# Square root of minus one

sonhouse
Posers and Puzzles 27 Oct '07 13:46
1. wolfgang59
Mr. Wolf
05 Nov '07 12:45
Correct - rather nice I think.
2. Palynka
Upward Spiral
05 Nov '07 14:21
Originally posted by wolfgang59
Correct - rather nice I think.
I don't think it's as nice as the other result. After all, with i^i you have an answer that isn't complex so, in that sense, I find it an elegant result.

Of course, "nice" is not a mathematical term. ðŸ™‚
3. genius
Wayward Soul
05 Nov '07 15:56
Originally posted by Palynka
I don't think it's as nice as the other result. After all, with i^i you have an answer that isn't complex so, in that sense, I find it an elegant result.

Of course, "nice" is not a mathematical term. ðŸ™‚
What is nicer, n!=1x2x...xn or sqrt(2*Pi*n)*((n^n)/(e^n))?
4. Palynka
Upward Spiral
05 Nov '07 17:13
Originally posted by genius
What is nicer, n!=1x2x...xn or sqrt(2*Pi*n)*((n^n)/(e^n))?
What does that have to do with anything?

The answer to this second problem requires an expression that depends on i, while the first one has an answer defined in Real numbers. That's the difference.

+-(1 + i)/sqrt(2) doesn't seem much different than leaving it as sqrt(i).
5. genius
Wayward Soul
05 Nov '07 17:18
Originally posted by Palynka
What does that have to do with anything?

The answer to this second problem requires an expression that depends on i, while the first one has an answer defined in Real numbers. That's the difference.

+-(1 + i)/sqrt(2) doesn't seem much different than leaving it as sqrt(i).
the first looks nice, visually, while the second is much easier to see the value churned out, and easier to work with. They are approximatly equal, for large n.
6. Palynka
Upward Spiral
05 Nov '07 17:20
Originally posted by genius
the first looks nice, visually, while the second is much easier to see the value churned out, and easier to work with. They are approximatly equal, for large n.
I'm sorry, but I still don't understand what your point is...
7. genius
Wayward Soul
06 Nov '07 10:01
Originally posted by Palynka
I'm sorry, but I still don't understand what your point is...
Eessentially, that "nice" isn't a mathematical term...
8. Palynka
Upward Spiral
06 Nov '07 10:07
Originally posted by genius
Eessentially, that "nice" isn't a mathematical term...
No, but I think there is beauty in some mathematical results. And beauty is not a mathematical term, either.