pronic

English edit

Etymology edit

Apparently from New Latin pronicus, a misspelling of Latin promicus, from Ancient Greek προμήκης (promḗkēs, “elongated, oblong”), but the spelling has been pronic from its earliest known occurrence in English (

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(Can we date this quote?) Leonhard Euler, Opera Omnia, series 1, volume 15).^[1]^[2]

Pronunciation edit

IPA^(key): /ˈpɹɒnɪk/

Adjective edit

pronic (not comparable)

(mathematics) Of a number which is the product of two consecutive integers
- 1478 - Pierpaolo Muscharello, Algorismus p.163.^[3]
  Pronic root is as if you say, 9 times 9 makes 81. And now take the root of 9, which is 3, and this 3 is added above 81: it makes 84, so that the pronic root of 84 is said to be 3.
- 1794 - David Wilkie, Theory of interest, p.6, Edinburgh: Peter Hill, 1794.
  When a = 2, and d = 2 also, in this case, in equation 1st, s=n² + n = a pronic number, which is produced by the addition of even numbers in an arithmetic progression beginning at 2; and the pronic root $\scriptstyle n={\frac {{\sqrt {4s+1}}-1}{2}}$ .
- 1804 - Paul Deighan, "Recommendatory letters", A complete treatise on arithmetic, rational and practical, vol.1, p.viii, Dublin: J. Jones, 1804.
  As I admire each proposition fair,
  
  the pronic number and the perfect square,
  
  the puzzling intricate equation solv'd,
  
  as Grecia's chief the Gordian knot dissolv'd;
  - John Bartley
- 1814 - Charles Butler, Easy Introduction to Mathematics, p.96, Barlett & Newman, 1814
  A pronic number is that which is equal to the sum of a square number and its root. Thus, 6, 12, 20, 30, &c. are pronic numbers.
- 1998, Wayne L. McDaniel, “Pronic Lucas Numbers”, in The Fibonacci Quarterly, pages 60–62:
  It may be noted that if L_n is a pronic number, then L_n is two times a triangular number.
- 2005 - G. K. Panda1 and P. K. Ray, "Cobalancing numbers and cobalancers", International Journal of Mathematics and Mathematical Sciences, vol.2005, iss.8, pp.1189-1200.
  Thus, our search for cobalancing number is confined to the pronic triangular numbers, that is, triangular numbers that are also pronic numbers.

Synonyms edit

heteromecic

Related terms edit

Translations edit

Translations

Finnish: proninen
German: pronisch
Polish: not used in Polish

References edit

^ David J. Darling, The universal book of mathematics: from Abracadabra to Zeno's paradoxes, pp.257-258, John Wiley and Sons, 2004 →ISBN.
^ "A002378: Oblong (or promic, pronic, or heteromecic) numbers: n(n+1)", Online Encyclopedia of Integer Sequences, accessed and 21 May 2011.
^ Jens Høyrup, "What did the abbacus teachers aim at when they (sometimes) ended up doing mathematics?", New perspectives on mathematical practices, pp.47-75, World Scientific, 2009 →ISBN.

[1] David J. Darling, The universal book of mathematics: from Abracadabra to Zeno's paradoxes, pp.257-258, John Wiley and Sons, 2004 →ISBN.

[2] "A002378: Oblong (or promic, pronic, or heteromecic) numbers: n(n+1)", Online Encyclopedia of Integer Sequences, accessed and 21 May 2011.

[3] Jens Høyrup, "What did the abbacus teachers aim at when they (sometimes) ended up doing mathematics?", New perspectives on mathematical practices, pp.47-75, World Scientific, 2009 →ISBN.

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