Skip to content # Optimal Locations of Firehouses (Taxi-cab Metric)

## Activity Guide

# This guide looks at the activity in detail and goes into the underlying math.

Sabloff, Josh. (2020). Optimal Locations of Firehouses (Taxi-cab Metric). In S. Bowen (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/taxi-cab-metric

Contributor(s): Joshua M. Sabloff

Math Circles: MTC Network

- Activity Description
- Topics Covered
- Session Styles
- Mathematical Practices

This session asks participants to expand their notion of “distance,” using a nontraditional taxicab metric instead of the usual Pythagorean notion. Participants are guided to construct the equivalent of “circles” with this new metric and to look at the intersections of multiple such circles. In particular, two firehouses in Gridtown are a certain distance apart and at specific addresses. What firehouse should serve a given house with a specified address? What areas of town should each firehouse serve? What if there were three firehouses? The focus of the session is on a deeper understanding of the coordinate system and notions of measuring distance.