great-circle distance

The distance between two points is the length of a straight line segment between them. In the case of two locations on Earth, usually the distance along the surface is meant: either "as the crow flies" (along a great circle) or by road, railroad, etc. Distance is sometimes expressed in terms of the time to cover it, for example walking or by car. Sometimes a distance thus indicated is ambiguous because the means ...

Including:

• Distance - Distance covered
• Distance - Formal definition
• Distance - The distance formula
• Distance - Generalized distance in arbitrary dimensions: Norms
• Distance - Distances in other spaces

Read more here: » Distance: Encyclopedia - Distance

A distance between two points P and Q in a metric space is d(P,Q), where d is the distance function that defines the given metric space. We can also define the distance between two sets A and B in a metric space as being the minimum (or infimum) of distances between any two points P in A and Q in B. Alternatively, the distance between sets may indicate "how different they are", by taking the supremum over one set of the distance from a point in that set to the other set, and conversely, and taking the ...

See also:

Distance, Distance - Distance covered, Distance - Formal definition, Distance - The distance formula, Distance - Generalized distance in arbitrary dimensions: Norms, Distance - Distances in other spaces

Read more here: » Distance: Encyclopedia II - Distance - Formal definition

On the Earth, a circle of latitude or parallel is an imaginary east-west circle that connects all locations with a given latitude. The position on the circle of latitude is given by the longitude. Each is perpendicular to all meridians at the intersection points. Those parallels closer to the poles are smaller than those at or near the Equator. Circles of latitude are based on the rotation of the Earth. Four special ones are based on the relationship with the Earth's orbit arou ...

Read more here: » Circle of latitude: Encyclopedia - Circle of latitude

The idea of randomness, without clauses, suggests a probability distribution with "maximum symmetry" with respect to all outcomes. In the case of finite possible outcomes, symmetry with respect to them implies a discrete uniform distribution. In the case of a real interval of possible outcomes, maximum symmetry with respect to them corresponds to a continuous uniform distribution. In other cases, such as "taking a random integer" or "taking a random real number", only little symmetry is possible, there is not a particular probability distribution providing maximum symmetry, ...

See also:

Symmetry in mathematics, Symmetry in mathematics - Objects symmetric to each other, Symmetry in mathematics - Randomness, Symmetry in mathematics - Skew-symmetry, Symmetry in mathematics - Symmetry in probability theory

Read more here: » Symmetry in mathematics: Encyclopedia II - Symmetry in mathematics - Randomness

A function of two variables is skew-symmetric if f(y,x) = - f(x,y). The property implies f(x,x) = 0. A skew-symmetric matrix, seen as a function of the row- and column number, is an example. The property is also called antisymmetry and, in the case of operator notation, anticommutativity. In the definition of an antisymmetric relation, "minus" is replaced by "not", and the condition is necessarily relaxed, to be required only in the case x ≠ y. The corresp ...

See also:

Symmetry in mathematics, Symmetry in mathematics - Objects symmetric to each other, Symmetry in mathematics - Randomness, Symmetry in mathematics - Skew-symmetry, Symmetry in mathematics - Symmetry in probability theory

Read more here: » Symmetry in mathematics: Encyclopedia II - Symmetry in mathematics - Skew-symmetry