Lite

## Equidistant?

 Category: Trick Submitted By: eighsse Fun: (2.13) Difficulty: (2.71)

Sam and Lisa live in a city in the desert of Nevada, USA, whose altitude is equal at all points, and whose streets run perfectly north-to-south and east-to-west. They are at the intersection of Harrison Street, which is north-south, and Jefferson Street, which is east-west. They are both walking to an intersection that is a few blocks east and a few blocks south from where they are now. They both take direct routes, using only two streets each (and therefore making only one turn each), but Sam takes Harrison Street while Lisa takes Jefferson Street. Assuming that neither encounters any obstacles, and that the turns take the same distance to complete, is there any reason why Sam's path or Lisa's path could be considered longer than the other's?

Sam's route could be considered SLIGHTLY longer, though for practical purposes, the difference is negligible. Sam heads south first before heading east. Being in the Northern Hemisphere, this means that he is going closer to the Equator, where the latitude of the Earth is increased, before making the lateral component of the trip.

The effect can be made dramatically more recognizable and relevant if you imagine extremely long north-south and east-west roads. Consider a case in which you are beginning halfway between the North Pole and the Equator, and your destination is on the Equator, 1/4 of the way around the Earth laterally. The north-south component will be equal no matter which of the two routes you take. However, the east-west component must take you 1/4 of the way around the Earth in each route, which is much less halfway between the pole and the Equator, than at the Equator. Of course, no grid of roads large enough for this to be an issue exists, but it is true to a slight degree.