n. The bounding or limiting parts of a body; the parts of a body which are immediately adjacent to another body or to empty space (or the air); superficies; outside: distinguished as a physical surface.n. The boundary between two solid spaces not adjacent to a third: distinguished as a mathematical surface.n. Outward or external appearance: what appears on a slight view or without examination.n. In fortification, that part of the side which is terminated by the flank prolonged and the angle of the nearest bastion.n. A centrosurface.n. A special case of the above, with four conical points. Generally distinguished as Dupin's cyclide.n. where ϕ = 0 is a primitive surface.n. An elassoidal surface (which see, above): an ordinary use, but not quite accurate.n. A surface generated by the helicoidal motion of a right line.n. The surface often originally, and better, called the Roman surface [discovered by Jacob Steiner (1796-1863), undoubtedly the greatest of all geometricians], being a quartic surface of the third class, having three double lines. In its symmetrical form its appearance is thus described: Take a tetrahedron, and inscribe in each face a circle. There will be, of course, two circles touching at the mid-point of each edge of the tetrahedron; each circle will contain, on its circumference, at angular distances of 120°, three mid-points; and the lines joining these with the center of the tetrahedron, produced beyond the center, meet the opposite edges … joining the mid-points. … Now truncate the tetrahedron by planes parallel to the faces, so as to reduce the altitudes, each to three fourths of the original value; and from the center of each new face round off symmetrically up to the adjacent three circles; and within each circle scoop down to the center of the tetrahedron, the bounding surface of the excavation passing through [that is, containing] the three right lines, and the sections by planes parallel to the face being in the neighborhood of the face nearly circular, but, as they approach the center, assuming a trigoidal form, and being close to the center an indefinitely small equilateral triangle. We have thus the surface, consisting of four lobes united only by the lines through the mid-points of opposite edges—these lines being consequently nodal lines, the mid-points being pinch-points of the surface, and the faces singular planes, each touching the surface along the inscribed circle. (Cayley, Proceedings London Math. Soc., V. 14.)n. More generally, a surface generated by a curve the plane of which moves in any way so that every line in it remains parallel to itself.n. Synonyms Superficies, Exterior, etc. See outside.Of or pertaining to the surface; external; hence, superficial; specious; insincere: as, mere surface politeness or loyalty.To put a surface (of a particular kind) on, or give a (certain) surface to; specifically, to give a fine or even surface to; make plain or smooth.
