Cynthia Lanius

Geometry Online Introduction Distances Midpoints

School-Bus Geometry

Introduction

girl in a city scene

Ana just got off the school bus and she's really hungry. She sees a place to get a burger across the park. What route gives Ana the shortest distance to the burgers?

I'm sure you've heard that the shortest distance between 2 points is a straight line. So Ana's going to cut diagonally across the park.

 

Calculating distance is tied to a famous theorem. Can you name and state the theorem? Read about it here.

Ana's cutting across the park illustrates another theorem - that in any triangle, any one side is less than the sum of the other two sides.

girl in a city scene with triangle drawn in

 
school bus in city scene

 

Now look at the school bus to the left. If you talk about how far away the bus is from McDonald's, it's the same distance that Ana was. But that's pretty irrelevant, isn't it? The school bus can't tear out across the park.

Since these distances are irrelevant on city streets, we will apply a different measurement, a measurement that doesn't allow you to leave the streets. Most math teachers call this taxicab geometry, but we're going to call it school-bus geometry because kids seldom ride in taxis.

Geometry Online Introduction Distances Midpoints
URL http://math.rice.edu/~lanius/Geom/schbus1.html