Julia E. Diggins - String, Straight-edge and Shadow: The Story of Geometry

Nowadays, people build bridges that span the Golden Gate or the Firth of Forth. They make planes that go six times faster than the speed of sound, submarines that circle the globe without surfacing, missiles that reach outer space. They drill oil wells deeper than the height of Mount Everest. They have harnessed the power of the tiny atom, and placed people in orbit around the earth. But behind these modern wonders lies a long history packed with beauty, adventure and struggle.

Through the ages, people have searched to find the secrets of the universe. As these secrets were learned, they were written down in mathematical symbols. Today the search for secrets goes on: the mystery of the universe is still unfolding. Even the huge telescope at Mount Palomar is only a tiny window into a vast unknown, and when we finally travel to the moon and planets, there will be other worlds circling other stars for us to visit. In this unending search, mathematics has been a key from the very start.

A long, long time ago primitive humans observed the lines and curves and other forms of nature. They marvelled at them, and copied them as best they could.

Then, as need arose at the dawn of history, people learned to construct these lines, curves and forms accurately. They used the string to trace a circle, to lay off a right angle, to stretch a straight line. They used as a straight-edge anything with which they could draw a straight line. They came to realise that shadows are the suns handwriting upon the earth to tell the secrets of order in the universe.

By using these easy-to-find tools, the early civilisations learned how to tell time and direction. They designed their dwellings, temples and tombs, laid out their fields, and constructed irrigation ditches. They started to measure and record the apparent travels of the sun, moon and stars. They found ways of guiding their own travels across the sea and the trackless plains.

So, during thousands of years, the ancient peoples of the Near East built up a practical art that came to be known as geometry from geo, earth, and metria, measurement.

And then other peoples the Greeks turned from the tools to the rules.

Thinking people began to question and wonder why. They were still practical, but they were also interested in abstract rules about lines and curves and angles.

For centuries, many worked on these rules. Some studied beautiful geometric forms and tried to combine them with numbers into a pattern of the universe. One solved useful mechanical problems, such as how to raise water out of the hold of a leaky vessel. Others worked on useless puzzles, real brain-twisters. Out of their work came theoretical geometry.

The Greek geometers developed logical ways of thought. They discovered that the earth is a sphere, and they measured the girth of this sphere and the tilt of its axis. They discovered the properties of curves which they called the ellipse, the parabola, the hyperbola and the spiral curves that many centuries later were recognised as the paths of motion for bodies in space. They helped lay the foundations of modern science and invention.

But all that took an unbelievably long time and happened very, very slowly. Nowadays we live in an age of speed: new models of cars and mobile phones are perfected before the old ones are worn out or even paid for. So it may be hard to realise just how long it took to make those ancient discoveries.

For thousands of years, billions of humans have lived on the earth, and only a limited number of them have contributed to the development of geometry. Many of the facts are missing from the early part of their story. For the most faraway period, the records are gone and sometimes we have only a name or a legend.

So in this book, we shall try to tell a story instead only the highlights, the best characters, the dramatic incidents.

This will be the thrilling story of geometry in the ancient world, from the earliest prehistoric humans to the best-selling text in the history of mathematics, the Elements of Euclid. The story really is a thriller, with wonder and adventure and magic, and even a murder mystery!

As you read it, you will also see that it is a timeless tale, for the old discoveries are very much alive today. And all of them were made with just three wonderful tools: the string, the straight-edge and the shadow.