October 15, 2020

Geometry in Court

The TV series Numb3rs highlighted how mathematics can play a role in solving crimes.

Even though the episodes were sometimes rather fanciful, they still illustrated ways in which various types of math can help illuminate mysteries, confirm conjectures, and point to villains.

In real life, math can also be relevant in the courtroom or come up in legal disputes.

In 2005, the Pythagorean theorem was a deciding factor in a case before the New York State Court of Appeals. A man named James Robbins was convicted of selling drugs within 1,000 feet of a school. In the appeal, his lawyers argued that Robbins wasn't actually within the required distance when caught and so should not get the stiffer penalty that school proximity calls for.

The arrest occurred on the corner of Eighth Avenue and 40th Street in Manhattan. The nearest school, Holy Cross, is on 43rd Street between Eighth and Ninth Avenues.

Law enforcement officials applied the Pythagorean theorem to calculate the straight-line distance between the two points. They measured the distance up Eighth Avenue (764 feet) and the distance to the church along 43rd Street (490 feet), using the data to find the length of the hypotenuse, 907.63 feet.

Robbins' lawyers contended that the school is more than 1,000 feet away from the arrest site because the shortest (as the crow flies) route is blocked by buildings. They said the distance should be measured as a person would walk the route.

However, the seven-member Court of Appeals unanimously upheld the conviction, asserting that the distance in such cases should be measured "as the crow flies."

"Plainly, guilt under the statute cannot depend on whether a particular building in a person's path to a school happens to be open to the public or locked at the time of a drug sale," Chief Justice Judith S. Kaye wrote in the opinion, as reported in the Nov. 23, 2005, New York Times.

Originally posted November 27, 2006

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