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Words, grammatical forms and meanings linked to the ontology.

pronic en · ADJ

Pronunciation

  • /ˈpɹɒnɪk/

Etymology

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 (Leonhard Euler, Opera Omnia, series 1, volume 15).

Meanings

  1. (not-comparable) Being the product of two consecutive integers.
    • 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. 1814 - Charles Butler, Easy Introduction to Mathematics, p.96, Barlett & Newman, 1814
    • 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.
    • It may be noted that if Lₙ is a pronic number, then Lₙ is two times a triangular number. 1998, Wayne L. McDaniel, “Pronic Lucas Numbers”, in The Fibonacci Quarterly, pages 60–62:
    • 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=(√4s+1-1)/2.
    • 1478 - Pierpaolo Muscharello, Algorismus p.163. 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.
    • 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

Relateds

rectangular number · oblong number

Synonyms

heteromecic

Translations (5)

de pronisch (Translations) · fi proninen (Translations) · fr pronique (Translations) · fr hétéromécique (Translations) · fr oblong (Translations)