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polygonal, a. (n.)|pəˈlɪgənəl|
[f. L. polygōn-um polygon + -al1. So F. polygonal.]
1. a. Having the form of a polygon; having many, i.e. (usually) more than four, angles (and sides); many-sided. As applied to a solid body, denoting a prismatic or similar form whose base or section is a polygon.
1727–41Chambers Cycl., Polygonal column. 1756Phil. Trans. XLIX. 513 Its whole surface is covered with small shallow polygonal cells. 1857Henfrey Bot. §652 The mutual pressure of cells..converts the spheroidal into polygonal forms. a1878Sir G. G. Scott Lect. Archit. I. 195 The polygonal chapter-house is an equally English feature.
Comb.1847–9Todd's Cycl. Anat. IV. 516/1 Polygonal-celled serous membranes.
b. Containing or forming polygonal features.
1924Geogr. Jrnl. LXIII. 213 One is apt to mistake this polygonal system of ice-wedges for a continuous sheet of ground-ice. 1930Ibid. LXXVI. 417 Polygonal shrinkage fissures in clay are widespread. 1960B. W. Sparks Geomorphol. iii. 33 Basalt..often displays a very well defined, polygonal, vertical joint pattern. 1974T. L. Péwé in Smiley & Zumberge Polar Deserts & Mod. Man iii. 42/1 One of the most widespread geomorphic features associated with permafrost in the polar deserts is the microrelief pattern of the ground generally called polygonal ground or tundra polygons.
2. a. Arith. Applied to the several series of numbers, each beginning with unity, and obtained by continued summation of the successive terms of an arithmetical progression whose common difference is a whole number. So called because each of these numbers, represented (e.g.) by dots, can be arranged according to a certain rule in the form of the corresponding regular polygon (the term being here extended to a figure of any number of sides).
Thus the A. P. 1, 2, 3, 4, 5, 6{ddd}(comm. diff. 1) gives, by summation of successive terms (1, 1 + 2, 1 + 2 + 3, etc.), the series of triangular numbers 1, 3, 6, 10, 15, 21... Similarly, with comm. diff. 2, 3, 4, etc., are obtained the series of square, pentagonal, hexagonal, etc., numbers. The polygonal numbers constitute the first order of figurate numbers: see figurate ppl. a. 3 b.
1704J. Harris Lex. Techn. I, Polygonal Numbers, are such as are the Sums or Aggregates of Series of Numbers in Arithmetical Progression, beginning with Unity; and so placed, that they represent the Form of a Polygon. 1727–41Chambers Cycl. s.v. 1842Brande Dict. Sc., etc. s.v., A very general and remarkable property of polygonal numbers was discovered by Fermat:—Every number whatever is the sum of one, two, or three triangular numbers; the sum of one, two, three, or four squares; the sum of one, two, three, four, or five pentagonal numbers; and so on.
b. as n. A polygonal number. rare.
1795Hutton Math. Dict., Polygonal Numbers,..are called Polygonals, because the number of points in them may be arranged in the form of the several Polygonal figures in geometry.
Hence poˈlygonally adv.
1870Rolleston Anim. Life 254 A polygonally-shagreened capsule. 1884Bower & Scott De Bary's Phaner. 374 The outermost layer, which..consists of polygonally prismatic cells in uninterrupted connection. |