pronic

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English[edit]

Etymology[edit]

Apparently from New Latin pronicus, a misspelling of Latin promicus, from Ancient Greek προμήκης ‎(promḗkēs, elongated), but the spelling has been pronic from its earliest known occurrence in English ((Can we date this quote?) Leonard Euler, Opera Omnia, series 1, volume 15).[1][2]

Adjective[edit]

pronic ‎(not comparable)

  1. (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", The Fibonacci Quarterly, pp.60-62, 1998.
      It may be noted that if Ln is a pronic number, then Ln 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]

Related terms[edit]

References[edit]

  1. ^ David J. Darling, The universal book of mathematics: from Abracadabra to Zeno's paradoxes, pp.257-258, John Wiley and Sons, 2004 ISBN 0471270474.
  2. ^ "A002378: Oblong (or promic, pronic, or heteromecic) numbers: n(n+1)", Online Encyclopedia of Integer Sequences, accessed and archived 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 9812812229.