Who is Pythagoras? What is The Pythagoras Theorem?
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
PREFACE In the name of Allah swt., we could finish this report on time with no matterproblem. 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 andapplication of pythagoras theorem. Hopefully, this report can be useful in learning andteaching process. For sure we need developed critics and suggestions for our reports inthe future can be better. Bandung, 2 Oktober 2009 Writers
THE PYTHAGORAS THEOREM1. History of Pythagoras Theorem Pythagoras of Samos was a Greek philosopher responsible for importantdevelopments in mathematics, astronomy and the theory of music. He left Samosbecause of the tyrant who ruled there and went to southern Italy about 532 BC. Hefounded a philosophical and religious school in Croton that had many followers. Although the theorem now known as Pythagorass theorem was known to theBabylonians 1000 years earlier he may have been the first to prove it. Of his actual work nothing is known. His school practiced secrecy andcommunalism making it hard to distinguish between the work of Pythagoras and that ofhis 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 asquare is not a rational multiple of its side. This result showed the existence of irrationalnumbers. Not only did this disturb Greek mathematics but the Pythagoreans own beliefthat whole numbers and their ratios could account for geometrical properties waschallenged by their own results.2. Proof of Pythagoras Theorem2.1. 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
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 Theorem3.1. In Math To kind of triangle3.1.1. Amblygon Triangle c²> a² + b²3.1.2. Right Triangle c²= a² + b²3.1.3. Acuted Triangle c²< a² + b²
3.2. In Physic At the past, when we were at senior high school, we studied about impedance inphysic. In impedance, we studied how to know the value of total resist in an electricitysystem. 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. Itcan be resist from inductor, or resist from capacitor) as Y-axes. And Z (impedance) asresultant vector. To know the value of impedance, we use formula of vector in physics. Theformula 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
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 othertwo sides. Pythagoras theorem can use anything, example : account sides in right triangle,for material impedance in physic, and so on.