Changing Shapes With Matrices

Product Description


This book shows the work of young people (ages 7 and up, again) who use the multiplication of matrices to change each point on a


Review


On November 9, 1998, Kodansha expressed a desire to have this book translated and published in Japan. --
9

This book empowers 7 year olds and up, with the ability (and fun) to change a 2-D shape, quickly and easily, and to see how the resulting shape differs from starting shape. This process is the basis of computer graphics, Bruce Artwick's Flight Simulator computer program, TV graphics, morphs, and how living things differ in shape. This is an important piece of mathematics and in the process Don's students do a lot of arithmetic (multiplying and adding), use coordinate or Cartesian geometry - it's very visual, and they learn how to multiply matrices. When Don saw drawings of transformations from D'Arcy Thompson's book
On Growth and Form, first published in 1917, used in a book on computer graphics, published in 1987, he knew he was doing something important and headed in the right direction! --
From the Publisher


From the Publisher


TOC Preface: Why transformations and why matrices? A Map to Transformations Ch. 1:Plotting points- graphing linear equations Ch. 2:Grocery-store arithmetic to multiply matrices Ch. 3:Steps to do a transformation and a point-by-point restatement of Valorie's work Ch. 4:Questions & other student work Ch. 5:Some special matrices Appendix 1:Selected answers Appendix 2:Transformations without matrices Appendix 3:Graph paper to copy Appendix 4:Computer programs to do the transformations Appendix 5:Bibliography Appendix 6:The 81-2x2 matrices using only 1’s, 0’s, and -1’s, the transformations and their rules


About the Author


Don Cohen was born in Jersey City, N.J. He has a B.A. and M.A. from SUNY-Albany, NY and M.S.from RPI,in Troy, NY. He has taught all ages of students for 44 years, the last 22 of these as co-founder and teacher of The Math Program. After 7 years of teaching in a junior high school, he realized there must be a more enjoyable and effective way to teach math. He searched for alternatives. This led to designing new curriculum for N.Y. State; learning about mathematics and creativity from Bob Davis with The Madison Project; learning what real teaching is about by observing great teachers such as Sue Monell; teaching teachers; working on Plato (a computer-based education system at the U of I); all before Don and his partner invented The Math Program. These are the good old days! Don has three fine sons and six terrific grandchildren. He is a watercolor artist (see cover).