/sci/ - Science & Math

>>12226457
Gender field theory is an outdated model and the experimental anomalies show that we urgently need a new model of gender.
To this end, I am proposing that genders are really just cellular automata.

[math]\int_0^1\int_{\sqrt{x}}^1\ \cos(y^3)\ dydx\approx .28049[/math] :^3

>>6761852

FromDigits[Reverse[IntegerDigits[n]]]

Get on my level, plebs. Now let's talk about cellular automata.

Interpreting "most brilliant" as highest luminosity.

The most brilliant in the picture is the rectangular area bounded by [1500,900] and [1550,1100]

Is it just me or is it Wolfram who cannot calculate? I thought this would converge, because
ln(n)/n<ln(n+1)/(n+1) is correct when n>3, proof by Induction n=3 ok then ln(n+1)/(n+1)<ln(n+2)/(n+1) is correct if we suppose it is correct for n, therefore it should converge with Leibnitz

>>5186255
Oh heavens no. If you kept the same ordering, say the penguins are, top to bottom, A B and C, and they started from initial heights, hA, hB, and hC, and hA>hB>hC, then the differences in energy would only increase. The only way to make the problem interesting would be to mix up the orders of the h's. But still, the energy lost to drag is kind of trivial over even a height of 10's of meters. maybe even 100's, I'd have to do some figuring.

If you aren't ignoring drag, then the one at the top /would/ have the most PE+KE, since less of it's energy has been lost to drag. But it's being kind of dumb and picky about it.

>>5065583
The two functions arent lines, so >>5065643 is bullshit, but you can argue as follows:
Take the highest absolute value of an ak from both functions, and compare theim. Is one higher? Then at a sufficiently large n, the signficiance of that exponential (!) addend will have drowned out that of all the others in both functions, and from them on the functions will be forever separate. Since there cannot be infinite intersections at odd x in a finite x interval, both highest absolute values of the functions must be equal. Since we are looking at the difference between the functions, we can subtract from both that highest exponential addend and repeat the argumentation until none are left on both sides and equality is proven.

>>5065839
EJumpthatsavesyou=EJumpthatpropelsyouuptheshaft

>>5065698
Assuming that you intended to refer to >>5065671 , look exactly what I gave you the derivate of and what the first step in the wolframalpha steps view said.

>>5065664
d(x^n)/dx
=lim h->0 ((x+h)^n-x^n)/h
=lim h->0 ((x^n+n*h*x^(n-1)+h²*(...))-x^n)/h
=lim h->0 (n*h*x^(n-1)+h²*(...))/h
=lim h->0 n*x^(n-1)+h*(...)
=n*x^(n-1)

>>4600626
I was going to render the entire universe

but then I shut down Wolfram Alpha

YOU CAN THANK OP FOR THAT!

Fuck you OP, why are you guys so fucking mean? If you guys don't like Wolfram Alpha, then I'm shutting it down!

If you wouldn't mind helping me for a moment.
Pretty sure i am right, but a giant mathematical supercomputer says i'm wrong so i have to check with you guys.
Wolfram pic coming next.

Do not have the book open without a pen and paper handy, do not just read the examples and derivations, work them out in parallel, if there are problems handy, do them.

Not ultimately favorable for life systems.

>>3163442
for reference, compare with the earlier output that had constant masses

Ok, this is fucked up, i reran my galaxy simulation, having the initial mass vary as 1/r^1.5, and initial velocity vary as 1/r. and, well, the results speak for themselves.

>>3163640
yeah, it's kind of the way pygames grid works, it rasters from to left to bottom right, so [0,0] is the top left, which makes x-axis movement what you'd expect, but flips y-axis movement. But most physical laws have symmetry in a way that it doesn't matter.

>>3163605
yeah, some bone head goofs i had were
adding position to position, not velocity to position
not breaking forces into x-y components
multiplying the timestep in one case, and dividing in the other
having the wrong sign on the force, making gravity repulsive instead of attractive
lots of missed colons

also, i think i've got a stable quartet!
1000 140,0 0,5.25
1000 160,0 0,-2.75
1000 -140,0 0,-5.25
1000 -160,0 0,2.75

>>3163553
starts out with that one guy hauling ass outta of the system. neat spiral though, looks like the systems starting to process.

>>3163538
When i first started, all my orbits eventually turned into circles, even if they were supposed to be ellipses. That went away when i made the time step smaller though, I wonder why it is that the approximation always turns into a circle, it's probably because of the R^2 aspect, but I don't know more details than that.

Also, your starting conditions may have been off? did you try solving m/r^2=v^2/r to figure out your initial velocity? and put the vectors at right angles to each other?

>>3163519
It's most of what i did yesterday, I did a crummier one in november. Most of the new work was doing it in pygame instead of turtle, and making the file reading system. It was kind of baffling when I did what i thought was the exact same math, but get much better results, however. Nice kind of baffling, but still weird.

>>3163510
http://dpaste.com/549838/
The first subroutine, sysmaker is how i read the system of bodies from a file and set the initial conditions.
1000 140,0 0,4.75
1000 160,0 0,-3.25
1000 -140,0 0,-4.75
1000 -160,0 0,3.25