Pythagorean Theorem The best known mathematical proof is named for Pythagoras.

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Presentation transcript:

Pythagorean Theorem The best known mathematical proof is named for Pythagoras

Pythagorean Theorem The best known mathematical proof is named for Pythagoras Greek mathematician of about 500 B.C.E.

Pythagorean Theorem The best known mathematical proof is named for Pythagoras Greek mathematician of about 500 B.C.E. “if squares are drawn on the three sides of a triangle that has a right angle, the square on the longest side of the triangle (hypotenuse) will be equal in area to the other two squares put together..”

Pythagorean Theorem What did Pythagoras, Euclid, and President James A. Garfield have in common?

Pythagorean Theorem What did Pythagoras, Euclid, and President James A. Garfield have in common? They each proved the Pythagorean Theorem! (original proof/not one previously known, etc.) [Pythagoras in about 525 B.C.E., Euclid in 300 B.C.E., Garfield in 1876, while a member of the House of Representatives..]

Pythagorean Theorem What did Pythagoras, Euclid, and President James A. Garfield have in common? They each proved the Pythagorean Theorem! (original proof/not one previously known, etc.) In 1940, a book was published with 370 different proofs! Many more are known today!

Pythagorean Theorem Proof Consider a right triangle with side lengths a and b and hypotenuse c.

Pythagorean Theorem Proof Consider a right triangle with side lengths a and b and hypotenuse c. At this point we don’t know what the relation among a, b, and c is.

Pythagorean Theorem Proof Consider a right triangle with side lengths a and b and hypotenuse c. At this point we don’t know what the relation among a, b, and c is. The only fact we can extract is that the area of this triangle is ab/2.

Pythagorean Theorem Proof How can this figure be used to prove the Pythagorean Theorem?

Pythagorean Theorem Proof How can this figure be used to prove the Pythagorean Theorem? Hint: How can we express the area of the interior square? How else can we think of the area of the interior square?

Alternative Proof of the Pythagorean Theorem How can this figure be used to prove the Pythagorean Theorem?

Alternative Proof of the Pythagorean Theorem How can this figure be used to prove the Pythagorean Theorem? Hint: How can we express the area of the interior square? How else can we express it?

Pythagorean Theorem Consider the problem of getting a circular tabletop with a diameter of 7.5 feet through a doorway with a height of 7 feet and a width of 3 feet.

Pythagorean Theorem Consider the problem of getting a circular tabletop with a diameter of 7.5 feet through a doorway with a height of 7 feet and a width of 3 feet. Is this possible?

Pythagorean Theorem Consider the problem of getting a circular tabletop with a diameter of 7.5 feet through a doorway with a height of 7 feet and a width of 3 feet. Is this possible? How can you solve it?