# pronic

## 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?) Leonhard Euler, *Opera Omnia*, series 1, volume 15).^{[1]}^{[2]}

### 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*=*n*^{2}+*n*=*a***pronic**number, which is produced by the addition of even numbers in an arithmetic progression beginning at 2; and the**pronic**root .

- When
**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.

- A
**1998**- Wayne L. McDaniel, "Pronic Lucas Numbers",*The Fibonacci Quarterly*, pp.60-62, 1998.- It may be noted that if
*L*_{n}is a**pronic**number, then*L*_{n}is two times a triangular number.

- It may be noted that if
**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.

- Thus, our search for cobalancing number is confined to the

#### Synonyms[edit]

#### Related terms[edit]

### 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 0471270474. - ^ "A002378: Oblong (or promic, pronic, or heteromecic) numbers: n(n+1)",
*Online Encyclopedia of Integer Sequences*, accessed and archived 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 9812812229.