Pythagorean theorem

Let's get started on the lesson the Pythagorean theorem

Pythagoras

Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy,and the theory of music. The theorem now known as Pythagorean theorem was know to the Babylonians 1000 years earlier but he may have been the first to prove it.
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Did you know .....?

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Chou pei suan ching

A Chinese astronomical and mathematical treatise called chou pei suan ching. (The arthimetical Classic of the Gnomon and the circular paths of Heaven) , possibly predating Pythagoras, gives a statement of a geometrical deminstration of the Pythagorean theorem.
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Real life examples using the Pythagorean theorem

1) what size tv should you buy? Mr James saw an advertisement of a tv in the newspaper where it is mentioned that the tv is 16 inches high and 14 inches wide. Calculate the diagonal length of its screen for Mr. James. By using Pythagoras theorem it can be calculated as ,

(16)2+(14)2=

256+196=c2

Radical 452=c

21inches approx =c

2)Finding the right sized computer. Mary wants to get a computer monitor for her desk which can a 22 inch monitor. She has found a monitor 16 inches wide and 10 inches high. Will the computer fit into Mary's cabin? Use Pythagoras theorem to find out.

(16)2 + (10)2 =

256 + 100 = c2

Radical 356 = c

18 inches approx = c

3) Buying a suitcase. Mr. Jerry wants to purchase a suitcase. The shopkeeper tells Mr. Jerry that he has a 30 inch of suitcase available at present at the height of the suitcase 18 inches. Calculate the actual length of this suitcase for Mr. Jerry using Pythagoras theorem. It is calculated this way.

(18)2 + (b)2 =

(B)2 = 900 _ 324 =

B =radical 576

=24 inches

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How to proof the Pythagorean trheorem

In mathematics, the Pythagorean theorem, also known as Pythagoras theorem, is a fundemetal relation in Euclidean geometry among the three sides of a right triangle. (It states that the square of the hypotenuse ( the side oppose to the right triangle) is equal to the sum of the squares of the other two sides.

The converse of the Pythagorean theorem

Pythagorean theorem converse.if the square of one side of a triangle is equal to the sum of the squares of the other two sides,then the triangle is a right triangle.

Some pictures about the lesson

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OTHER WAYS PROVING THE PYTHGOREAN THEOREM

Professor R. Smullyan in his book 5000 B.C. and other philosophical fantasies tells of an experiment he ran in one of his geometry classes. He drew a right triangle on the board with squares on the hypotenuse and legs and observed the fact that the square on the hypotenuse had a larger area than either of the other two squares.Then he asked,"suppose these three squares were made of beaten gold, and you were offered either the one large square or the two small squares. Which square would you choose?"Interestingly enough, about half of the class opted for the one large square and half for the two small squares. Both groups were equally amazed when told that it would make no difference
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