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# Distance
Distance is a [measure](metric.md) of how far away from each other two points are. Most commonly distance refers to physical separation in space, e.g. as in distance of planets from the Sun, but more generally distance can refer to any kind of parameter space and in any number of [dimensions](dimension.md), e.g. the distance of events in time measured in seconds (1D distance) or distance of two text strings as the amount of their dissimilarity ([Levenshtein distance](levenshtein_distance.md)). Distances are very important in [computer science](compsci.md) and [math](math.md) as they allow us to do such things as [clustering](clustering.md), path searching, physics simulations, various comparisons, [sorting](sort.md) etc.
Distance is a [measure](metric.md) of how far away from each other two [points](point.md) are. Most commonly distance refers to physical separation in space, e.g. as in distance of planets from the Sun, but more generally distance can refer to any kind of parameter space and in any number of [dimensions](dimension.md), e.g. the distance of events in time measured in seconds (1D distance) or distance of two text strings as the amount of their dissimilarity ([Levenshtein distance](levenshtein_distance.md)). Distances are very important in [computer science](compsci.md) and [math](math.md) as they allow us to do such things as [clustering](clustering.md), path searching, physics simulations, various comparisons, [sorting](sort.md) etc.
Distance is similar/related to [length](length.md), the difference is that distance is computed between two points while length is the distance of one point from some implicit origin.
Distance is similar/related to [length](length.md), the difference is that distance is computed between two points while length is the distance of one point from some implicit origin. I.e. distance is computed between two [vectors](vector.md) while length is computed from just one vector.
There are many ways to define distance within given space. Most common and implicitly assumed distance is the **[Euclidean distance](euclidean_distance.md)** (basically the "straight line from point A to point B" whose length is computed with [ Euclidean Theorem](euclidean_theorem.md)), but other distances are possible, e.g. the [taxicab distance](taxicab_distance.md) (length of the kind of perpendicular path taxis take between points A and B in Manhattan, usually longer than straight line). Mathematically a space in which distances can be measured are called [metric spaces](metric_space.md), and a distance within such space can be any [function](function.md) *dist* (called a *distance* or *metric* function) that satisfies these [axioms](axiom.md):