Calculating Paths in a Map Using a Matrix

Masahiro Takizawa

Otawara Senior High School
Tochigi Prefecture


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.