Hidden harmonies : the lives and times of the Pythagorean theorem

__A__ squared plus __b__ squared equals __c__ squared. It sounds simple, doesn't it? Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, acclaimed authors Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the life of the Pythagorean theorem, from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons-not to mention the elusive Pythagoras himself, who almost certainly did not make the statement that bears his name. How can a theorem have more than one proof? Why does this one have more than two hundred-or is it four thousand? The Pythagorean theorem has even more applications than proofs: Ancient Egyptians used it for surveying property lines, and today astronomers call on it to measure the distance between stars. Its generalizations are stunning-the theorem works even with shapes on the sides that aren't squares, and not just in two dimensions, but any number you like, up to infinity. And perhaps its most intriguing feature of all, this tidy expression opened the door to the world of irrational numbers, an untidy discovery that deeply troubled Pythagoras's disciples. Like the authors' bestselling __The Nothing That Is__ and __Chances Are . . .__-hailed as "erudite and witty," "magnificent," and "exhilarating"-__Hidden Harmonies__ makes the excitement of mathematics palpable.

A squared plus b squared equals c squared. It sounds simple, doesn't it? Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, acclaimed authors Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the life of the Pythagorean theorem, from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons—not to mention the elusive Pythagoras himself, who almost certainly did not make the statement that bears his name.

How can a theorem have more than one proof? Why does this one have more than two hundred—or is it four thousand? The Pythagorean theorem has even more applications than proofs: Ancient Egyptians used it for surveying property lines, and today astronomers call on it to measure the distance between stars. Its generalizations are stunning—the theorem works even with shapes on the sides that aren't squares, and not just in two dimensions, but any number you like, up to infinity. And perhaps its most intriguing feature of all, this tidy expression opened the door to the world of irrational numbers, an untidy discovery that deeply troubled Pythagoras's disciples.

Like the authors' bestselling The Nothing That Is and Chances Are . . .—hailed as "erudite and witty," "magnificent," and "exhilarating"—Hidden Harmonies makes the excitement of mathematics palpable.

A squared plus b squared equals c squared. It sounds simple, doesn't it? Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, acclaimed authors Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the life of the Pythagorean theorem, from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons-not to mention the elusive Pythagoras himself, who almost certainly did not make the statement that bears his name. How can a theorem have more than one proof? Why does this one have more than two hundred-or is it four thousand? The Pythagorean theorem has even more applications than proofs: Ancient Egyptians used it for surveying property lines, and today astronomers call on it to measure the distance between stars. Its generalizations are stunning-the theorem works even with shapes on the sides that aren't squares, and not just in two dimensions, but any number you like, up to infinity. And perhaps its most intriguing feature of all, this tidy expression opened the door to the world of irrational numbers, an untidy discovery that deeply troubled Pythagoras's disciples. Like the authors' bestselling The Nothing That Is and Chances Are . . . -hailed as "erudite and witty," "magnificent," and "exhilarating"- Hidden Harmonies makes the excitement of mathematics palpable. A squared plus b squared equals c squared. It sounds simple, doesn't it? Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, who trace the life of the Pythagorean theorem from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons--not to mention the elusive Pythagoras himself. Why does this theorem have more than two hundred proofs--or is it four thousand? And it has even more applications than proofs: Ancient Egyptians used it for surveying, and today astronomers call on it to measure the distance between stars. It works not just in two dimensions, but any number you like, up to infinity. And perhaps most intriguing of all, it opened the door to the world of irrational numbers.--From publisher description. The mathematician as demigod Desert virtuosi Through the veil Rebuilding the cosmos Touching the bronze sky Exuberant life Number emerges from shape Living at the limit The deep point of the dream Magic casements. Presents a history of the famous relation "A squared plus B squared equals C squared" that assesses its contributors from da Vinci to the Freemasons while analyzing its numerous proofs and applications The untold history of the most famous relation in mathematics and what it illustrates about the nature of human reasoning