Chapter 9.8, Problem 1E

Exercises 1-25 are taken from an issue of Student Math Notes, published by the National Council of Teachers of Mathematics. They were written by Dr. Tami S. Martin, Mathematics Department, Illinois State University, and the authors wish to thank N.C.T.M. and Tanti Martin for permission to reproduce this activity. Because the exercises should be done in numerical order, answers to all exercises (both even- and odd-numbered) appear in the answer section of the student edition of this text. Most of the mathematical objects you have studied have dimensions that are whole numbers. For example, such solids as cubes and icosahedrons have dimension three. Squares, triangles, and many other planar figures are two-dimensional. Lines are one-dimensional, and points have dimension zero. Consider a square with side of length one. Gather several of these squares by cutting out or using patterning blocks.

The size of a figure is calculated by counting the number of replicas (small pieces) that make it up. Here, a replica is the original square with edges of length one.

What is the least number of these squares that can be put together edge to edge to form a larger square?

The original square is made up of one small square, so its size is one.