This document discusses the Pythagorean theorem. It provides a brief history of Pythagoras and his contributions to mathematics. It then presents two proofs of the Pythagorean theorem - using the area of squares and the area of triangles. Finally, it discusses applications of the theorem in mathematics and physics, such as determining if a triangle is right, acute, or obtuse and calculating impedance in electrical systems.

1. THE PYTHAGORAS THEOREM
This report is made to complete
our english presentation
Group 5 :
1. Panji Wiraldy Hasibuan (0907065)
2. Nuni Yustini (0902294)
3. Poppy Diara (0900687)
4. Rena Ernawati (0902126)
5. Nilah Karnilah (0908130)
6. Dwi Endah (0900779)
INDONESIA UNIVERSITY OF EDUCATION
2009-2010

2. PREFACE
In the name of Allah swt., we could finish this report on time with no matter
problem.
We would to say thank you to Mr. Suharno who has teached us in english class.
This report is focus about history of pythagoras,proof of pythagoras theorem and
application of pythagoras theorem. Hopefully, this report can be useful in learning and
teaching process. For sure we need developed critics and suggestions for our reports in
the future can be better.
Bandung, 2 Oktober 2009
Writers

3. THE PYTHAGORAS THEOREM
1. History of Pythagoras Theorem
Pythagoras of Samos was a Greek philosopher responsible for important
developments in mathematics, astronomy and the theory of music. He left Samos
because of the tyrant who ruled there and went to southern Italy about 532 BC. He
founded a philosophical and religious school in Croton that had many followers.
Although the theorem now known as Pythagoras's theorem was known to the
Babylonians 1000 years earlier he may have been the first to prove it.
Of his actual work nothing is known. His school practiced secrecy and
communalism making it hard to distinguish between the work of Pythagoras and that of
his followers. His school made outstanding contributions to mathematics.
Pythagoreans believed that all relations could be reduced to number relations.
This generalization stemmed from observations in music, mathematics and astronomy.
The most important discovery of this school was the fact that the diagonal of a
square is not a rational multiple of its side. This result showed the existence of irrational
numbers. Not only did this disturb Greek mathematics but the Pythagoreans' own belief
that whole numbers and their ratios could account for geometrical properties was
challenged by their own results.
2. Proof of Pythagoras Theorem
2.1. Using Square Area
square area ABCD = (a + b)2 = a2 + 2ab + b2
square area EFGH = c2
we can get equalities :
a2 + 2ab + b2 = c2 + 4
a2 + 2ab + b2 = c2 + 2 ab
a2 + 2ab + b2 – 2ab = c² + 2ab - 2ab
a2 + b2 = c2

4. 2.2. Using Triangle Area
ABC = DBA =DAC
AB.AB = BD.DC and AC.AC = DC.BC
AB. we can get equalities :
AB + AC.AC = BD.DC + DC.BC
AB2 + AC2 = BD.BC + BC.DC
AB2 + AC2 = BC ( BD + DC )
3. The Application of Pythagoras Theorem
3.1. In Math
To kind of triangle
3.1.1. Amblygon Triangle
c²> a² + b²
3.1.2. Right Triangle
c²= a² + b²
3.1.3. Acuted Triangle
c²< a² + b²

5. 3.2. In Physic
At the past, when we were at senior high school, we studied about impedance in
physic. In impedance, we studied how to know the value of total resist in an electricity
system. In an electricity system, usually there were so many resist; resist from resistor,
resist inductor, or resist from capacitor.
If we draw them into axes of coordinates, it will be:
Z2+R2=X2
There is R (resist from resistor) as X-axes. X (resist from the other sources. It
can be resist from inductor, or resist from capacitor) as Y-axes. And Z (impedance) as
resultant vector.
To know the value of impedance, we use formula of vector in physics. The
formula is: Z2 = R2 + X2
Actually, this formula is based on Pythagoras formula. Because at the picture,
there are 3 vectors; R, X, and Z. And they make a form of right triangle with Z
(impedance) as hypotenuse. So, we can use Pythagoras theorem. And the formula is:
Z2= R2 + X2

6. CONCLUSION
Pythagoras theorem was founded by a greek philosopher, named is Pythagoras.
In a right triangle square of hypotenuse is equal to the sum of squares of other
two sides.
Pythagoras theorem can use anything, example : account sides in right triangle,
for material impedance in physic, and so on.