## Calculating Paths in a Map Using a Matrix

*Masahiro Takizawa*

`taki3262@green.ocn.ne.jp`

**Otawara Senior High School**

Tochigi Prefecture

Japan

### Abstract

Finding paths between two points on a map is a visual task easily carried out by our brain; however, if we try to compute the result, several questions arise: How are the calculations implemented? What data is needed? This paper shows how to obtain the paths using simple matrix products. In addition to the paths, we can also easily obtain the total number of paths and distances based on the calculations, not on our intuition. I implemented these calculations with a computer assisted instruction program to help high school students understand the underlying theory and matrix operations.

© ATCM, Inc. 2001.