polygon, n. and a.
(ˈpɒlɪgən)
Also 7 polygone.
[ad. L. polygōnum, a. Gr. πολύγωνον, prop. neut. of πολύγωνος adj. polygonal, f. πολυ-, poly- + -γωνος, from stem of γωνία angle. Cf. F. polygone, † poligone (Cotgr. 1611). Used at first in Latin forms polyˈgōnum, polyˈgōnium.]
A. n.
1. Geom. a. A figure (usually, a plane rectilineal figure) having many, i.e. (usually) more than four, angles (and sides); a many-sided figure.
complete polygon, a polygon in which lines are drawn connecting each angular vertex with every one of the others. stellated polygon, a polygon which wraps its interior more than once, the continuous joining of alternate or more remote angles, producing a stellate or starlike figure, as in the pentagram (q.v.) which is a stellated pentagon wrapping its interior twice. So with similar figures of 7, 8, 9, 10, etc. points, in which the variety of form increases with the number of different points that can be continuously joined.
| 1571 Digges Pantom. i. Elem. B iij b, Polygona are such Figures as haue moe than foure sides. Ibid. ii. xx. O iv, To diuide the superficies of any irregular Pollygonium. 1656 Blount Glossogr., Polygon, a Geometrical figure, that hath many corners. 1753 Hogarth Anal. Beauty iv. 22 Instead of..circular bases, polygons of different but even numbers of sides, have been substituted. 1881 R. Routledge Science ii. 37 The circle is..said to be the limit of the inscribed polygon. |
b. polygon of forces: a polygonal figure illustrating a theorem relating to a number of forces acting at one point, each of which is represented in magnitude and direction by one of the sides of the figure, analogous to the parallelogram of forces; hence, the theorem itself. So polygon of velocities, etc.
| 1842 Brande Dict. Sc., etc., Polygon of forces,..a theorem, the discovery of which is attributed to Leibnitz. 1879 Thomson & Tait Nat. Phil. I. i. §256. 1882 Minchin Unipl. Kinemat. 1 Linear velocities follow the same laws of composition and resolution as Forces in Statics; and with these (such as the parallelogram and polygon of velocities) the student is assumed to be already familiar. |
c. Arith. A polygonal number: see polygonal 2. Hence extended to higher orders of figurate numbers, as the pyramidal numbers, etc. rare. (Cf. square, cube.)
| 1842 Brande Dict. Sc., etc. s.v. Figurate Numbers, First sums, or polygons of the first order. Tri. 1, 3, 6, 10. Sq. 1, 4, 9, 16. Pent. 1, 5, 12, 22. Hex. 1, 6, 15, 28. Second sums, or polygons of the second order. 1, 4, 10, 20. 1, 5, 14, 30. 1, 6, 18, 40. 1, 7, 22, 50. |
2. a. A material object of the form of a polygon. funicular polygon: see funicular 2.
| 1669 Staynred Fortification 1 The Semidiameter of the Outward Polygon. 1706 Phillips, Polygon... Also a spot of Ground of that Figure, which is, or may be fortify'd according to the Rules of Art. 1796 Kirwan Elem. Min. (ed. 2) I. 318 Very seldom in pellucid needles, tables, or polygons. 1853 Stocqueler Milit. Encycl., Polygon, the name applied to the many-angled forms in which the outer walls of all fortified places are built. 1899 Allbutt's Syst. Med. VII. 608 Four large vessels which here form the remarkable anastomosis known as the circle, or polygon, of Willis. |
b. Physical Geogr. One of the approximately polygonal figures characteristic of patterned ground (cf. patterned ppl. a. b).
| 1913 Amer. Jrnl. Sci. CLXXXVI. 459 The shale surfaces are flat, the polygons not being concave upward as is commonly the case in the Mauch Chunk and Newark shales. 1914 T. Thoroddsen in Rosenvinge & Warming Bot. Iceland I. i. 258 The surface is divided into squares or less regularly formed polygons, by bands of small stones or gravel, while the clay of the interior of the squares or polygons is destitute of stones. 1921 Geogr. Jrnl. LVIII. 308 The snow falls, and when it melts, the spare gravel that remains on the clay substratum has taken upon itself the same system of polygons..which we see in Polar lands. 1950 [see patterned ppl. a. b]. 1960 B. W. Sparks Geomorphol. xiv. 318 Boulders weighing..over one hundredweight..have been observed in some Greenland polygons. 1974 Environmental Conservation I. 58/1 He found no serious thermokarst conditions along the trails, except where ice-wedges of polygons were crossed. |
† B. adj. Having many angles; polygonal. ? Obs.
| 1570 Billingsley Euclid iv. xvi. 125 A Poligonon figure is a figure consisting of many sides. 1681 J. Chetham Angler's Vade-m. vii. §7 (1689) 77 The best Rivers to angle in, are..such as have many Polygone windings, and turnings. 1761 Da Costa in Phil. Trans. LII. 103 The rocks..rise into polygon pillars. 1796 Morse Amer. Geog. II. 182 The surface of the causeway exhibiting to view a regular and compact pavement of polygon stones. |