names. $\endgroup$ Feb 19 at 9:50

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