[seqfan] Re: Who named Catalan numbers?

gould at math.wvu.edu gould at math.wvu.edu
Sat Feb 8 08:33:22 CET 2014

```Euler, Johann Andreas von Segner, Nicolaus von Fuss and Catalan (and
others) all studied the same numbers. It doesn't really much matter what
name we use as long as we agree on how we 'define' the numbers. In my work
over the past 60 years I have sometimes called the numbers 1, 2, 2, 5, 14,
42,  ... the 'Euler-Fuss-Segner-Catalan' numbers, especially in my
well-known Bibilography. But I always agreed with my old friends John
Riordan and Leonard Carlitz  that the single name 'Catalan' was sufficient
unto the purpose thereof.
I was reminded 60 years ago by Professor E. J. McShane that the
Cauchy inequality was also discovered by Schwartz and Bouniakovsky,
but the appellation 'Cauchy-Schwartz-Bouniakovsky Inequality' is
rather a mouthful to keep saying and so in his lectures he sometimes
just called it 'inequality 3.19'.
In the same manner we could speak of  the 'Gram-Schmitt-Eberhart'
orthogonalization process as there were several people who wrote
We know that Vandermonde had little to do with the 'Vandermonde
convolution' and Richard Askey always called it the 'Chu-Vandermonde"
formula to give the ancient Chinese some credit. Since 1955 I have
popularizd a generalization of this by calling it the 'Hagen-Rothe
convolution'. Heinrich August Rothe really came first in his 1793
Leipzig thesis. It was from Johann Georg Hagen's 'Synopsis der
Mathematik' that I came to know of Rothe's work. I was assured in
1955 by the late historian Raymond C. Archibald that perhaps only one
copy of Rothe's 1793 thesis seemed to still exist, in the Royal
Astronomical Society Library in Edinburgh, and he helped me to obtain
a photocopy. I decided to use the descriptor 'Hagen-Rothe
convolution' to give credit to Rothe and to Hagen for calling
attention to it in 1891. FINALLY, we all know that the 'Fibonacci'
numbers were not studied per se by Fibonacci. The first truly
exhaustive study was done by Edouard Lucas in his long memoir in an
early issue of the American Journal of Mathematics. The dual sequence
of numbers he studied 2, 1, 3, 4, 7, 11, 18, 29 . . .   were later
rightly called Lucas numbers.

> FTAW> Names are names. The only "misnomer" would be if the name implies a
> FTAW> property that is not correct. Any effect to give recognition where
> it
> FTAW> is due is strictly a side benefit.
>
> Hmm, if a name is a name than an inappropriate name is an inappropriate
> name.
> And according to [1] a 'misnomer' is defined as an inappropriate name.
>
> "But a misnomer is often just embarrassing, like trying to impress a
> friend by
> referring to a Burgundy wine as a 'Bordeaux.'" [1]
>
> This is how I feel: it is embarrassing to see Riordan choose the term
> 'Catalan
> numbers' although he clearly knew of Euler's and Segner's pioneer work.
>
> "Sometimes, however, what began as a misnomer has become a standard term:
> the game of Chinese checkers  does not come from China;" [1]
>
> This is exactly what happened here: "Riordan clearly made a conscious
> decision
> to popularize the term back in 1948, and eventually succeeded." [2]
>
> Peter
>
> [1] http://dictionary.reference.com/browse/misnomer
> [2] http://igorpak.wordpress.com/2014/02/05/who-named-catalan-numbers/?
>
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```