What is the square root of pi?

Me ^

[lonevoice]

You forgot to carry the 1.

I don't think he forgot, I think he did it on purpose. Never turn your back on someone who could write that post.

[supercat]

The square root of -1 is i, and the square root of any negative number is simply i* the square root of the absolute value of the number that you are taking the square root of.

Calling the square root of -1, i is just convention, but the square root of i can be derived mathematically as +/-(i+1)*sqrt(2)/2. I'm sure you knew that, but others here may not.

[Nogbad]

e and pi are the only numbers I know to be transcendental

Any number of the form Alpha^Beta is transcendental,
if Alpha and Beta are non-rational algebraic numbers.
This theorem was proven in 1926 by Gelfond.

[WIMom]

Imaginary that! ....sorry BADJOE, there is, well actually there are 2.

[seams2me]

There is no square root for pi. You always cut pi in triangles, therefore there cannot be a square root.

All your pi are belong to us.

[Nogbad]

Of course, to prove the transcendentality of pi,
you have to prove the transcendentality of e first.
Proving this for e is tough.
Proving this for pi (from the results from e) is extremely tough.

Not so tough, David Hilbert did it in two pages,
one page for e, one page for pi.
I believe it was his first published paper.

[Bill Rice]

"Never turn your back on someone who could write that post."

ROFLMAO! Nevermind the math logic, I'm throwing popcorn over all the different subscripts and text sizes in HTML!

[WIMom]

Click here to learn about imaginary numbers

An imaginary number is a quantity of the form ix, where x is a real number and i is the positive square root of -1. The term "imaginary" probably originated from the fact that there is no real number z that satisfies the equation z² = 1. But imaginary numbers are no less "real" than real numbers. The quantity i is called the unit imaginary number. In engineering, it is denoted j, and is known as the j operator.

The unit imaginary number has some intriguing properties. For example:

(-i)² = -1
but -i is different from i

i³ = i²i = (-1)i = -i

i⁴ = i²i² = (-1)(-1) = 1

i⁵ = i³i² = (i³)(-1) = (-i)(-1) = i

iⁿ = i^(n-4)
when n is a natural number larger than 4

As i is raised to higher natural-number powers, the resultant cycles through four values: i, -1, -i, and 1 in that order. No real number behaves like that!

The set I of imaginary numbers consists of the set of all possible products iw, where w is an element of the set R of real numbers. Therefore, the sets I and R are in one-to-one correspondence. The sum v + iw of a real number v and an imaginary number iw forms a complex number. The set C of all complex numbers corresponds one-to-one with the set R ? R of all ordered pairs of real numbers. The set C also corresponds one-to-one with the points on a geometric plane.

Imaginary and complex numbers are used in engineering, particularly in electronics. Real numbers denote electrical resistance, imaginary numbers denote reactance, and complex numbers denote impedance.

[Tennessee_Bob]

Better yet, let's bomb France with Roblochon!

[185JHP]

That's one of the things about hard science - they get to say "It doesn't matter - don't worry your head about it", and "define away" problems like the one you post. But I'm glad we got 'em - I like my 32-valve V8.

[WIMom]

I watched the Matrix tonight on television.......

[WIMom]

AAAAARRRRGGGGGHHHHHH! I don't EVER want to do one of those again!

[supercat]

Real numbers denote electrical resistance, imaginary numbers denote reactance, and complex numbers denote impedance.

What's particularly useful is that Ohm's law holds with complex numbers. If one has a linear circuit (a circuit consisting of nothing but resistors, caps, inductors, and 'perfect' amplifiers) and wishes to see how it will behave when driven at a particular frequency, after computing the reactances of all the caps and inductors at that frequency one can easily figure the voltage at any point in the circuit or current through any wire. If a voltage is, e.g., 3+(3i) volts, that means that there will be a sine wave there with an amplitude of about 4.2 [sqrt(3^2+3^2)] volts, whose phase leads that of the driving signal by 45 degrees.

[WIMom]

Yes, it is very useful...for electrical engineers. Luckily, I only had to take 2 semesters of those courses. LOL! I'll stick with the interesting manufacturing processes and machines *VBG*

[RaceBannon]

That's easy. Radical PI.

Thank you.

[Excuse_Me]

Actually looking over the code, I realize that even though I was calculating Pi to 2000 places, I was truncating it to 1000 places during the square root calculation. So I modified the program and ran it again, this time truncating the output to 1000 places, but leaving all calcs at 2000. There was a minor change. the last 3 digits changed from 670 to 692. So, I do think that with that change, the answer is now accurate for actual SQRT(Pi) to 1000 places.

[Always Right]

As I recall from my college days, a googleplex was 10 raised to 100th power.

10 raised to the 100th power is a 1 with a hundred zeros, or otherwise simply a google. A googleplex is 10 raised to the google power, or in short, 10 to the 10th to the 100th.

[poet]

It says blueberry pie is best eaten with fingers

[gjenkins]

That my friend is the TAMU campus!

[TheCPA]

Nobel prizes are no longer tax free.