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Taxicab geometry, considered by Hermann Minkowski in 19th century Germany, is a form of geometry in which the usual distance function of metric or Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates. The taxicab metric is also known as rectilinear distance, ''L''1 distance or norm (see ''L''''p'' space), city block distance, Manhattan distance, or Manhattan length, with corresponding variations in the name of the geometry.〔(Manhattan distance )〕 The latter names allude to the grid layout of most streets on the island of Manhattan, which causes the shortest path a car could take between two intersections in the borough to have length equal to the intersections' distance in taxicab geometry. == Formal definition == The taxicab distance, , between two vectors in an ''n''-dimensional real vector space with fixed Cartesian coordinate system, is the sum of the lengths of the projections of the line segment between the points onto the coordinate axes. More formally, : where are vectors : For example, in the plane, the taxicab distance between and is 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Taxicab geometry」の詳細全文を読む スポンサード リンク
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