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Looking for Pythagoras

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by

Michelle Chambers

on 11 February 2014

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Transcript of Looking for Pythagoras

What is the Pythagorean theorem?
It allows us to find the length of the third side on any right triangle!
Looking for Pythagoras
What are Triples?
Triples are sets of 3 whole numbers that satisfy the Pythagorean Theorem.
... But who was Pythagoras?
Proofs
If you have a right triangle...
a
b
c
...Then a + b = c
2
2
2
( or the converse: if a + b = c , then the triangle is a right triangle)
http://2.bp.blogspot.com/_jeSuLa5ZscU/TDenS0PBd-I/AAAAAAAAlp8/A089efUzSu4/s1600/pythagoras.JPG
Born: 569 BC, in Samos, Greece
Died: around 500 BC
Nickname: The first Pure Mathematician
Pythagoras led a following called the "Mathematikoi", who lived together in a secret society to study Math.
Among other things, they believed in vegetarianism and were allowed no personal possessions.
... They also once drowned a man who tried to reveal to the public that the square root of 2 is irrational.
http://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/A_First_Letter_Square_root_of_2.svg/216px-A_First_Letter_Square_root_of_2.svg.png.
a
b
c
a
c
b
a = 3, b= 4, c = 5
a + b = c
3 + 4 = 5
2
2
2
2
2
2
9 + 16 = 25
25 = 25
+
=
a + b = c
3 + 4 = 5
5 + 12 = 13
2
2
2
2
2
2
2
2
2
The Leafed Pythagorean Tree
Fractal Seed
Stage 1
Stage 2
Stage 3
Stage 4
Can we use this Theorem in Real Life?
We can find the hight of this pyramid...
...or the length of this crane...
...or even the length of this ramp!
... or the sides of this corner...
There are even Pythagorean calculators that can find the third number when two parts of a triple are given!
We can memorize triples, because we can then sometimes know side lengths without having to calculate squares and square roots.
http://www.roycerealestate.net/sites/default/files/sidebar-images/29-Calculator-Jumbo.jpg.
http://s1.hubimg.com/u/6876726_f520.jpg.
http://img.ehowcdn.com/article-new-thumbnail/ehow/images/a07/gn/bp/projects-pythagoras-theorem-middle-schools-800x800.jpg.
http://i1.ytimg.com/vi/fH-5KszlRU0/hqdefault.jpg.
http://s2.hubimg.com/u/6876663_f520.jpg.
... and it just keeps going!
1/2 3.14r + 1/2 3.14r = 1/2 3.14r
2
2
2
1/2 (3.14 x 1.5 ) + 1/2 (3.14 x 2 ) = 1/2 (3.14 x 2.5 )
2
2
2
1/2 (7.065) + 1/2 (12.56) = 1/2 (19.625)
3.5325 + 6.28 = 9.8125
9.8125 = 9.8125
The End
Full transcript