Plane a.  Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface.
 Note: ☞ In science, this word (instead of plain) is almost exclusively used to designate a flat or level surface.
 Plane angle, the angle included between two straight lines in a plane.
 Plane chart, Plane curve. See under Chart and Curve.
 Plane figure, a figure all points of which lie in the same plane. If bounded by straight lines it is a rectilinear plane figure, if by curved lines it is a curvilinear plane figure.
 Plane geometry, that part of geometry which treats of the relations and properties of plane figures.
 Plane problem, a problem which can be solved geometrically by the aid of the right line and circle only.
 Plane sailing Naut., the method of computing a ship's place and course on the supposition that the earth's surface is a plane.
 Plane scale Naut., a scale for the use of navigators, on which are graduated chords, sines, tangents, secants, rhumbs, geographical miles, etc.
 Plane surveying, surveying in which the curvature of the earth is disregarded; ordinary field and topographical surveying of tracts of moderate extent.
 Plane table, an instrument used for plotting the lines of a survey on paper in the field.
 Plane trigonometry, the branch of trigonometry in which its principles are applied to plane triangles.


 Skew, a. Turned or twisted to one side; situated obliquely; skewed; -- chiefly used in technical phrases.
 Skew arch, an oblique arch. See under Oblique.
 Skew back. Civil Engin. (a) The course of masonry, the stone, or the iron plate, having an inclined face, which forms the abutment for the voussoirs of a segmental arch. (b) A plate, cap, or shoe, having an inclined face to receive the nut of a diagonal brace, rod, or the end of an inclined strut, in a truss or frame.
 Skew bridge. See under Bridge, n.
 Skew curve Geom., a curve of double curvature, or a twisted curve. See Plane curve, under Curve.
 Skew gearing, or Skew bevel gearing Mach., toothed gearing, generally resembling bevel gearing, for connecting two shafts that are neither parallel nor intersecting, and in which the teeth slant across the faces of the gears.
 Skew surface Geom., a ruled surface such that in general two successive generating straight lines do not intersect; a warped surface; as, the helicoid is a skew surface.
 Skew symmetrical determinant Alg., a determinant in which the elements in each column of the matrix are equal to the elements of the corresponding row of the matrix with the signs changed, as in (1), below.
 
 (1)  0 2 -3-2 0 53 -5 0   (2)  4 -1 71 8 -2-7 2 1
 
 Note: This requires that the numbers in the diagonal from the upper left to lower right corner be zeros. A like determinant in which the numbers in the diagonal are not zeros is a skew determinant, as in (2), above.


 Twist·ed, a. Contorted; crooked spirally; subjected to torsion; hence, perverted.
 Twisted curve Geom., a curve of double curvature. See Plane curve, under Curve.
 Twisted surface Geom., a surface described by a straight line moving according to any law whatever, yet so that the consecutive positions of the line shall not be in one plane; a warped surface.

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 Curve, n.
 1. A bending without angles; that which is bent; a flexure; as, a curve in a railway or canal.
 2. Geom. A line described according to some low, and having no finite portion of it a straight line.
 Axis of a curve. See under Axis.
 Curve of quickest descent. See Brachystochrone.
 Curve tracing Math., the process of determining the shape, location, singular points, and other peculiarities of a curve from its equation.
 Plane curve Geom., a curve such that when a plane passes through three points of the curve, it passes through all the other points of the curve. Any other curve is called a curve of double curvature, or a twisted curve.