Pythagoras was an ancient Greek philosopher, mathematician and founder of the Pythagorean brotherhood in the 6th century BCE. He established an academy in Croton, Italy that formulated principles influencing later thinkers like Plato and Aristotle. Pythagoras is best known for the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The theorem is fundamental to mathematics and is used today to determine viewing sizes of televisions and identify right triangles through pythagorean triplets.

1. Pythagoras, (born c. 570 bce, Samon, Ionia[Greece]—died c. 500–490 bce, Metapontum, Lucanium [Italy]), Greek
philosopher, mathematician, and founder of the Pythagoreanbrotherhoodthat, althoughreligious innature, formulated
principles that influencedthe thought ofPlatoandAristotle and contributedto the development of mathematics and
Western rationalphilosophy. Pythagorasemigratedto southernItalyabout 532 bce, apparentlyto escape Samos’s
tyrannicalrule, andestablished his ethico-politicalacademyat Croton(nowCrotone, Italy).. Ina right triangle the area of
the square on the hypotenuse is equal to the sumof the areas of the squares ofits remainingtwo sides. (Lengthof the
hypotenuse)2 = (one side)2 + (2nd side)2.. 1The fourth approachstarts withthe same four triangles, except that, this time,
theycombine to forma square withthe side (a+b) anda hole withthe side c. We cancompute the area of the bigsquare
in two ways. Thus simplifyingwhichwe get the neededidentity. (a + b)2 = 4·ab/2 + c .2This proofis a variationon#6. On
the small side AB adda right-angled triangle ABDsimilar to ABC. Then, naturally, DBCis similar to the other two. From
area(ABD) + area(ABC) = area(DBC), AD = AB2/ACand BD= AB·BC/ACwe derive (ab2/AC)·AB+ AB·AC= (AB·BC/AC)·BC.
DividingbyAB/ACleads to AB2 + AC2 = BC2.3Draw a circle withradius c and a right triangle withsidesa andb as shown. In
this situation, one mayapplyanyof a few well knownfacts. For example, inthe diagram three points F, G, H located onthe
circle formanother right triangle withthe altitude FKof length a. Its hypotenuse GH is split inthe ratio (c+b)/(c-b). So, as in
Proof #6, we get a2 = (c+b)(c-b) = c2 - b2…Dailylife makesuse of the Pythagorean theorem invarious ways, such as
determining the viewing size of a television, which is sometimes a factor usedin purchasing decisions. Giventhe length
and height of the screen, the diagonal viewingarea canbe determined withthe theorem…When the side lengths ofa
right triangle satisfythe pythagorean theorem,these three numbers are known as pythagorean triplets or triples.
The mostcommon examples ofpythagorean triplets are.. 3,4,5 triangles.a 3,4,5 triplet simplystands for a
triangle that has a side oflength 3, a side of length 4 and a side of length 5. If a triangle has these side lengths,
then it MUST be a right triangle. 8, 15, 17 triangles 5,12, 13 righttriangles7,24,25 righttriangles.