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Pythagoras And The Pythagorean Theorem

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Information about Pythagoras And The Pythagorean Theorem

Published on August 8, 2008

Author: acavis

Source: slideshare.net

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Pythagoras

History of Pythagoras Pythagoras was born in Samos, Greece around 570 BCE (it is difficult to pinpoint the exact year) He is often described as the first pure mathematician. Around 535 BCE, Pythagoras journeyed to Egypt to learn more about mathematics and astronomy

Pythagoras was born in Samos, Greece around 570 BCE (it is difficult to pinpoint the exact year)

He is often described as the first pure mathematician.

Around 535 BCE, Pythagoras journeyed to Egypt to learn more about mathematics and astronomy

History of Pythagoras (cont.) Pythagoras founded a philosophical and religious school/society in Croton (now spelled Crotone, in southern Italy) His followers were commonly referred to as Pythagoreans. The members of the inner circle of the society were called the “mathematikoi” The members of the society followed a strict code which held them to being vegetarians and have no personal possessions

Pythagoras founded a philosophical and religious school/society in Croton (now spelled Crotone, in southern Italy)

His followers were commonly referred to as Pythagoreans.

The members of the inner circle of the society were called the “mathematikoi”

The members of the society followed a strict code which held them to being vegetarians and have no personal possessions

History of Pythagoras (cont.) There is not much evidence of Pythagoras and his society’s work because they were so secretive and kept no records One major belief was that all things in nature and all relations could be reduced to number relations

There is not much evidence of Pythagoras and his society’s work because they were so secretive and kept no records

One major belief was that all things in nature and all relations could be reduced to number relations

Pythagoras and Music Pythagoras made important developments in music and astronomy Observing that plucked strings of different lengths gave off different tones, he came up with the musical scale still used today. Was an accomplished musician at playing the lyre

Pythagoras made important developments in music and astronomy

Observing that plucked strings of different lengths gave off different tones, he came up with the musical scale still used today.

Was an accomplished musician at playing the lyre

Pythagoras and Math Pythagoras made many contributions to the world of math including: Studies with even/odd numbers Studies involving Perfect and Prime Numbers Irrational Numbers Various theorems/ideas about triangles, parallel lines, circles, etc. Of course THE PYTHAGOREAN THEOREM

Pythagoras made many contributions to the world of math including:

Studies with even/odd numbers

Studies involving Perfect and Prime Numbers

Irrational Numbers

Various theorems/ideas about triangles, parallel lines, circles, etc.

Of course THE PYTHAGOREAN THEOREM

The Theorem: The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other 2 sides (legs) a 2 + b 2 = c 2 But what does it mean???

The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other 2 sides (legs)

a 2 + b 2 = c 2

But what does it mean???

Pythagorean Theorem

It’s Uses Determine side length of triangles Height, distance of objects The Distance Formula Range finding

Determine side length of triangles

Height, distance of objects

The Distance Formula

Range finding

Real World Uses Architecture, Engineering, Surveying CAD (Computer Aided Drafting) Military Applications Cartography (Map-Making/Directions)

Architecture, Engineering, Surveying

CAD (Computer Aided Drafting)

Military Applications

Cartography (Map-Making/Directions)

Example Problems (1 of 2) Find the measure of C in the triangle above: a 2 + b 2 = c 2 6 2 + 8 2 = C 2 36 + 64 = C 2 100 = C 2  100 =  C 2 so 10 = C

Find the measure of C in the triangle above:

a 2 + b 2 = c 2

6 2 + 8 2 = C 2

36 + 64 = C 2

100 = C 2

 100 =  C 2 so 10 = C

Example Problems (2 of 2) Find the measure of C in the triangle above: a 2 + b 2 = c 2 5 2 + 12 2 = C 2 * 25 + 144 = C 2 * 169 = C 2 *  169 =  C 2 so 13 = C

Find the measure of C in the triangle above:

a 2 + b 2 = c 2

5 2 + 12 2 = C 2

* 25 + 144 = C 2

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