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Some lines in the pencil through A. In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane, or the set of circles that pass through two given points in a plane.
The corresponding concept to hyperbolic line arrangements for pseudolines is a weak pseudoline arrangement, [52] a family of curves having the same topological properties as lines [53] such that any two curves in the family either meet in a single crossing point or have no intersection.
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
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry . Analytic geometry is used in physics and engineering , and also in aviation , rocketry , space science , and spaceflight .
A general straight-line thread connects the two points (0, k−t) and (t, 0), where k is an arbitrary scaling constant, and the family of lines is generated by varying the parameter t. From simple geometry, the equation of this straight line is y = −(k − t)x/t + k − t. Rearranging and casting in the form F(x,y,t) = 0 gives:
The analytic topology is the initial topology for the family of affine functions into the complex numbers, where the complex numbers carry their usual Euclidean topology induced by the complex absolute value as norm. This is also the initial topology for the family of holomorphic functions. The analytic topology has a base consisting of polydiscs.
A linear system of divisors algebraicizes the classic geometric notion of a family of curves, as in the Apollonian circles. In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.
A family of algebraic sets in projective space; for example, a line system is a family of lines. syzygetic Paired. Opposite of azygetic, meaning unpaired. Example: syzygetic triad, syzygetic tetrad, syzygetic set, syzygetic pencil. syzygy 1. A point is in syzygy with some other points if it is in the linear subspace generated by them.