Facts about Pythagoras

• He lived in southern Italy during the 6th century B.C

• He was considered the 1st true mathematician

• He was 1st to teach that the Earth was a sphere that revolves around the Sun

• He proved the Pythagoras Theorem (named after him)

Facts about the Theorem

• Named after the Greek mathematician Pythagoras

• The Egyptian surveyors, the Chinese and Babylonians knew this rule already about 2000 BC, but they couldn’t prove it

• The theorem is important to the evolution of the Greek concept of number and the proof demonstrates how the Greeks used such proofs

a2+b2=c2

What is the Pythagoras Theorem?

“For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger square”

This is a more accurate way of showing the theorem as it doesn’t show a designated amount of squares

The Right Angle Triangle

• The longest side is called the hypotenuse (side c)

• The other sides (a and b) are called the legs

• Pythagoras developed a formula for finding the length of the sides on any right angle triangle

Proof

Applications

• The Pythagorean theorem has far-reaching uses in other fields (such as the arts), as well as practical applications

• The theorem is invaluable when computing distances between two points, such as navigation and land surveying

• Another important application is the design of ramps. Ramp designs for handicap-accessible sites and for skateboard parks are very much in demand

The Ladder Problem

A ladder leans against a second-story window of a house.

If the ladder is 25m long, and the base of the ladder is 7m from the house, how high is the window?

Ladder Problem Solution

• First draw a diagram that shows the sides of the right angle triangle

• Label the sides• Use a2 + b2 = c2

to find the missing side length

Ladd

er: 2

5mDistance from house: 7m

Heig

ht o

f wi n

dow

?

Ladder ProblemSolution

72 + b2 = 252

49 + b2 = 625b2 = 576b = 24m

How did you do?

a = 7m

c =

25m

b =

24

m

Conclusion

• The Pythagoras Theorem is one of the greatest mathematical breakthroughs and is a very significant discovery

• The Theorem is used in every-day life and therefore a very important theory

• It should be respected and learned by all people who want to be successful in life

Thank You

For

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