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The circle of radius with center at (,) in the – plane can be broken into two semicircles each of which is the graph of a function, + and , respectively: + = + (), = (), for values of ranging from to + .
A circle with an equilateral chord (red). One sixtieth of this arc is a degree. Six such chords complete the circle. [6] The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year.
The degree sequence of an undirected graph is the non-increasing sequence of its vertex degrees; [5] for the above graph it is (5, 3, 3, 2, 2, 1, 0). The degree sequence is a graph invariant, so isomorphic graphs have the same degree sequence. However, the degree sequence does not, in general, uniquely identify a graph; in some cases, non ...
Degrees, therefore, are subdivided as follows: 360 degrees (°) in a full circle; 60 arc-minutes (′) in one degree; 60 arc-seconds (″) in one arc-minute; To put this in perspective, the full Moon as viewed from Earth is about 1 ⁄ 2 °, or 30 ′ (or 1800″). The Moon's motion across the sky can be measured in angular size: approximately ...
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
In many cases, such an equation can simply be specified by defining r as a function of φ. The resulting curve then consists of points of the form (r(φ), φ) and can be regarded as the graph of the polar function r. Note that, in contrast to Cartesian coordinates, the independent variable φ is the second entry in the ordered pair.
K n has n(n – 1)/2 edges (a triangular number), and is a regular graph of degree n – 1. All complete graphs are their own maximal cliques. They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices. The complement graph of a complete graph is an empty graph. If the edges of a complete ...
Convert all angles to corresponding points on the unit circle, e.g., ... Consider the following three angles as an example: 10, 20, and 30 degrees. Intuitively ...