Thales of MiletusThales of Miletus““Father of Geometry”Father of Geometry”

Background on Thales

• Thales the "father of geometry," was a sort of Greek Benjamin Franklin.

• The known facts of his life are few. – He was a merchant. – He traveled extensively to the older centers of

civilization and learned much on his travels.– He is believed to have been the first to

experiment with electricity, the static kind in a piece of rubbed amber.

• Other than a scientist, Thales was well known as a philosopher.

• Plato told a story of Thales gazing at the night sky, not watching where he walked, and so fell into a ditch. The servant girl who came to help him up then said to him "How do you expect to understand what is going on up in the sky if you do not even see what is at your feet?"

Background on Thales

How High is the Pyramid?

• In the Land of the Nile-so the legend goes-Thales amazed and frightened his guides by telling them, as if by magic, the exact height of the Great Pyramid.

• The story is worth reviewing in some detail. It shows us Thales' new geometry in action, and enables us to compare it with the old Egyptian kind.

Naturally, Thales' visit to Egypt was not complete without a sightseeing trip to the desert at Giza, to see the three pyramids

and the Sphinx half-buried in the sand nearby.

In 6oo B.C. the pyramids were already about 2000

years old.

Thales engaged guides and took a Greek friend along. When they reached those mighty monuments, the guides seemed proud to boast that the Egyptian pyramids had been standing when the ancestors of the Greeks were "long-haired barbarians."

Thales stood for a time admiring the most gigantic of the tombs: the Great Pyramid of Cheops, which covers more than twelve acres! He looked tip the great slope, rising to a peak against the cloudless Egyptian sky, and noticed how the brilliant sunlight hit directly against one face and drew a pointed shadow over the desert sands. Then he asked his celebrated question…

"How high is this pyramid?"

The guides were dumbfounded and got into a lengthy discussion. No sightseer had ever asked them that before.

Visitors were always content with the dimensions of the pyramid's square base-252 paces along each side. Sometimes the Greek tourists didn't believe that, and had to pace it off for themselves. But this one wanted to know something more: the height.

Nobody knew the height of the Great Pyramid.

Perhaps, long ago, the builders had known. But by the present dynasty, everyone had forgotten.

And, of course, you couldn't measure it. A rope dragged all the way up to the top (and who was going to risk that?) would just give the length of the sloping side. They couldn't think of any way to find out the height, short of boring a hole from the top of the pyramid down to its base. But that was impossible!

While the argument went on, Thales and his friend had been walking around quietly, staying close to

the pyramid's shadow, where it was cool. Suddenly the Thales hallooed...

"Never mind my question! I know the answer. The Great Pyramid at Giza rises to a height of

160 paces!" Terrified, the guides flung themselves on their

faces before Thales, fully convinced that he was a magician.

To be sure, Thales did not get the answer by magic. he simply measured two shadows on the

sand, and then used an abstract rule from his new kind of geometry.

Where others saw only the men and the structures, and their shadows in the hot sunlight, Thales saw abstract right triangles as well! All these triangles

were made the same way: an upright object, a pointed obelisk or white-clad Egyptian; a slanting sun ray that hit the top of the object; and the flat

shadow that it cast on the ground. But Thales saw far more than that. He saw the

motion of the lengthening shadows. Surely others had seen it too, as they sat waiting, but he saw it

with an "X-ray eye."

For as Thales watched, he noticed something truly remarkable. All tile shadows changed together, in length

and direction.

At first, they were all half as long as the objects that cast them. Later, they were all the same length as the objects.

Later still, the shadows were all twice as long as the height of the objects.

Probably many men had observed something like that, over the centuries. But the lonian traveler tried to find a constant

pattern.

He had to prove it was always so, and to find out why. And he did!

The tale traveled far and wide, so far and wide that it has

come down to us after 2500 years. And the story has even

more meaning today.

For the Great Pyramid was a sturdy monument to ancient

practical geometry.

But Thales' shadow-reckoning of its height was an even more

stalwart monument in the development of reasoning.