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In this context, a diameter is any chord which passes through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. [7] Half of any such diameter may be called a semidiameter, although this term is most often a synonym for the radius of a circle or sphere. [8] The longest diameter is called the ...
In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of a set, for the set of vertices of the graph, and for the shortest-path distance in the graph. Diameter may be considered either for weighted or for unweighted graphs.
The diameter is the maximum distance between any pair of convex hull vertices found as the two points of contact of the parallel lines in this sweep. The time for this method is dominated by the time for constructing the convex hull: O ( n log n ) {\displaystyle O(n\log n)} for a finite set of n {\displaystyle n} points, or time O ( n ...
Diameter (graph theory), the longest distance between two vertices of a graph; Diameter (group theory), the maximum diameter of a Cayley graph of the group; Equivalent diameter, the diameter of a circle or sphere with the same area, perimeter, or volume as another object; Hydraulic diameter, the equivalent diameter of a tube or channel for fluids
Given a chord of length y and with sagitta of length x, since the sagitta intersects the midpoint of the chord, we know that it is a part of a diameter of the circle. Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length.
A diameter of one hyperbola is conjugate to its reflection in the asymptote, which is a diameter of the other hyperbola. As perpendicularity is the relation of conjugate diameters of a circle, so hyperbolic orthogonality is the relation of conjugate diameters of rectangular hyperbolas.
where C is the circumference of a circle, d is the diameter, and r is the radius. More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width. = where A is the area of a circle. More generally, =
The circle and the triangle are equal in area. Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle.