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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, 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.

For the record, it was me who suggested positive exponents

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.

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!!!

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)

How'd you get this?

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!

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

*rereads next posts*
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

Huh... Well then, I messed up. Thanks for correcting me!