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The word line may also refer, in everyday life, to a line segment, which is a part of a line delimited by two points (its endpoints). Euclid's Elements defines a straight line as a "breadthless length" that "lies evenly with respect to the points on itself", and introduced several postulates as basic unprovable properties on which the rest of ...
A straight line in the plane of triangle ABC whose equation in trilinear coordinates has the form f ( a, b, c) x + g ( a, b, c) y + h ( a, b, c) z = 0. where the point with trilinear coordinates ( f ( a, b, c) : g ( a, b, c) : h ( a, b, c) ) is a triangle center, is a central line in the plane of triangle ABC relative to the triangle ABC. [25] [26]
A curvilinear triangle is a shape with three curved sides, for instance, a circular triangle with circular-arc sides. This article is about straight-sided triangles in Euclidean geometry, except where otherwise noted. Triangles are classified into different types based on their angles and the lengths of their sides.
In topology, a curve is defined by a function from an interval of the real numbers to another space. [49] In differential geometry, the same definition is used, but the defining function is required to be differentiable. [53] Algebraic geometry studies algebraic curves, which are defined as algebraic varieties of dimension one. [54]
In any triangle the following sets of points are collinear: The orthocenter, the circumcenter, the centroid, the Exeter point, the de Longchamps point, and the center of the nine-point circle are collinear, all falling on a line called the Euler line. The de Longchamps point also has other collinearities.
For example, in Book I of Euclid's Elements, a line is defined as a "breadthless length" (Def. 2), while a straight line is defined as "a line that lies evenly with the points on itself" (Def. 4). Euclid's idea of a line is perhaps clarified by the statement "The extremities of a line are points," (Def. 3). [ 3 ]
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The three splitters concur at the Nagel point of the triangle. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter, and each triangle has one, two, or three of these lines. [2] Thus if there are three of them, they concur at the incenter.