## Monday, 10 October 2022

### #16 Pronic, oblong, rectangular numbers..from old math terms notes

Pronic Numbers are numbers that are the product of two consecutive integers; 2, 6, 12, 20, 30... They are also called rectangular or oblong numbers. Pronic seems to be a misspelling of promic, from the Greek promekes, for rectangular, oblate or oblong. Neither pronic nor promic seems to appear in most modern dictionaries. Richard Guy pointed out to the Hyacinthos newsgroup that pronic had been used by Euler in series one, volume fifteen of his Opera, so the mathematical use of the "n" form has a long history.

Oblong is from the Latin ob (excessive) + longus (long). The word oblong is also commonly used as an alternate name for a rectangle. In his translation of Euclid's "Elements", Sir Thomas Heath translates the Greek word eteromhkes[hetero mekes - literally "different lengths"] in Book one, Definition 22 as oblong. . "Of Quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right angled but not equilateral..."

The pronic numbers are a special class of oblong numbers in which the numbers differ by one. differ by one twice the triangular numbers, and represent the lengths that produce the musical intervals:
Octave 1:2
fifth 2:3
fourth 3:4
major third 4:5 ... etc