B

ook

info to help with dis

#3

When we look at and touch the objects in our world, we encounter the physical form and spatial

relationships of matter. We see shapes

—

some interesting, some ordinary, and some attractive.

Geometry is the study of those shapes. Geometric

relationships give us a basic sense of order,

coherence, and beauty. The lines, circles, and spatial patterns of the physical world give depth to our

intuition about shape and enable us to develop insights and recognize patterns in things geometric.

Geomet

ry captures the structure and nuances of our physical reality.

4.1 PYTHAGORAS AND HIS HYPOTENUSE

How a Puzzle Leads to the Proof of One of the Gems of Mathematics

I'm very well acquainted, too, with matters mathematical, I understand equations, both t

he simple and

quadratical, About Binomial Theorem I'm teeming with a lot of news, With many cheerful facts about

the square of the hypotenuse.

WILLIAM S. GILBERT, THE PIRATES OF PENZANCE

It can't be wrong when it looks so right!

Some geometric relationsh

ips are so profound that they have changed the shape of civilization

—

both

literally and figuratively. Perhaps the best known and most fundamental theorem in all of mathematics

is the Pythagorean Theorem. While we have seen this basic fact in high school, h

ere we examine it more

deeply.

The Pythagorean Theorem.

In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the

lengths of the other two sides.

This theorem and its proof form one of the classical intel

lectual accomplishments of humankind,

comparable to a work of Shakespeare. The proof presented here, which was discovered by the Indian

Book info to help with dis#3

When we look at and touch the objects in our world, we encounter the physical form and spatial

relationships of matter. We see shapes—some interesting, some ordinary, and some attractive.

Geometry is the study of those shapes. Geometric relationships give us a basic sense of order,

coherence, and beauty. The lines, circles, and spatial patterns of the physical world give depth to our

intuition about shape and enable us to develop insights and recognize patterns in things geometric.

Geometry captures the structure and nuances of our physical reality.

4.1 PYTHAGORAS AND HIS HYPOTENUSE

How a Puzzle Leads to the Proof of One of the Gems of Mathematics

I'm very well acquainted, too, with matters mathematical, I understand equations, both the simple and

quadratical, About Binomial Theorem I'm teeming with a lot of news, With many cheerful facts about

the square of the hypotenuse.

WILLIAM S. GILBERT, THE PIRATES OF PENZANCE

It can't be wrong when it looks so right!

Some geometric relationships are so profound that they have changed the shape of civilization—both

literally and figuratively. Perhaps the best known and most fundamental theorem in all of mathematics

is the Pythagorean Theorem. While we have seen this basic fact in high school, here we examine it more

deeply.

The Pythagorean Theorem.

In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the

lengths of the other two sides.

This theorem and its proof form one of the classical intellectual accomplishments of humankind,

comparable to a work of Shakespeare. The proof presented here, which was discovered by the Indian