Comments on the "Mrs. Perkins's Quilt" Puzzle

This problem is related to a broader problem known as “Squaring the Square” (not to be confused with “Squaring the Circle”).

The problem is to take an n x n square (in the case of Mrs. Perkins’s Quilt puzzle it was a 13 x 13 square) and divide it into smaller squares.  The squares do not have to be the same size, but they might be.  The goal is to use the fewest number of squares possible.

For example, suppose you have a 2 x 2 square:

The only way to divide the space inside the square into smaller square is:

The minimum number of smaller squares to “Square a 2 x 2 Square” is to use four 1 x 1 squares.

Now take a look at a 3 x 3 square:

It offers an opportunity to solve the puzzle using 6 squares with(as shown below:

Now you have been working on a puzzle that starts with a 13 x 13 square (and I do hope that you worked on it) you have found out that even simple problems in mathematics can be difficult to solve.

This puzzle can be classified as “recreational mathematics”, but I prefer to classify it as “pure mathematics”.  Pure mathematics is mathematics that does not have any practical applications: it doesn’t help you design jet airplanes, or run a business, or solve medical problems – it is just mathematics.  Some mathematicians only work on pure mathematics – they actually become a little disappointed if a practical application is found for their work.

We have found that often the problems brought to us by physicists, engineers, doctors, businesses, etc. can be solved by using techniques that have already been worked out by “pure mathematicians”.  In other words – the mathematics has been worked out before we had the problem to work on.

For those of you who took on this challenging puzzle – Welcome to the world of Pure Mathematics!

REFERENCES:

http://en.wikipedia.org/wiki/Squaring_the_square

http://www.squaring.net/sq/ss/ss.html

http://celebrationofmind.org/COLUMNS/miller-squares.html
(an excellent article about Martin Gardner and the problem of Squaring the Square.

David