Euclidean vs. Manhattan Metrics
February 9th, 2006 by SplineGuy
I had to post a reference to this article from last year. The question came up in Calculus as to what I meant by a Euclidean measure of distance. Put simply for the non-math-enthusiats out there, Euclidean measure is what we typically think of as straight line distance. On the other hand there are many other ways to measure distance. One example is the Manhattan metric, which basically measures distance as you would in city with nice rectangular blocks. You have to travel down the streets to get to where your going so measure along the route instead of in straight lines.
I referenced the following article in class as an example where that question of which distance measure to use might come up in every day life, not to mention its vital importance to mathematics.
November 23, 2005
Conviction With an Angle Is Upheld by Court of AppealsBy MICHAEL COOPER
ALBANY, Nov. 22 - Pythagoras won his day in court on Tuesday. The question before the state’s highest court, the Court of Appeals, was whether a man named James Robbins was guilty of selling drugs within 1,000 feet of a school - which carries a longer sentence - when he was arrested in March 2002 on the corner of Eighth Avenue and 40th Street in Manhattan and charged with selling drugs to an undercover police officer.
The nearest school, Holy Cross, is on 43rd Street between Eighth and Ninth Avenues. How to measure? On foot, Mr. Robbins’s lawyers argued, the school is more than 1,000 feet away from the site of the arrest, because the shortest route is blocked by buildings. But as the crow flies, the authorities said, it is less than 1,000 feet away.
Law enforcement officials calculated the straight-line distance using the Pythagorean theorem () measuring the distance up Eighth Avenue (764 feet) as one side of a right triangle, and the distance to the church along 43rd Street (490 feet) as another, to find that the length of the hypotenuse was - 907.63 feet.
Lawyers for Mr. Robbins argued that the distance should be measured as a person would walk it because “crows do not sell drugs.” But in a unanimous ruling, the seven-member Court of Appeals upheld his conviction and held that the distance in such cases
