Oreški Ivana 779 Osijek 2010.. an Ionian Greek philosopher and founder of the religious movement...

Oreški Ivana779

Osijek 2010.

an Ionian Greek philosopher and founder of the religious movement called Pythagoreanism

developed mathematics, astronomy, and music

best known for the Pythagorean theorem,which bears his name

first introduced by Babylonian 1000 years earlier before Pythagoras did that

proved byPythagoras

created chaos in ancient Greece

a relation in Euclidean geometry among the three sides of a right triangle 

Pythagoras explains the theorem by demonstrating a right triangle

If and only if we have a right-angledtriangle then the square of the hypotenuse is equal to the sum of the squared sides

In terms of areas:

PYTHAGOREAN TRIPLES

A Pythagorean triple has three positive integers: a, b, c.

Such a triple is commonly written (a, b, c) The following is a list of primitive

Pythagorean triples with values less than 50:(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41

PYTHAGOREAN TRIGONOMETRIC IDENTITY

The sine: The cosine:

From that it follows:

This relation between sine and cosine sometimes is called the fundamental Pythagorean trigonometric identity.

The main use of Pythagorean theorem is trigonometry:calculating :

height of triangles, diagonals of square, space diagonals of cube angle values of each triangle

Projecting buildings,distance measurement

John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?

Answer:

c2 = a2 + b2

c2 = 62 + 82

c2 = 36 + 64

c2 = 100

c = √100

c = 10

The distance from school to home is 10 blocks.

A 13 meter ladder is placed 5 meters away from a wall. The distance from the ground straight up to the top of the wall is 13 meters. Will the ladder reach the top of the wall?

Answer:

c2 = a2 + b2

132 = 52 + b2

169 = 25 + b2

b2 =169 - 25

144 = b2

b = √144 = 12

The ladder will never reach the top since it will only reach 12 meters high from the ground yet the top is 13 meters high.