Customer Reviews

String, Straight-Edge, and Shadow: The Story of Geometry

5 star:		(4)
4 star:		(0)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

I've been reading several books on the history of mathematics lately. This one is the best! It makes concepts so clear by the marriage of text and illustrations. For example, I've read about Thales solving how high the Great Pyramid of Cheops was in two other books. This book used four diagrams and several pages of text to clearly explain how Thales answered his own question. Author Julia Diggins goes into depth on geometry but on a level children can understand.

Proceed slowly, letting your children try to solve a problem before reading about its solution. For example, pose the problem of drawing a perfect circle using a string. Once they have solved the problem or given up, read that part of the book. Then go to the beach or a park and use a volleyball pole and a rope to draw circles in the sand with your feet.

Then set them to figuring out how to divide a circle into six equal parts using the string. After they solve or give up, read that part of "String, Straightedge, & Shadow." Let them follow the instructions and illustrations in chapter six to reproduce the results. Play with a Spirograph, too.

Since this book is out of print, try to locate it at a thrift store or library sale; it is worth the effort. But I hope I find it before you.

This book is a 'living book', written by Julia Diggins, a math teacher. She begins with a description of nature and the patterns found therein, working through the same observations that early man must have made. As we visit Egypt and other ancient near eastern cultures, Diggins shows how bits of early geometry might have been discovered, and how it was used in daily life. Builders, village leaders and ordinary people solved real, practical problems, using only shadows, ropes(string), and straight edges.

In successive chapters, Diggins takes us to ancient Greece and attempts to reconstruct the way ancient thinkers could have worked out many concepts crucial to geometry. She covers Thales, Pythagoras (and his followers) and Eudoxus of Cnidus in particular detail.

While Diggins gives informative, story-like backgrounds, she concentrates on HOW they could have made their findings--in a manner that students can understand and replicate. These expainations make this book different from biographies of mathemeticians, such as in books like "Mathematicians are People Too".

This is a book of discoveries, not a text book with problems. In each of the book's 17 chapters, Diggins takes us thru the observations and "tests" that people would make along the path to discovering both practical and theoretical geometry. These observations and tests can be duplicated by the reader (depending on age, you may need to assist). Some are explicitly written with that intent (i.e. she suggests you try it) while others are more subtle. For instance, she describes in detail how a rope was laid out and knotted to assist in the equitable division of land--she doesn't tell you to try it, but the detail and illustrations are clear enough to allow you do so, albeit on a smaller scale.

The illustrations are 2 color (black and white with red), and are especially useful in the later chapters.

Facts and theorems can be difficult to swallow. They often get gunked up in the throat, remain lodged in the esophagus, useless for nourishment or growth. But stories! Stories get gulped down with eagerness and along with them much useful knowledge is digested. Julia E. Diggins tells the compelling story of geometry in String, Straight-Edge, and Shadow. Written for children, it would be beneficial to anyone interested in learning geometry.

"They used the string to trace a circle, to lay off a right angle, to stretch a straight line.
They used as a straightedge anything else with which they could draw a straight line.
They came to realize that shadows are the sun's handwriting upon the earth to tell the
secrets of order in the universe."

Diggin's story would be a great stand-alone read; individual chapters, however, could supplement studies of Mesopotamia, Egypt, Babylon, or Greece. The solutions that geometry offers are told in the context of the problems people faced. In the question of ancient property rights and surveying farmer's fields, boundaries could not be casually (by freehand) drawn. They needed to know how to trace an accurate right-angle corner. The answer is in roper-stretchers, knotted rope, stakes...and the 3-4-5 right triangle. Corydon Bell's illustrations make geometry easier to understand. What a pleasant introduction to Thales, Pythagorus, Eudoxus, Archimedes and Eratosthenes.

This is a wonderful book, filled with great stories and information. I have gotten it from the library and used it with my Montessori elementary class, and am searching for a copy of my own.