Pythagroas triples.
Date Submitted: 11/21/2002 04:02:15
My formulas are
1.2n + 1
2.2n2 + 2n
3.2n2 + 2n + 1
4.4n2 + 6n + 2
5.2n3 + 3n2 + n
To get these formulas I did the following
1.Take side 'a' for the first five terms 3, 5, 7, 9, 11. From these numbers you can see that the formula is 2n + 1 because these are consecutive odd numbers (2n + 1 is the general formula for consecutive odd numbers) You may be able to see the formula if you draw a graph
2.From looking at my table of results,
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you equate these equations to 0 you get
a2 - 3d2 - 2ad = 0
Change a to x
x2 - 3d2 - 2dx = 0
Factorise this equation to get
(x + d)(x - 3d)
Therefore
x = -d
x = 3d
x = -d is impossible as you cannot have a negative dimension
a, a+d, a + 2d
Is the same as
3d, 4d, 5d
This tells us that the only Pythagorean triples are 3, 4, 5 or multiples of 3, 4, 5 e.g. 6, 8, 10 or 12, 16, 20 etc.
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