Encyclopedia > Diameter

  Article Content

Diameter

The diameter of a circle is the length of a straight line segment that passes from a point on the circle to the opposite point (and therefore passes through the centre of the circle). This length is twice the radius. The line segment itself is also called a diameter.

The diameter of a connected graph is the distance between the two vertices which are furthest from each other. The distance between two vertices a and b is the length of the shortest path connecting them (for the length of a path, see Graph theory).

The two definitions given above are special cases of a more general definition. The diameter of a subset of a metric space is the least upper bound of the distances between pairs of points in the subset. So, if A is the subset, the diameter is

sup { d(x, y) | x, y in A }.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Constable

... a sworn oath and warrant, rather than being delegated powers that he has simply because he is employed as a Police officer. Technically this means that each swor ...