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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.
I LOVE your Gravity Simulator!
 testtubegames
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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.
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.
Re: Welcome!
For the record, it was me who suggested positive exponents
Convincing people that 0.9999... = 1 since 2012
Re: Welcome!
Welcome to the forums Stargate38!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.
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^(nk))(b^k))/(k!(nk)!))
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)
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
Re: 1^i
Simple.exfret wrote:How'd you get this?
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

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Re: Welcome!
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.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)
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
$1 = 100¢ = (10¢)^2 = ($0.10)^2 = $0.01 = 1¢ [1]
Always check your units or you will have no money!
Always check your units or you will have no money!
Re: Welcome!
Huh... Well then, I messed up. Thanks for correcting me!
Convincing people that 0.9999... = 1 since 2012