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/sci/ - Science & Math

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1103704 No.1103704 [Reply] [Original]

famous mathematician Vladimir Arnold died yesterday, at the age of 72. he is the most cited russian scientist.

http://en.wikipedia.org/wiki/Arnold's_cat_map
http://en.wikipedia.org/wiki/Arnold's_rouble_problem
quote
>Who can't calculate the average value of the one hundredth power of the sine function within five minutes, doesn't understand mathematics - even if he studied supermanifolds, non-standard calculus or embedding theorems.

>> No.1103737

how do I calculate the average value of the one hundredth power of the sine function?

>> No.1103747

>>1103704
so

>> No.1103749
File: 3 KB, 118x126, 1272618766045.jpg [View same] [iqdb] [saucenao] [google]
1103749

is it 1/2 ?

>> No.1103765

>>1103749
depends on theta

>> No.1103773

could you use DeMovrie's formula?

>> No.1103788

>>1103765
no it fucking doesn't you stupid tripfag. fuck off.

>> No.1103795
File: 40 KB, 293x473, dexter.jpg [View same] [iqdb] [saucenao] [google]
1103795

of natural causes or ...?

>> No.1103796

aaaahhhh i bet you the answer is so close to 0.. something like .01/pi

>> No.1103797

>>1103765
cereal here, WTF is theta.
also, just made a geuss, actualy it isn't

>> No.1103815

wouldnt it be zero?? Its bouncing between 1 and negative 1

>> No.1103818

I think we're missing the point here guize

>> No.1103829

this thread gave me cancer...that's the worst math quote i've ever read.

things that computers can do in 2 seconds aren't things mathematicians need to practice

>> No.1103834

oh my god i hope you are all trolls.

>> No.1103839

>>1103815
lol even power, negative... I'm sure you will get the answer eventually bro.

>> No.1103837

>>1103795
Assassinated by the KGB, shortly after accidentally discovering Russian superhuman cyborg prototypes of world domination.

>> No.1103836

>>1103815
>one hundredth power

you just went full retard.jpg

>> No.1103842

>>1103818

A problem came up for the kids, don't expect them to worry about the dead guy

>> No.1103853

>>1103829
you cant simply brute force into mordor, engineerfag.

>> No.1103856

Also, the average value of a sine is 0. Always, to whatever power.

>> No.1103862
File: 32 KB, 431x496, shaniqua-be-all-like.jpg [View same] [iqdb] [saucenao] [google]
1103862

>>1103856
>>1103815

>> No.1103866

>>1103856

dont mind me, I thought he was on about a thing looking like "sin(sin(sin...sin(x))))...))))"

But then, about the sin(x)*sin(x)*sin(x)....

>> No.1103938 [DELETED] 
File: 2 KB, 126x115, 1272618729671.jpg [View same] [iqdb] [saucenao] [google]
1103938

Cereal reporting
<div class="math">\int_{0}^{2\pi}\sin^{2n}{x} \, dx= \int_{0}^{2\pi} -\sin ^{2n-1}x \, d{\cos x} = 0 + \int_{0}^{2\pi} {(2n-1)}\sin ^{2n-2}x
\cos ^2x \, dx = \int_{0}^{2\pi} {(2n-1)}(\sin ^{2n-2}x - \sin^{2n}x) \, dx</div>

<div class="math">{2n}\int_{0}^{2\pi}\sin^{2n}{x} \, dx = (2n-1)\int_{0}^{2\pi}\sin^{2n-2}{x} \, dx</div>

<div class="math">\int_{0}^{2\pi}\sin^{2n}{x} \, dx = \frac{2n-1}{2n}\int_{0}^{2\pi}\sin^{2n-2}{x} \, dx</div>

<div class="math">\int_{0}^{2\pi}\sin^{2n}{x} \, dx = \frac{1\cdot 2 \cdot 3 \cdot \ldots \cdot (2n-1)}{2 \cdot 4 \cdot 6 \cdot \ldots \cdot 2n} \cdot 2\pi</div>

the average value is <div class="math">\frac{1\cdot 2 \cdot 3 \cdot \ldots \cdot (2n-1)}{2 \cdot 4 \cdot 6 \cdot \ldots \cdot 2n}</div>

>> No.1103945

protips: he meant a close approximation.
try stirling's approximation and taylor expansion

>> No.1103949
File: 2 KB, 126x115, 1272618729671.jpg [View same] [iqdb] [saucenao] [google]
1103949

Cereal reporting
<div class="math">\int_{0}^{2\pi}\sin^{2n}{x} \, dx= \int_{0}^{2\pi} -\sin ^{2n-1}x \, d{\cos x} = 0 + \int_{0}^{2\pi} {(2n-1)}\sin ^{2n-2}x
\cos ^2x \, dx = \int_{0}^{2\pi} {(2n-1)}(\sin ^{2n-2}x - \sin^{2n}x) \, dx</div>

<div class="math">{2n}\int_{0}^{2\pi}\sin^{2n}{x} \, dx = (2n-1)\int_{0}^{2\pi}\sin^{2n-2}{x} \, dx</div>

<div class="math">\int_{0}^{2\pi}\sin^{2n}{x} \, dx = \frac{2n-1}{2n}\int_{0}^{2\pi}\sin^{2n-2}{x} \, dx</div>

<div class="math">\int_{0}^{2\pi}\sin^{2n}{x} \, dx = \frac{1\cdot 3 \cdot 5 \cdot \ldots \cdot (2n-1)}{2 \cdot 4 \cdot 6 \cdot \ldots \cdot 2n} \cdot 2\pi</div>

the average value is <div class="math">\frac{1\cdot 3 \cdot 5 \cdot \ldots \cdot (99)}{2 \cdot 4 \cdot 6 \cdot \ldots \cdot 100}</div>

>> No.1103961

>>1103949
Fancy that

>> No.1103962

I don't need to calculate this because it is given by my superior problem oriented textbook as a core formula in calculus 1.

what now, great mathematician?

>> No.1103975
File: 24 KB, 182x195, 1272618646633.png [View same] [iqdb] [saucenao] [google]
1103975

>>1103949
Cereal continued:
<div class="math">\frac{1\cdot 3 \cdot 5 \cdot \ldots \cdot (2n-1)}{2 \cdot 4 \cdot 6 \cdot \ldots \cdot 2n} = \frac {{{2n}\choose{n}}}{4^n}</div>

>> No.1103994

>>1103945

Protip: He meant an exact value.

Wallis product.

>> No.1103996

Cereal win.

>> No.1104015

>>1103994
Arnold originally wanted you to numerically compute the result within 5% or 10% in five minutes. infa 100%

i think cereal is cool guy and doesnt afraid of anything but you will still need stirling approximation for that last rational number, to stay under 5 minutes.

>> No.1104033
File: 27 KB, 720x400, 0630.jpg [View same] [iqdb] [saucenao] [google]
1104033

>>1103962
you know math.

>> No.1104053

>>1103949
That isn't the average value though. Use correct definiton of average value for a function please.

>> No.1104058 [DELETED] 

testing my cereal tripcode

>> No.1104062 [DELETED] 
File: 16 KB, 228x244, 1267994942922.png [View same] [iqdb] [saucenao] [google]
1104062

cereal test

>> No.1104069 [DELETED] 

>>1104053
hi multiplied with 2pi on the reight hand side in the end, everything is correct.

>> No.1104073

>>1104053
he multiplied with 2pi on the right hand side in the end, everything is correct.

>> No.1104099
File: 7 KB, 182x195, 1271083098409s.jpg [View same] [iqdb] [saucenao] [google]
1104099

>>1104015
the answer is approximately 0.0795892373871787614981270502421704614029315404247333213573

>> No.1104113

>>1104073
shouldn't that be 1/2pi braaah

>> No.1104123
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1104123

>>1104113
as you can see, the number is rational >>1103949

>> No.1104133

this is like semester 1 maths at every university on earth... lulz how to intugrayte (sinx)^n... come on

>> No.1104134

why is there <span class="math"> sin^(2n)[/spoiler]?

>> No.1104131 [DELETED] 

why is there <span class="math">sin^2n[/spoiler]?

>> No.1104142

>>1103949

How do you get from the first formula to the second one?

>> No.1104144

>>1104133
>herp

>> No.1104152

>>1104142
integration by parts and then theres an obvious recursion in the end

>> No.1104166

>>1104134
I mean <span class="math">^{2n}[/spoiler] dammit

>> No.1104186

test

>> No.1104208

>>1104166
JUNK raised to the 2n power. You would handle any case where the power is an even number in the same fashion, OBV

>> No.1104225

>>1104186
don't even fucking start tripfagging

>> No.1104261

test

>> No.1104272
File: 40 KB, 1168x768, sin.png [View same] [iqdb] [saucenao] [google]
1104272

There's a function for C++ and it says it's 1/2
also the algorithm uses the fact that
<span class="math">\int \sin^n(t) \mathrm{d}t = \frac{1}{n} \left( \sin^{n-1}(t) \cos(t) + (n-1) \int \sin^{n-2}(t) \mathrm{d}t \right)[/spoiler]

>> No.1104299

>>1104272
probably something else
>>1104099 is the right solution
or you can check at wolfram alpha

>> No.1104386

well, sin(x) is less than one for all x.

so even though negative parts become positive when squared, they still decrease in magnitude with each power.

so, as n goes to infinity, (sin(x))^n goes to zero. i'd guess something close to zero.

- a concerned music performance fag

>> No.1104391

>>1104386
shit, meant than less than or equal to

>> No.1104428

>>1104299
>>1104272
on a second look, 0.5/(2pi) is pretty close to 0.079589

>> No.1104564
File: 3 KB, 126x126, 1271079250617s.jpg [View same] [iqdb] [saucenao] [google]
1104564

>>1104428
close but not equal

>> No.1105302 [DELETED] 
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1105302

>>1103949
wow

>> No.1105445
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1105445

cereal guy is my hero

>> No.1106057
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1106057

bumpin good thread

>> No.1106086

This guy seems like a jerk..."lol i can do large thoughtless calculations faster than u, doesnt matter if u no more math that requires actual thinking, im smarter then u"

>> No.1106112

>>1103788
You can't square sine you faggot, it isn't a value, there has to be a number beside it, sin(x). sin^100 means shit.

>> No.1106115

0.

I don't know if you guys are trolling or not.

>> No.1106126

>>1106115
how did you get 0? what value did you put for theta?

>> No.1106131

>>1106112

Yeah you can, retard. It comes out to an expression. The average value of this expression is 0.

>> No.1106140

>>1106126

You don't need theta because it's asking for the AVERAGE not a SPECIFIC (instantaneous) POINT.

>> No.1106162

>>1106131
http://www.wolframalpha.com/input/?i=sin^100

wolfram says you are a faggot. We don't fucking know theta, THEREFORE we cannot calculator the value of an unknown due to a lack of info. I don't understand, was this mathematicians quote supposed to be a joke/trick question?

>> No.1106193

>>1106162

No, you're the retard.
However, the answer is a non-zero positive value.

>> No.1106203

>>1106140

I haven't done that kind of calculus yet...

>> No.1106225

>>1105445
Get out of here, child.

>> No.1106230
File: 21 KB, 432x432, phil raptor.jpg [View same] [iqdb] [saucenao] [google]
1106230

gotta be 1/2, right?

>> No.1106232

>>1106225
wat

>> No.1106236

>>1106162
http://en.wikipedia.org/wiki/Average#Averages_of_functions

>> No.1106237

>>1106140
Lol.

The mean average of a function is defined as

<div class="math">\frac{ \int_a^b f(x) dx }{b-a}</div>.

That looks to me like that needs some bounds.

>> No.1106242 [DELETED] 
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1106242

>>1106237
>That looks to me like that needs some bounds.
>periodical function

>> No.1106250
File: 6 KB, 236x240, 1274793482731.jpg [View same] [iqdb] [saucenao] [google]
1106250

>>1106237
>That looks to me like that needs some bounds.
>periodic function
2/10

>> No.1106257

Oh, you can solve this equation.

Let's just say Vladimir Arnold was a huge troll.

Hints: Use the average value of a function. Set bounds from 0 to pi (because the function is repeating). Solve. ???? PROFIT!!

>> No.1106254

>>1106230
see
>>1103949
>>1103975
>>1104099

>> No.1106261

>>1106257
Since it's a sine the bounds are -1 and 1. avg is 0.

>> No.1106271

>>1106261

Trolling?

This is a sine function that is to the hundredth power. It does not have a negative range. Also I defined the domain as 0 to pi. Lern2math.

>> No.1106277

>>1106271
If it does not go negative, how the fuck can the AVERAGE by 0?

>> No.1106282

>>1106261
facepalm.jpg

http://www.wolframalpha.com/input/?i=%28integral+of+%28sin%28x%29%29%5E100+from+x+%3D+0+to+x+%3D+pi%
29%2Fpi

/thread

>> No.1106285

>>1106250
>Implying sinusoidal functions are <span class="math">always[/spoiler] from 0 to 2<span class="math">\pi[/spoiler].
Wut?

>> No.1106290

>>1106282
"hey guys, lets just arbitary numbers 0 and pi just so I get the answer I want"

>> No.1106291

>>1106282

THIS

/thread

>> No.1106293

>>1106282
http://www.wolframalpha.com/input/?i=sin^100

>> No.1106298

>>1106293
Plot[Sin[x]^100, {x, -6.6, 6.6}]

it goes negative faggots.

>> No.1106296

>>1106290

"Hey guys I'm a retard that can't see that the graph repeats on intervals of pi"

>> No.1106302

>>1106282


This is the answer, the rest of you are idiots.

>> No.1106311

>>1106302
>>1106293

>> No.1106315

>>1106293

What is this supposed to show me? That you're a retard?

>> No.1106317

>>1106315
The OP quote said sin to the hundredth power, WHICH IS EXACTLY what I'm fucking linking.

>> No.1106324

>>1106317

And? The answer was:

http://www.wolframalpha.com/input/?i=%28integral+of+%28sin%28x%29%29%5E100+from+x+%3D+0+to+x+%3D+pi%
29%2Fpi

What do you want?

>> No.1106330

>>1106324
My answer is more right.

>> No.1106335

>>1106330

What was your answer?

>> No.1106337

>>1106335

>>1106293

>> No.1106339

0.07958923738717876149812705024217046140293154042473332135734787051717376016313210129737854003906249
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999747555689199382527168413631144544305417376821072571...

Am I cool yet Vladimir?....Vladimir?

>> No.1106344

>>1106337

That's not even the answer my young friend.

>> No.1106350

one hundredth = 0.01