/sci/ - Science & Math

By what method must this be solved? Can we use calculus?

<div class="math">1 - \sqrt{3} + \frac{\pi}{3}</div>
>it's much harder than it looks
I did this in my head. Drunk.

>>1736694
Yes, but the integral you have to solve is a bitch.
>>1736696
Well fuck you.

>>1736696
Might I ask how exactly you did that?

>>1736714
Integration.

That's what I'm doing

i'd start by drawing the equation of the circle (x^2 + y^2 = 4) and then substituting in either x or y = 1.
the other is √3

we now know the points (√3, 1) and (1, √3)

i'm not sure what the EASY way of doing this is, but you can then draw up the equations of the lines from (0,0) to these points, and then work out the angle inbetween

Work out the area of the sector and minus the area of the white part.

did i do it right theoretically?

solvable by any high school student who has spent like 2 lessons on integration.

>>1736714
I've had <span class="math">\int \sqrt{1-x^2} dx = \frac{x \sqrt{1-x^2} + \sin^{-1} x}{2}[/spoiler] had memorized. Just changed the numbers, plugged shit in, made 2[]+1+?=pi and solved.

>>1736731
lol see

I'm:>>1736720
but I don't have that memorized. I'm doing it the long, tedious, dx dy way lol

>>1736731
Oh I see. I asked 'cos it took me longer than I'm willing to admit to figure out <span class="math"> \int \sqrt{4-x^2} dx[/spoiler]

>>1736724
disregard this, i just realised the entire integration thing

>>1736744
Just look in your textbook for the identity.
it turns into a nasty looking equation and probably takes many difficult identities lol.

I'm>>1736720
>>1736738

>>1736731
I'm still a little confused. How do you find the area of that tiny sector? Do you have to use a definite integral or something?

>>1736696

I'm getting:

-sqrt(3)/2 + 2π/3 -1

Using:

∫ sqrt(4-x^2) dx - ∫ 1 dx

Between the points 2 and 1.

>>1736763
yes. You can find the area of the quarter circle. then you just subtract the area you found by integrations from it. bang.

>>1736763
I found area under curve from 0 to 1 and subtracted 1x1=1, called it [], then noted 2[]+1+? equals the entire fourth of the circle so = pi.

>>1736673
What? This is a trivial integral. Sorry I don't know whatever cool math symbol language this board knows (yet).

Let c be x value of the solution to the intersection of y = 1 and x^2 + y^2 = 2^2 in the first quadrant.

The area is
[integral from 1 to c] of [sqrt(2^2 - x^2) dx]

>>1736763
different person here,
boundaries are 1 and √3

also minus √3 from the solution

>>1736765
not between 2 and 1. its between sqrt3 and 1.

>>1736763
Yes, it's THAT >>1736744
integral from 1 to sqrt(3), minus the rectangle below (1*(sqrt(3)-1))

>>1736775
Err, slight correction. My bad:

The area is
[integral from 1 to c] of [(sqrt(2^2 - x^2) - 1) dx]

If you stretch it to be a 1x1 square, you can cut it in half and get the area = 0.5
The lengths are not exactly equal to 1 on either side, so lets reduce them to lets say, .8 on each side.
.8x.8 = .64 /2 for half a square = .32
actual answer = .315
.315/.32 = 99% accuracy in the estimation

Engineer here.

>>1736787
Still think it's a trivial integral? Do it yourself. Don't look it up.

>>1736792
faggot.

>>1736792
thats how trolls should be

>>1736792
>Engineer here.
I can tell. Get the fuck off here.

>>1736797
So you need to do some trig substitution, so what?

>>1736806
>some
>so what
I lol'd

>>1736787
Why the fuck do you call yourself 'scientist' if you're posting in a lowly 11th (at average) grade level thread?

>>1736797
Not the same person. The integral is trivial. It is a regular trig substitution.

>>1736765

Woops. I fucked that up. I don't know why I did it between 2 and 1. It should have been between sqrt(3) and 1.

I'm so used to just checking the x axis for numbers and plugging them into the integral that I didn't stop to even fucking check. My bad.

Now I AM getting 1-sqrt(3) + π/3

>>1736806
So it's a pain in the ass.

>>1736811
Why do you troll me?

>>1736803
Have fun arguing over your integrals while I'm off doing real science.

Protip, in the real world you would never get an 'exact answer' anyway. Everything has a tolerance.

>>1736842
Cool
Will you lick my balls now?

>>1736842
Protip: calculus like this gives you precise enough measurements and theory to actually build the cool shit.

>>1736867
Protip: calculus is what retards use when they can't estimate things.
It took me like 5 seconds to guess that, whereas you fags have been arguing for over half an hour as to what the area is.
I think my method is more efficient.

>>1736880
this post... its beautiful
truly a art

>>1736880
5/10

>>1736880
Come back to me when you can estimate the time dilation due to general relativity, asshat.

>>1736889
Hey kid, move aside, I'm going to solve the universe using engineering science.
Go play with your calculus toys somewhere else.

>>1736897
>time dialation
Does your equation take this into account?
Better go draw up another integral to account for it. Try doing it in the laplace domain I swear it will make it easier.
Oh wait, I already solved it. LOL SCIENCE

>>1736694

http://www.youtube.com/watch?v=axsSiQg9vU8

This problem is fairly easy. It can be done in one integral in the following manner:
Consider the circle of radius 2 centered at (-1,-1). The desired area is the the integral of the upper semi-circle of this circle from 0 to <span class="math"> \frac{\sqrt{3}}{2}-1 [/spoiler].
The equation for the upper semi-circle is:
<div class="math"> y=\sqrt{4-(x+1)^2}-1 </div>
Hence <div class="math"> \int_{0}^{\sqrt{3}-1}[\sqrt{4-(x+1)^2}-1]dx=1-\sqrt{3}+\int_{1}^{\sqrt{3}}\sqrt{4-x^2}dx=1-\sqrt{3}+
\int_{\pi/6}^{\pi/3}2\cos^2 udu=1-\sqrt{3}+\int_{\pi/6}^{\pi/3}[1-cos2u]du=1-\sqrt{3}+\pi/6-\frac{sin(2\pi/3)-sin(\pi/3)}{2}=1-\
sqrt{3}+\pi/6-\frac{\sqrt{3}/2-\sqrt{3}/2}{2}=1-\sqrt{3}+\pi/6 </div>

>>1736912
Checkmate mathfags.
Enjoy your 30k starting

This problem is fairly easy. It can be done in one integral in the following manner:
Consider the circle of radius 2 centered at (-1,-1). The desired area is the the integral of the upper semi-circle of this circle from 0 to <span class="math"> \sqrt{3}-1 [/spoiler].
The equation for the upper semi-circle is:
<div class="math"> y=\sqrt{4-(x+1)^2}-1 </div>
Hence <div class="math"> \int_{0}^{\sqrt{3}-1}[\sqrt{4-(x+1)^2}-1]dx=1-\sqrt{3}+\int_{1}^{\sqrt{3}}\sqrt{4-x^2}dx=1-\sqrt{3}+
\int_{\pi/6}^{\pi/3}2\cos^2 udu=1-\sqrt{3}+\int_{\pi/6}^{\pi/3}[1-cos2u]du=1-\sqrt{3}+\pi/6-\frac{sin(2\pi/3)-sin(\pi/3)}{2}=1-\
sqrt{3}+\pi/6-\frac{\sqrt{3}/2-\sqrt{3}/2}{2}=1-\sqrt{3}+\pi/6 </div>

>>1736912
>shows up to the party after it's already over, doesnt get answer rite anyway

This problem is fairly easy. It can be done in one integral in the following manner:
Consider the circle of radius 2 centered at (-1,-1). The desired area is the the integral of the upper semi-circle of this circle from 0 to <span class="math"> \sqrt{3}-1 [/spoiler].
The equation for the upper semi-circle is:
<div class="math"> y=\sqrt{4-(x+1)^2}-1 </div>
Hence <div class="math"> \int_{0}^{\sqrt{3}-1}[\sqrt{4-(x+1)^2}-1]dx=1-\sqrt{3}+\int_{1}^{\sqrt{3}}\sqrt{4-x^2}dx=1-\sqrt{3}+
\int_{\pi/6}^{\pi/3}4\cos^2 udu=1-\sqrt{3}+2\int_{\pi/6}^{\pi/3}[cos2u+1]du=1-\sqrt{3}+\pi/3+sin(2\pi/3)-sin(\pi/3)=1-\sqrt{3}+\
pi/3-\sqrt{3}/2-\sqrt{3}/2=1-\sqrt{3}+\pi/3 </div>

Taken intro to java here.

import java.lang.Math;

public class arc {
public static void main (String args[] ) {

double x = 0;
double y = 0;
double a = 0;

double area = 0;
double sector = 0;


// first take the integral from x = 0 to x = 1

x = 0;
y = 0;
sector = 0;
while (x <= 1) {
x = x + 0.01;

a = 4 - (x*x);
// x^2 + y^2 = 4
// y^2 = 4 - x^2
// y = sqrt(4 - x^2)

y = Math.sqrt(a);

sector = sector + (y*0.01);

} // close while

// then doulbe sector
sector = sector + sector;
sector = sector - 1;

area = Math.PI;
area = area - sector;

System.out.println(area);

// area from x = 0 to x = 2 is equal to pi

} // close main

} // close arc

================

prints 0.317

>>1736909

He may have been asked to find it via a certain method, which is why I asked. If not, I agree: it shouldn't matter which method you use, so long as it gives you the correct answer.

Senior in engineering here:

I have no fucking idea how to do this. I probably did at some point back when I was taking math but not anymore.

Dunno why everyone is using calculus; trig is easier.

double integral set up using
x^2+y^2=4 ?

or you can change to polar coords.

or plenty of other things

>>1737003

>>1737003
That's... actually pretty great.

0.1830127

>>1737003

Find the angle subtended by the two diagonals connecting to the edges of the red, shaded area, work out the area of the sector, and then subtract the triangles?

Ok, I had a hole proof worked up with a unit circle and some identities. But WTF is this new Capcha shit. Leave for a few months and this?


Few drinks and this. Shame. I blame public schools.

>>1737003
dude, you're a genius.

red area = 1/4 circle wedge area - 2 * cyan triangle area - 2 * yellow wedge area + 1

wedge area= 2 * angle
1/4 circle area = pi
cyan triangle hieght = sqrt(3) (pythagorean theorem)
cyan triangle area = bh/2 = sqrt(3)/2
yellow wedge angle = arccos(1) = 30 degrees = pi/6
yellow wedge area = pi/3

so red area = pi - sqrt(3) - 2/3 pi + 1
= 1 - sqrt(3) + pi/3
QED

>>1737095
*and by arccos(1) I of course mean arcsin(1/2)

>>1737003

exactly sir, it's a geometry problem with some trig identities. and a few law of cosines, and blam, answer.

Granted I just too analytic geometry last semester, so I remember this shit.

Not feigning experience, just laughing at the jerks getting trolled, essential, by an arc lenght, GEOMETRY, problem.

I guess that's why this troll succeeds

Wish me luck, mr troll, on my car loan tomorrow. Pre Cert for 3.9, but the banks being gay about income.

this captcha shit is needed in /sci/ seriously?
I can see in /b/ or /s[cp]/

>>1737100
Pretty good work there sir.

>>1737126
Oh, good, it's "scientist" aka "25 and never been kissed" aka "anthropomorphic principle" aka nitwit.

>>1737133
Having fun with your ad hominems there?

>>1737135
An ad hominem is when you call someone a name to undermine their argument. I'm calling you names just because you're a nitwit. And yes, I'm having a great time, thanks.

>>1737133
I saw the other two in that thread earlier, but "anthropomorphic principle"?

It's funny because he probably thinks we're samefagging.

>>1737141
I made a mistake. Can we move on?

>>1737141
it was another thread where he badly explained the anthropic principle and called it the anthropomorphic principle.

>>1737143
Badly explained eh? I'm curious now. What was so bad about it?

>>1737142
No, because then you had the audacity to insult the sanctity of mathematics.

>>1737142
> Scientist
LOL

>>1737152
Ok. And I will do so again. Sanctity is not a word that should be used on the science and mathematics board. Math is not sacred.

>>1737154
Protip: real scientists admit that they do not know it all. I admit that I do not know it all. I admit I am quite ignorant on a large variety of topics. I admit that through science humanity will never be able to answer all questions of empirical fact.

To claim to be a scientist is simply a claim that one follows the scientific method as a way to learn about the natural world.

>>1737148
Well, for one thing, its the ANTHROpic principle because it pertains the questions of why we live in a universe apparently fine-tuned to allow for such things as people (aka anthropos).

You started out by saying that the anthropomorphic principle was that when you get a certain hand at cards and the odds of getting whatever specific hand you got was 1 after the fact... there are other names for what you were trying to describe anthropic principle is not one. (you later applied it to the universe, but by then it was really too late).

>>1737160
I said that I was opening with an analogy. The analogy was that observing an event changes the effective probably that the event occurred, as opposed to trying to calculate the probability of the event before the event occurred.

I opened with an analogy of playing a bunch of poker at Vegas.

I then applied the same reasoning to humans on this Earth and the odds that the Earth can support human life. I only called this last thing the (misspelled) anthropic principle.

>>1737159
Well then, I'm also a scientist. Guess I better name myself so people can tell I'm not a troll.

>>1737152

Dude, I make fun of math jerks all day long. If that makes me audacious, I'm a regular Holden Caulfield.

>>1737169
works for me

>>1737168
>25 male never-been-kissed, original
The hole you're digging is getting deeper by the second, dude.

Sorry to derail this thread from an interesting math problem. I enjoyed working out the problem based on geometry here >>1737095 after the suggestion of doing it that way rather than using calculus. I will now return to my work, where I will further use glorious math to calculate economic damages sustained by claimants in a class action lawsuit. Good day to you all.

>>1737172
But you're not the one claiming to be a Scientist.

>>1737174
Meh? I'm a loser who spends all his time practicing math, reading 4chan, and following the C++ newsgroups. Whatever that means to you.

>>1737172
Yeah, your Holden Caulfield, buddy.

>>1737178
Scientists have to respect math as "sacred"? What the fuck is wrong with you? You're not a mathematician nor a scientist.

who, i guess whom, for these insatiable erudites, is doing fucking shots?

Don't want to go the '20 style route, but, as it's im getting hammered and playing the guitar. YEAH SON.

>>1737184
You're right, I'm better.

>>1737194
So, why are you trolling the science and math board then?

>>1737168
In the end, your explanation of the anthropic principle was wrong anyway. You said it was that, since we've already observed it, the likelihood of earth having life is 1. Just like the odds of getting the hand we got is 1. That is NOT the anthropic principle.

The first version of the anthropic principle was the observation that many of the constants of physics seemed fine tuned to allow for a complex universe, and so also life. The version that you are thinking of is that it would be impossible for life to observe any other universe than one that was suitable for developing life. Thus that the odds are 1 because otherwise there would be no life to observe it, NOT because we have already observed it. That's missing the point of the principle.

>>1737198
>The version that you are thinking of is that it would be impossible for life to observe any other universe than one that was suitable for developing life.
Don't think so.

Anyway, I think you're being overly pedantic, and they're mostly equivalent. The general idea is that an observed event cannot be called "unlikely" simply because the event happening again would be exceedingly unlikely.

>>1737198
Aren't those just the weak and strong versions?

>>1737205
I admit that it's way too late at night for me to follow this incredibly pedantic reasoning. I think I got the jist of it right.

>>1737202
No, that is not the anthropic principle. I'm not being pedantic. There's another name for what you're saying but I don't remember it.

>>1737211
You suck at explaining. One sec. I'm checking wiki to see if they do a better job.

>>1737216
http://en.wikipedia.org/wiki/Anthropic_principle
>In physics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental physical constants necessary to accommodate conscious life. As a result, they believe that the fact that the Universe's fundamental constants are within the narrow range thought to allow life is not remarkable.

So, is your problem that the anthropic principle deals exclusively and explicitly with fundamental constants of physics and the general "model" and "method" of physics? If so, then yes, I agree that I didn't fit that definition as I applied the anthropic principle to explain why Earth could sustain life.

Otherwise, I'm still lost.

>>1737220
No. What you said was essentially, we've already observed that the earth can sustain life, so at this point the likelihood that the earth can sustain life is 1.

What the anthropic principle would say is, any beings capable of asking the question would necessarily find themselves on a planet capable of sustaining life.

I should get a tripcode :(

>>1737227
>any beings capable of asking the question would necessarily find themselves on a planet capable of sustaining life.
>the probability of an intelligent being existing on a planet which supports life is 1
>the probability of intelligent being, which notices that it is alive, existing on a planet is 1
>we (intelligent beings) have already observed that the earth can sustain life, so at this point the likelihood that the earth can sustain life is 1.

Seems pretty equivalent to me.

>>1737155
Otherfag here.
I was going to defend you against this character assassination, but after that statement....
YOU SHUT YOUR WHORE MOUTH

Hey guys I call myself a scientist even though I dont do research or shit, I just 'follow scientific method' LOL

Anyway I'll just stop shitting a calculus thread with this bullshit

cool story huh

>>1737238
lol
I wonder if you would even believe me if I say that I have a Bachelors from U of M (Ann Arbor) in Mathematical Sciences - Discrete And Algorithmic Methods. Also a Bachelors in Computer Science. Both In 4 years.

Sanctity is not a word that applies to math nor science.

>>1737241
Yeah, pretty cool story, except for the part where the guys making fun of Scientist were the ones shitting all over this board, making irrelevant and off topic posts.

>>1737238
lol *brofist*

>>1737242
Bachelor of Arts, amirite?

>>1737247
No, two Bachelors of Sciences through the LSA college.

>>1737242
Double degrees like that usually take four years where I live. Personally, mine are in Science (major in Physics) and Computer Science. Can we be best buddies now, even though I have a huge urge to insult you?

>>1737235
Almost, but not quite, the first 3 are probability statements without reasons, the last one is a direct
cause-->effect
(we observe)-->(probability=1)

The anthropic principle is (oversimplified)
(universe can create life) --> (life forms) --> (life observes and asks question, answer is 1)
(universe cannot create life --> (no life forms) --> (no life to observe and ask question, answer is 0)

because there would be no life in the case where the answer is zero, the mere fact that life is around to ask means it must be 1, it doesn't matter if we observe/ask or not, the answer will always be 1 if we are here.

>>1737254
Ok. I'm starting to see the subtlety.

>>1737252
So, what languages? I'm partial to Java and C++. My friend is going crazy over D right now.

I put enough pics of me doing coke to conclude this thread,

K?

also rubik's cube check mate. So die thread die.

>>1737275
>implying rubik's cube is not for pathetic wannabe intelligent people
Just sayin' bro, relax your anus.

>>1737275
>>1737172
>>1737100
fuck you you are gay

>>1737279
I've never figured out how to do a fucking rubics cube ;_;