# Pythagoras' Theorem.

Essay by keyser_soze42High School, 11th grade September 2003

Pythagoras

Pythagoras' Theorem is a2 + b2 = c2. 'a' being the shortest side usually the adjacent 'b' being the middle length side usually the opposite and 'c' being the longest side always the hypotenuse. This theorem only works in 'Right angled triangles'.

The numbers 3, 4 and 5 satisfy the condition.

32 + 42 = 52

This is because 32 = 9 and 42 = 16, 9 + 16 = 25, and 52 = 25, therefore 32 + 42 = 52.

The numbers 5, 12 and 13 and 7, 24 and 25 also satisfy the condition.

52 + 122 = 132

52 = 25

122 = 144

132 = 169

25 (52) + 144 (122 ) = 169 (132 )

72 + 242 = 252

72 = 49

242 = 576

252 = 625

49 (72) + 576 (242) = 625 (252)

Perimeter (3, 4 and 5)

3 + 4 + 5 = 12

Area (3, 4, and 5)

ÃÂ½ x 3 x 4 = 6

Perimeter (5, 12 and 13)

5 + 12 + 13 = 30

Area (5, 12 and 13)

ÃÂ½ x 5 x 12 = 30

Perimeter (7, 24 and 25)

7 + 24 + 25 = 56

Area (7, 24 and 25)

ÃÂ½ X 7 X 24 = 84

From the first 3 terms I have noticed the following:

ÃÂ'a' increases by 2 in each term

ÃÂ'a' is equal to the term number multiplied by 2 then add 1

ÃÂthe last digit of 'b' is in a pattern 4, 2, 4

ÃÂthe last digit of 'c' is in a pattern 5, 3, 5

ÃÂthe square root of ('b' + 'c') = 'a'

ÃÂ'c' is always +1 to 'b'

ÃÂ'b' increases by 4 each term

ÃÂ('a' x 'n') + n = 'b'

From the...