Story of the Greeks and geometry

Our first topic of discussion is geometry, which is the study of shapes (lines, circles, triangles, squares, etc.)

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In the ancient western world, the Greeks were fascinated by shapes in nature, and spent a great deal of time studying them. As a result of their studying they came to believe that there were two worlds- the natural world in which we live, and the mathematical world- what they called the 'world of perfect forms'- which co-existed with this world.

According to the Greeks, every object in the natural world had its counterpart in the world of perfect forms. The important difference was that, in the world of perfect forms, that object was perfect. Consider the example of a knife blade. In the natural world, the knife blade might be pretty straight, but still a bit crooked, and it might be pretty sharp, but still a bit dull. In the world of perfect forms, however, the knife blade would be perfectly straight, and infinitely sharp- so sharp and thin that it could cut through any object.

The Greeks then came up with the idea of mathematical shapes- perfect shapes that existed in the world of forms- that would correspond to familiar shapes in our natural world

Objects in Natural World	Object in Mathematical World	Picture of Mathematical Object
sun, surface of a round lake, doorknob	circle (perfectly round)
road, knife edge, paper edge	line (perfectly straight, perfectly thin)
speck of dust, point of a needle	point ( perfectly small- no size at all- just a point in space)	.

When talking about the natural world, the Greeks might say that the sun was a circle in the sky, but by this they meant that the shape of the sun corresponded with the perfect circle shape that only existed in the world of perfect forms.