A plaque remaining from the Big Apple Night Club at West 135th Street and Seventh Avenue in Harlem.

Above, a 1934 plaque from the Big Apple Night Club at West 135th Street and Seventh Avenue in Harlem. Discarded as trash in 2006.

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Entry from March 06, 2005
Manhattan Distance
"Manhattan distance" is a mathematical term based on the grid system for Manhattan's street.

(Oxford English Dictionary)
attrib. Math. Designating geometries, graphics, etc., which use only straight lines intersecting at right angles (like the streets of the central part of Manhattan); Manhattan distance, a distance measured as the sum of the displacements along a vertical and horizontal axis.
1974 P. H. A. SNEATH in M. J. Carlile & J. J. Skehel Evol. in Microbial World 9 The most popular resemblance measures for cladistics are Manhattan distances, that reckon distances between points by adding displacements on each character axis, like the moves of a rook on a chess-board.
1985 R. F. SPROULL et al. Device-Independent Graphics x. 284 The approximation for distance is sometimes called the 'Manhattan distance', because the distance between two points in New York City is best thought of as the distance along city streets at right angles to one another.
1988 T. DILLINGER VLSI Engin. vi. 212 The Manhattan distance is the rectilinear distance between two points: d = |x1 - x2| + |y1 - y2|.
1988 B. T. PREAS & M. J. LORENZETTI Physical Design Automation viii. 350 The intersection of two lines in Manhattan geometry can be computed quickly and with no loss of precision.

June 1965, Journal of the Society for Industrial and Applied Mathematics, "Random Minimal Trees" by E. N. Gilbert, pg. 377:
Manhattan norm
For example, if [P] denotes Manhattan distance the unit circle is a square with corners on the x and y axes and with sides of (Euclidean) length 2 1/2(power - ed.).

August 1967, The American Mathematical Monthly, pg. 901:
We assume the existence of n points in mdim. space such that the "Manhattan distance" between points equals the specified distance between corresponding cities.

April 1979, Management Science, pg. 302:
This has also been called the "Manhattan" distance [5] because it corresponds to distance travelled via perpendicular city streets.
Posted by Barry Popik
New York CityNames/Phrases • Sunday, March 06, 2005 • Permalink