Re: 1^2 =3, Discovered
- From: "Anthony A. Aiya-Oba" <aaiyaoba@xxxxxxxxxxxx>
- Date: Sun, 11 Nov 2007 02:58:00 EST
Congratulations Brian Quincy Hutchings, for opening the door to 1^2 = 3. Your analogy is very useful.
I have indicated on this thread that the solution to 1^2=3,is resident in the geometry of the isosceles structure of natural numbers, as in the new theorem:
Natural Number Isosceles Triple Theorem:
"Every natural number is a base of an isosceles triplet, whose total sum is square of the base(the number)."
Hence,
1 is (1, 1, 1) = (1 + 1 + 1) = 3 = 1^2
2 is (2, 1, 1) = (2 + 1 + 1) = 4 = 2^2
3 is (3, 3, 3) = (3 + 3 + 3) = 9 = 3^2
4 is (4, 6, 6) = (4 + 6 + 6) =16 = 4^2 . . .
Such that,
n^2 = 2(n^2 - n)/2 + n
Where n, is any possible natural number as can be seen above. -Aiya-Oba.
.
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