## Welcome!

A spot for all things TestTube
Stargate38
Posts: 67
Joined: Thu Aug 15, 2013 3:06 pm
Location: Visible Universe
Contact:

### Re: Welcome!

Nice Forum! I came here after finding your Gravity Simulator, since I was searching for a simulator that has a variable gravity exponent. I was amazed at how r^1 worked. All objects have the same orbital period, but if there are more than 2 objects, one will be sent spiraling outwards, then after many orbits, come back in.

testtubegames
Posts: 1078
Joined: Mon Nov 19, 2012 7:54 pm

### Re: Welcome!

Welcome, Stargate38!

I had the same reaction to r^1 at first. I wasn't expecting anything strange, but suddenly we had closed orbits again! It took me a moment to realize why (r^1 is the force law for springs, hence the nice behavior)... but it was sure fun to relearn that fact through a virtual experiment. I'll have to go back and try it with three objects again, like you mentioned.

robly18
Posts: 413
Joined: Tue Jun 04, 2013 2:03 pm

### Re: Welcome!

For the record, it was me who suggested positive exponents
Convincing people that 0.9999... = 1 since 2012

19683
Posts: 151
Joined: Wed Jun 05, 2013 12:15 pm

### Re: Welcome!

Stargate38 wrote:Nice Forum! I came here after finding your Gravity Simulator, since I was searching for a simulator that has a variable gravity exponent. I was amazed at how r^1 worked. All objects have the same orbital period, but if there are more than 2 objects, one will be sent spiraling outwards, then after many orbits, come back in.
Welcome to the forums Stargate38!
I'm 19683.

I agree, the variable exponents on the gravity simulator are amazing!
r^1 is my personal favorite too. I love how objects always orbit elipticcally around the barycenter.
Binomial Theorem: ((a+b)^n)= sum k=0->k=n((n!(a^(n-k))(b^k))/(k!(n-k)!))

exfret
Posts: 585
Joined: Sun Jul 28, 2013 8:40 pm

### Hi

Hello! I am exfret. I've been here for a while, but I thought I'd just post into here just to officially say hi. Try out my brand new series of levels in the Velocity Raptor forums if you're interested!!!
Nobody ever notices my signature. ):

robly18
Posts: 413
Joined: Tue Jun 04, 2013 2:03 pm

### Re: Welcome!

I'm back.

I probably should've announced myself, but there. I went on a painful week without computer, no access to science of any kind except for my brain.

On the bright side, I got to work on mathemathics and I even found myself finding something new about imaginary exponents!

(the ending result was that -1^i = -1 meaning i is odd. Mind=blown)
Convincing people that 0.9999... = 1 since 2012

exfret
Posts: 585
Joined: Sun Jul 28, 2013 8:40 pm

### Re: -1^i

How'd you get this?
Nobody ever notices my signature. ):

robly18
Posts: 413
Joined: Tue Jun 04, 2013 2:03 pm

### Re: -1^i

exfret wrote:How'd you get this?
Simple.
First, I knew that 1 to any power equals 1. Not sure if I can provide axiomatic proof, but I'm sure of this.
Then, what I did was, I put ((-1)^i)^i. This equals (-1)^(-1) which equals -1. Then, I used basic rules of odd and even numbers. For instance:

Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even

In this case, if we assume that i is odd, it all fits together. If on the other hand, we decide to call it even, it doesn't quite work out. At all.

So if i is odd, that must mean that (-1)^i = -1

And uh... Yeah, that's about it!
Convincing people that 0.9999... = 1 since 2012

A Random Player
Posts: 523
Joined: Mon Jun 03, 2013 4:54 pm

### Re: Welcome!

robly18 wrote:I'm back.

I probably should've announced myself, but there. I went on a painful week without computer, no access to science of any kind except for my brain.

On the bright side, I got to work on mathemathics and I even found myself finding something new about imaginary exponents!

(the ending result was that -1^i = -1 meaning i is odd. Mind=blown)
Wait a second. At first I thought that meant all a+bi where a+b mod 2 = 0 is even, = 1 is odd (cf Gaussian integers, though not exactly).. But I realized that wasn't quite right ((-1)^(i+1) != -1, it's a transcendental number). So I realized, with help from Wolfram: Yes, -1^i = -1. But that sure don't mean (-1)^i = 1! In fact, (-1)^i = e^-pi.
So just another case of forgetting parenthesis, I'm afraid

Wait, you derived it? But even with parens around -1, it's still not -1. But the even/odd rules do work with i as odd, and not as even, though
Conclusion: this (along with my first line) only works in basic arithmetic without exponentiation. Either that or I got confused somewhere.
Somewhat relevant: http://www.wolframalpha.com/input/?i=pl ... 8x%2Byi%29
\$1 = 100¢ = (10¢)^2 = (\$0.10)^2 = \$0.01 = 1¢ [1]
Always check your units or you will have no money!

robly18
Posts: 413
Joined: Tue Jun 04, 2013 2:03 pm

### Re: Welcome!

Huh... Well then, I messed up. Thanks for correcting me!
Convincing people that 0.9999... = 1 since 2012