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# I found a new theorem!

saratdear
Well, kind of.

It came to me somehow, and although it isn't anything path breaking, anything somebody couldn't discover themselves, and which I am not sure somebody has already discovered, I present it here:

The theorem, which shall be known henceforth as Sarat's theorem of square roots ( Copyrighted to me, of course)

The square root of a number is the product of its cube root and the square root of the cube root.

Mathematically, x^1/2 = [x^1/3*(x^1/3)^1/2]

It's easy to prove:

Take the RHS : x^1/3*x^1/6 = x^(1/3+1/6) = x^1/2

Eg : Square root of 64 ( 8 ) = Cube root of 64(4)*Square root of 4(2)

Sarat
Stubru Freak
Like you said, it's easy to prove, and you could do it for a lot of fractions. Probably someone thought of that already. So it's not a spectacular find. But the proof is nice!
nilsmo

Theorem. The sum of a third and half of a third is one half.

since I understand exponentiation.

I remember in first grade I noticed this fact when we were folding papers into equal sections. To make half of a third (a sixth of a paper), we got a half of a paper and took off a third of a paper. I thought it was kind of cool the way the fractions worked out. (This is a true story, without sarcasm.)
Stubru Freak
It all depends on your mathematics education. I once thought that the fact that e^(i*pi) = -1 was spectacular, now it's as obvious as 1+1 = 2.
Another interesting thing that few people realise, but anyone could find out is that 1/i = -i. Most people don't believe it when they hear it, then they check it:
1*i / (i*i), they get i/(-1) = -i, and they go "hey, i never noticed".
saratdear
 Stubru Freak wrote: It all depends on your mathematics education. I once thought that the fact that e^(i*pi) = -1 was spectacular, now it's as obvious as 1+1 = 2. Another interesting thing that few people realise, but anyone could find out is that 1/i = -i. Most people don't believe it when they hear it, then they check it: 1*i / (i*i), they get i/(-1) = -i, and they go "hey, i never noticed".

Well that last bit I didn't know either. Thanks for sharing that.
guissmo
That's cool. It's kind of a law of exponents thing.
Keep on discovering. Who knows you might find something no one's ever found yet.
nilsmo
 Stubru Freak wrote: It all depends on your mathematics education.

Yup, it's all a matter of digesting new concepts. The human capability to learn; that is, our capability of making something someone worked on for a long time obvious just by basically reading a little bit, is amazing.

guissmo, in order to find something interesting that's new, one would need to delve into other areas of math. High school math is pretty well understood by a lot of people by now.
iman
It's basically the law of exponents. But beware of negative numbers.
Flarkis
if u pump this through a CAS (computer algebra system) and ask it to simplify, it simplifies the other side. Since it can be simplified it is hardly a new theorem.
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