PLANE. The simplest definition of plane given by the Greek geometers is that of Heron of Alexandria (c. 20o) :—a surface "such that if a straight line passes through two points on it, the line coincides wholly with it at every spot, all ways." Crelle (1834) defined it as the surface containing all the straight lines (throughout their entire lengths) passing through a fixed point and also intersecting a straight line in space. (For plane, a tool, see EDGE TOOLS.) See H. Schotten, Inhalt and Methode des planimetrischen Un terrichts (Leipzig, 189o, 1893) ; Sir T. L. Heath, The Thirteen Books of Euclid's Elements (1926). (See also SURFACE.) In botany, plane is the common name of a handsome tree known botanically as Platanus orientalis (family Platanaceae), a native of Greece and western Asia, a favourite shade-tree of the ancient Greeks and Romans, and introduced by the latter to south-west Europe. It is one of the most successful trees in London and other large towns ; the smooth face of the leaf is easily washed by rain; and the periodical peeling of the bark also serves to get rid of surface deposits of soot, etc. It is a large tree with widely spreading branches and alternate, palmately five lobed leaves, resembling those of the sycamore in shape, but quite hairless and of a brighter green. The bud in the leaf aril is protected during its development by the hollow base of the leaf-stalk, which lifts off like an extinguisher when the leaf falls in autumn. The minute, unisexual flowers are borne in dense
pendulous heads, which contain either male or female flowers ; the small one-seeded fruits are densely crowded in a ball, from which they gradually separate in drying, and are readily carried by the wind. A variety of forms are known in cultivation, the com monest being the maple-leaved (acerifolia), the London plane, which has usually three-lobed leaves ; var. laciniata has very deeply much divided leaves, and var. variegate, variegated foli age. Platanus occidentalis, an allied species, is a native of the United States, being most abundant and growing to its largest size in the basin of the lower Ohio and the Mississippi rivers. It was introduced into England early in the I7th century, and is occasionally met with in western and central Europe ; it is known in America as sycamore and buttonwood. It differs from P. orientalis in its less deeply lobed, more leathery pubescent leaves and in the usually solitary balls of fruit. Both the native syca more and the London plane are extensively planted as ornamental trees in the eastern United States. The California sycamore (P. racemosa) and the Arizona sycamore (P. Wrightii), of the ex treme South-west, are much smaller than the eastern species.