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e. In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light. Lines are spaces of dimension one, which may be embedded in spaces of dimension two, three, or higher.
In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it. Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two- dimensional surface of a sphere [ a ] or the n -dimensional surface of higher dimensional spheres.
In a small triangle on the face of the earth, the sum of the angles is very nearly 180°. Models of non-Euclidean geometry are mathematical models of geometries which are non-Euclidean in the sense that it is not the case that exactly one line can be drawn parallel to a given line l through a point that is not on l.
The Malvern Hills in the United Kingdom, said by Alfred Watkins to have a ley line passing along their ridge. Ley lines (/ leɪˈlaɪnz /) are straight alignments drawn between various historic structures, prehistoric sites and prominent landmarks. The idea was developed in early 20th-century Europe, with ley line believers arguing that these ...
The axioms. [] Hilbert's axiom system is constructed with six primitive notions: three primitive terms: [ 5 ] point; line; plane; and three primitive relations: [ 6 ] Betweenness, a ternary relation linking points; Lies on (Containment), three binary relations, one linking points and straight lines, one linking points and planes, and one ...
e. In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses. The idealized ruler, known as a straightedge, is assumed to be ...
Parallel straight lines are equidistant. (Poseidonios, 1st century B.C.) All the points equidistant from a given straight line, on a given side of it, constitute a straight line. (Christoph Clavius, 1574) Playfair's axiom. In a plane, there is at most one line that can be drawn parallel to another given one through an external point.
Curve. A parabola, one of the simplest curves, after (straight) lines. In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago ...