Use linear transforms. Scaling, translation, and rotation, in particular. It's a matrix multiply to go from one coordinate space to another once you plug in all the parameters.

you learned this in high school? lucky fuck i had to take a university course to know how to do that. fuckin north america

hitler will rise again and the universe will turn inside out

>>8355
oh how i do look forward to the 2nd cuming of christ

>>8259
If this proof is the one I am thinking of then the conclusion has a catch. You can say one of these things about your number you just made:

1. it is prime
   

OR
2. there was a prime we did not account for which can divide it.

>>8363
example?

6n + 1 = prime number.

The ratio thing is an issue of self similarity.
If you take any two successive line segments l, m and (l+m), where m/l is the golden ratio, (l + m)/m is also the golden ratio.
If you try it with line segments 2 and 4 cm long, 4/2 does not equal (2+4)/4.
Infact, that relation can be used to derive it, which shows that it's the only number that satisfies the condition.
(l + m)/m = m/l
l/m +m/m = m/l
l/m +1 = m/l

substitute m/l = x, l/m must equal 1/x
1/x + 1 = x
1 + x = x^2
0 = x^2 -x -1

Applying the quadratic formula, where a, b and c are the coefficients of the terms, thus 1, -1 and -1 respectively
x = -b/(2a) +/- sqrt(b^2 -4ac)/(2a)

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>>8373
This book may be of help; its informative and not very math intensive.
http://www.amazon.com/The-Golden-Ratio-Worlds-Astonishing/dp/0767908163

>>8373
To put it more simply for you, non-math guy:
First of all, you can't split an 8cm segment into to other segments of 2cm and 4cm.. because then you'd still have a third segment of 2cm. (4+2=6, not 8)

The thing about the golden ratio (among a huge amount of other things) is that if you have a given segment of C lenght, then you can split it into to other segments, A and B (A+B=C!!) with A<B, then
B/A = C/B
If that happens, then
A*phi = B
B*phi = C
With phi being the golden number.
(Also, for each given segment, there is one and only one way to split it into two smaller segments so that the above thing happens)

>>8376
Only if l=0 would that make sense, and we all know what happens if you were to successfully divide by 0... Black holes and such. the whole golden ratio notion should be banned from thought.

1 : 20^5

or 1 : 2000000?

>>8400
243/33554432

combinatorial!

1. V=lwh, find w when V= 72yd^3, l=0.75, and h=12yd.
   

72 = (.75)(12)(w)
72 = 9w
8 = w

fin

Number 1:
72yd^3 = lwh
= (0.75)(12yd)w
w=72yd^3/(0.75*12yd)
= 8d^2

Number 2:
L=prt
p = L/(rt)
= $135/(0.025*3 years)
= $1800 per year

can't be bothered with any more.

>>8385
It's a julia set of the burning ship fractal z(n+1)=(abs(Re(Z(n)))+i*abs(Im(Z(n))))^2+C but i don't have the exact coordinates saved, if that's what you're asking.

>>8385

Oh, thank you.

since we're posting fractals...
This one's different from most stuff you'll see - it has more to do with interference patterns.

http://www.youtube.com/watch?v=gj6i1K50aOY&
if the intro is boring skip to about 3:30

>>8390
Alright, thanks. I didn't know this fractal.
It seems this picture had post-processing. Do you used a software, or did you make the picture yourself ?

I'm actually very interested about fractal rendering, because I'm probably going to present fractal art at an art expo.
I may have to make a thread on this boards one day, asking for interesting fractals to show to people.

>>8391
You're welcome. If you like computer science oriented art, you should also check out cellular automatons (CHAOS EVERYWHERE).
http://www.youtube.com/watch?v=1XOjUz8cQYU this one is cool

>>8395
I rendered it with Fraqtive, which is free software. The formula i used is one of the built in options. The only post processing i did was converting the original 30mb png image to a jpg small enough to upload. FractalForums.com is also a good resource. I agree cellular automata are interesting, here's a 2d automaton i made in MatLab with a spiral weighted modulo loop.

Is this introductory, or is it actual theory?

Intro level macro or micro is only babbymath. If you can do arithmetic and draw graphs, you're fine. Also, there's so much overlap between intro to micro/macro that you'll probably have very little work to do until he end of the course.

>>8387
Normally I wouldn't worry much, but since this is condensed into two weeks, I sort of am. Guess it's a little more than an intro class.. It's a 200 level course.

Base prime FTW

balanced ternary master race

'things that isn't'. oh god.

>>8381

The verb "is" agrees with the subject "way" in number. There's nothing grammatically incorrect about that.

>>8382 Ah yes I just read it wrong

The direction vector going from between position vector p to the position vector q is q-p.
The line must consist of every scalar multiple of this direction vector, shifted by another vector mso as to be at that position when your variable is 0.

Hope that helps, trying not to spell it out too much.

P=(2,1,3)
Q=(1,2,-1)

Equation of the passing line:
L = t*(Q-P) + P (or +Q)
with t being any real number.
So, L = t * (-1,1,-4) + (2,1,3)
L= (-t+2,t+1,-4t+3)

>>8374

>vector problem
>point me in the right direction

mfw

Provided you're talking about integrating with respect to time, that would appear to be 'absement'. There's not much documentation about it so I suspect it isn't very useful, google for a few pages.

Thanks for the reply, bumping for further discussion

If P(t) is a parametrized function representing the position vector then you could integrate over said function. This is usually called a line integral and can be used to find arc length of a curve in space, among other things.

Also, I just realized you could there which much fewer steps.

In the inital equation just square both sides, and you'll get

x/y + 2 + y/x = 100
Then
x/y + y/x = 98

(It's the same i made before, but much shorter)

I think you might have misunderstood what I was trying to do. I don't need the original expression simplified, I'm just looking for some kind of proof that the expression below it is equal to 1. I'm not sure if it can be done, but apparently it is equal to 1, unless my previous work is incorrect.

>>8344
I'm not quite understanding you.
You want a proof that
(y^(3/2) - x) / (x^(3/2) - y) = 1 ??

Well thats not true my friend, and here is a counter-example

Take the pair (x,y) = (1,0)
Put that in your equation, and you get = -1

Take another random pair, and you'll most likely get something different from -1.
(pair (2,1), for example).
So no, that expresion cant be canceled out, for it depends on which x and y you take.

>>8328
Hi, I don't do pure maths so this might be *very* wrong, but its one solution at least. i.e there might be a lot more, infact due to using a square there'll be at least another one. I'm fairly sure if you play with it for a bit you'll be able to pull the others out.

as implicit probably makes more sense in polar co-ordinates therefore
define
y = r sin t
x = r cos t

dropping the t as its in everything (its still there just not writing it out)

sub into original:
sqrt(r cos / r sin) + sqrt( r sin / r cos) = 10
sqrt( cot) + sqrt (tan) = 10
square both sides and only consider one solution
cot + tan + 2 = 100

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>>8328
Ha, I spotted the trick way to do this whilst writing that brute force solution out. However you just have to 'see' these kind of substitutions in order to do stuff like this. So if this is some sort of exam I'd use polar co-ordinates whilst longer its a more reliable solution.

you're at the point
x/y + y/x = 98
sub t = y/x
t + t^-1 = 98
multiply through by t
t^2 -98 t +1 = 0
the roots to that are the two possible values of t.

since we've defined t = y/x then the two roots are two gradients i.e solutions are of the form y = tx
(noting that both roots are solutions so there are two lines so it will look like a cross on an xy plot)