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
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Editorial Reviews
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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
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
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1 of 1 people found the following review helpful:
3.0 out of 5 stars
Not enough depth to seal the deal of using matrices to transform images,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Changing Shapes With Matrices (Paperback)
While this material of this book does introduce some very interesting concepts that children will find enjoyable, it is only a start on what could be a fascinating exercise in mathematics. Matrices are easy constructs to understand, although the algorithm for multiplying two matrices is fairly complex for young children. Fortunately, in the two-dimensional world, matrix multiplication is reasonably easy to understand.
Matrices are powerful tools for transforming images and the author includes the work of several children in order to demonstrate that children ten and under can understand and perform matrix transformations. It works, but the topic is not covered in enough depth to close the deal. This is an area that I would like to include in my "Fundamentals of Arithmetic and Logic" class, but it would be necessary for me to add additional material if I were to use this book.
3 of 5 people found the following review helpful:
3.0 out of 5 stars
Needs improvment.,
By A Customer
This review is from: Changing Shapes With Matrices (Paperback)
This book needs some improvement. It does offer a fairly in-depth overlook, but does not offer enough detail to back its properties.
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Inside This Book
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First Sentence:
1. Make a shape. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Changing Shapes With Matrices New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
1. Make a shape. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Changing Shapes With Matrices New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
2
books
cite this book:
- On Growth and Form: The Complete Revised Edition (Dover Books on Biology) by D'Arcy Wentworth Thompson in Front Matter, and page 51
- Calculus by and for Young People (Ages 7, Yes 7 and Up) by Donald Cohen in Front Matter, and page 51
- Computer Graphics by Acm Press on page 51
- Prelude to Mathematics by W. W. Sawyer on page 51
- Calculus by and for Young People-Worksheets by Donald Cohen on page 51
- Calculus by and for Young People-Worksheets by Donald Cohen in Front Matter
- Homeschooling in Oregon: The 1998 Handbook by Ann Lahrson-Fisher on page 329
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