## RWA Distance Between Two Points

### Topic

Taxi Cab Geometry

### Vocabulary

- Distance
- Points
- Taxicab Geometry

### Student Exploration

#### Euclid is known as the “Father of Geometry”. Are you tired of Euclid’s way of doing things?

Try Taxi Cab Geometry.

“Three real life situations are proposed in Eugene F. Kraus e's book Taxicab Geometry. First a dispatcher for Ideal City Police Department receives a report of an accident at \begin{align*}X = (-1,4)\end{align*}. There are two police cars located in the area. Car C is at (2,1) and car D is at (-1,-1). Which car should be sent? Second there are three high schools in Ideal city. Roosevelt at (2,1), Franklin at ( -3,-3) and Jefferson at (-6,-1). Draw in school district boundaries so that each student in Ideal City attends the school closet to them. For the third problem a telephone company wants to set up payphone booths so that everyone living with in twelve blocks of the center of town is with in four blocks of a payphone. Money is tight, the phone company wants to put in the least amount of payphones possible such that this is true.

What makes these problems interesting is that we want to solve them not as a "crow flies” (diagonally), but with the constraints that we have to stay on city streets. This means the distance formula that we are accustomed to using in Euclidean geometry will not work. Fortunately there is a non Euclidean geometry set up for exactly this type of problem, called taxicab geometry. This system of geometry is modeled by taxicabs roaming a city whose streets form a lattice of unit square blocks” Read More ... http://www.math.umt.edu/tmme/vol2no1/TMMEv2n1a5.pdf

Learn more!

http://demonstrations.wolfram.com/TaxicabGeometry/

### Extension Investigation

- Taxicab Treasure Hunt - http://www.learner.org/teacherslab/math/geometry/shape/taxicab/
- Taxi Cab Goemtry Explorations -