Perimeter Odds
Perimeter = a + b + c
a= 2n + 1
b= 2n2 + 2n
c= 2n2 + 2n + 1
= 4n2 + 6n + 2
Proving that this formula is correct:
If I take n=3
= 4x9 + 18 + 2
= 36 + 18 + 2
= 56
So if you look along the odds table on n=3 the perimeter is 56 this proves my formulae is correct.
Perimeter Evens
Perimeter = a + b + c
a = 2n + 4
b = n2 + 4n + 3
c = n2 + 4n + 5
= 2n2 + 10n + 12
Proving my formulae is correct:
If I take n=3
= 18 + 30 + 12
= 60
Follow n=3 across on the evens table the perimeter says 60 my formulae is correct.
Odds Side c
c = b + 1
c = 2n2 +2n + 1
So from looking at the table and extending it, I have managed to come up with the conclusion that:
ODDS
a = 2n + 1
b = 2n2 + 2n
c = 2n2 + 2n + 1
Evens Table
From looking at this table straight away I can see that the even number 4 does not fit in the table. This is because a, is bigger than b so it is not a Pythagorean triple.
From looking at this table I can see c = b + 2 and
n + 2 x a = b + c also I have noticed, if you look at c starting down from 10 it is 3x6, 4x8, 5x10 ect.
Area - Odds
Area- a x b
2
(2n+1) (2n2 + 2n)
2
= 4n3 + 4n2 + 2n2 + 2n
2
= 4n3 + 6n2 + 2n
2
= 2n3 + 3n2 + n
To prove this is correct I will take n=3:
=2 x 32 + 3 x 32 + 3
=54 + 27 + 3
= 84
Follow n=3 across to area on the odds table and its 84 this proves my formula is correct.
