Distance

Distance is how far one thing is from another thing. It is also a measure of the space between two things. It can be measured along any path. Thus, someone who goes around in a circle has traveled a distance, even though his position has not changed.

In geometry, the distance between two points A and B is sometimes written as [math]\displaystyle{ \overline{AB} }[/math]. Pythagorean theorem is often used in the calculation of distance. Distance is a scalar, and thus is different from displacement. Displacement is a vector that measures distance with a straight line (and in only one path). Displacement is the shortest way to travel the distance.

Examples

• One ball is 5 feet from another ball. The distance between the two balls is 5 feet.
• John walks at a speed of 6 kilometres per hour for one hour. John walks a distance of 6 kilometres.
• A circle is a curved line. Each point on the circle is the same distance from the centre of the circle.

Distance Media

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  A board showing distances near Visakhapatnam, India

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  Airline routes between Los Angeles and Tokyo approximately follow a great circle going west (top) but use the jet stream (bottom) when heading eastwards. The shortest route appears as a curve rather than a straight line because the map projection does not scale all distances equally compared to the real spherical surface of the Earth.

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  Manhattan distance on a grid

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  Animation visualizing the function (abs(x)^r + abs(y)^r)^(1/r) for various values of r.

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  The distances between these three sets do not satisfy the triangle inequality:d(A,B)>d(A,C)+d(C,B)

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  Distance along a path compared with displacement. The Euclidean distance is the length of the displacement vector.

Related pages

• Euclidean distance
• Norm (mathematics)