## Search found 33 matches

- Sun Jul 19, 2015 6:46 am UTC
- Forum: Science
- Topic: Pluto down, next stop...interstellar?
- Replies:
**30** - Views:
**6133**

### Re: Pluto down, next stop...interstellar?

How do you plan to get a signal back to earth from however many lightyears away? It's hard enough talking to Pluto.

- Sat Apr 25, 2015 5:27 am UTC
- Forum: Mathematics
- Topic: Sum of sin^2(pi/n)/n
- Replies:
**2** - Views:
**1634**

### Sum of sin^2(pi/n)/n

Does the sum of sin^2(pi/n)/n (from 1 to infinity) have a known closed form? It appears to converge quickly to ~1.09751258244.

- Thu Nov 06, 2014 10:46 pm UTC
- Forum: Mathematics
- Topic: Multiply 2 terminating numbers and get a repeating decimal?
- Replies:
**6** - Views:
**3024**

### Re: Multiply 2 terminating numbers and get a repeating decim

If the set of prime factors of the denominator in your base is a subset of the prime factors of the base (without repetition), the decimal expansion will terminate; otherwise it will repeat. a*b = 7761021455127555974443/23283064365386962890625 23283064365386962890625 = 5^32 -> the fraction will term...

- Fri Sep 12, 2014 5:20 am UTC
- Forum: Mathematics
- Topic: The Shortest String Containing all Permutations of n Symbols
- Replies:
**29** - Views:
**28066**

### Re: The Shortest String Containing all Permutations of n Sym

Doesn't finding a short length-5 sequence automatically imply the existence of shorter sequences of length 6 and up?

- Thu Jan 23, 2014 4:25 am UTC
- Forum: Mathematics
- Topic: Matlab alternatives
- Replies:
**4** - Views:
**2219**

### Re: Matlab alternatives

If you like python, numpy/scipy are great. Throw in matplotlib (not as popular) and you have all of matlab's functionality. Sympy if you want to do symbolic manipulation.

- Sun Dec 08, 2013 5:42 am UTC
- Forum: Mathematics
- Topic: a sumatory (summatory?) problem
- Replies:
**7** - Views:
**2160**

### Re: a sumatory (summatory?) problem

http://xkcd.com/1047/

See also http://oeis.org/A073009, it seems nobody has managed to connect this sum to any other known values.

See also http://oeis.org/A073009, it seems nobody has managed to connect this sum to any other known values.

- Thu Nov 07, 2013 7:31 pm UTC
- Forum: Mathematics
- Topic: Dogma in Math
- Replies:
**98** - Views:
**14279**

### Re: Dogma in Math

0! = Γ(1) = integral of x^(1-1)*e^(-x) dx from 0 to infinity = integral of e^(-x) dx from 0 to infinity = 1

- Sat Nov 02, 2013 4:21 am UTC
- Forum: Mathematics
- Topic: Optimization Woes with Pizza
- Replies:
**22** - Views:
**5290**

### Re: Optimization Woes with Pizza

And what about the 3 dimensional (or n dimensional) case(s)?

- Fri Sep 13, 2013 3:04 am UTC
- Forum: Science
- Topic: Solid Expansion
- Replies:
**9** - Views:
**2031**

### Re: Solid Expansion

Of course not. You also don't notice its decrease in mass arising from E = mc^2. Both effects are way too small to measure anecdotally.

- Wed Aug 14, 2013 12:20 am UTC
- Forum: Mathematics
- Topic: Throwing a random die
- Replies:
**20** - Views:
**5031**

### Re: Throwing a random die

In some cases there would be no clear up-face. For eg: a tetrahedron. (In that case, convention says that the down-face is the one 'rolled'.) I should have said, when I said "lands on" I meant the down-face, otherwise like you said it would be ambiguous in most cases. Am I right in assumi...

- Tue Aug 13, 2013 8:18 pm UTC
- Forum: Mathematics
- Topic: Throwing a random die
- Replies:
**20** - Views:
**5031**

### Throwing a random die

Given an arbitrary convex polyhedron, are there any algorithms (other than a brute force physics simulation) that allow you to determine the probability of landing on a particular face from a "random" throw (as in dice)? I realize there are probably problems with formalizing what a random ...

- Fri Apr 12, 2013 6:57 pm UTC
- Forum: Mathematics
- Topic: Combinatorial game with infinite width game-tree
- Replies:
**26** - Views:
**3685**

### Re: Combinatorial game with infinite width game-tree

My idea for how to study the game would be first to limit the number of stones, and then see what happens to the game as the number approaches infinity and see what you can generalize.

- Wed Apr 03, 2013 1:54 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1193: Externalities
- Replies:
**505** - Views:
**148187**

### Re: 1193: Externalities

I did get a little carried away (but I should really get some sleep right now), 10 24 might be vaguely close to the number of total hashes generated, but obviously only a small fraction are sent to the server, and not all actually improve the score. I'm going to blame the fatigue on the DST. 10^24?...

- Wed Apr 03, 2013 12:05 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1193: Externalities
- Replies:
**505** - Views:
**148187**

### Re: 1193: Externalities

Some of the top entries are being deleted. Makes me wonder what's going on behind the scenes...

- Tue Mar 26, 2013 7:08 pm UTC
- Forum: Mathematics
- Topic: Name this curve
- Replies:
**23** - Views:
**5018**

### Re: Name this curve

It's a pretty straightforward numerical integration (assuming I didn't screw something up). I get an area of -0.198140234735592 (which is not, by the way, equal to 1 - 1 / Gauss's constant) and a curve length of 1.639346234237188 (with 0 <= t <= 1).

- Sun Mar 24, 2013 7:41 am UTC
- Forum: Mathematics
- Topic: Optimization Problem
- Replies:
**4** - Views:
**2200**

### Re: Optimization Problem

For all of these questions you want to make the piece of fabric as close to square as possible, since that's the shape where you can maximize the diameter. You can always make a square from a rectangle in 1 cut, so all 3 of your questions have the same answer. Make a straight horizontal cut at some ...

- Wed Mar 20, 2013 2:30 am UTC
- Forum: Mathematics
- Topic: Number of days between consecutive Easters
- Replies:
**2** - Views:
**1716**

### Re: Number of days between consecutive Easters

Using http://www.smart.net/~mmontes/nature1876.html this algorithm and calculating the delta between Easters on consecutive years between 1 and 10000 I get: 357: 3866 385: 3176 350: 2450 378: 506 So 378 is the least common. The date of Easter has a period of 5.7 million years, IIRC, and if use a bet...

- Mon Jan 14, 2013 8:54 pm UTC
- Forum: Mathematics
- Topic: [HOMEWORK] Arccot problem
- Replies:
**3** - Views:
**1760**

### Re: [HOMEWORK] Arccot problem

Another hint:

arccot(x) = arctan(1/x)

arctan(x) = -i * ln((1 + ix) / sqrt(1 + x^2))

tan(x) = i * (e^(-ix) - e^(ix)) / (e^(-ix) + e^(ix))

arccot(x) = arctan(1/x)

arctan(x) = -i * ln((1 + ix) / sqrt(1 + x^2))

tan(x) = i * (e^(-ix) - e^(ix)) / (e^(-ix) + e^(ix))

- Fri Dec 21, 2012 1:07 am UTC
- Forum: Mathematics
- Topic: Modular matrix power for very large exponents
- Replies:
**2** - Views:
**2006**

### Modular matrix power for very large exponents

I'm trying to implement a modular matrix power function for large exponents (A^e (mod m) for e = 10^10^100 or more). I know about the binary decomposition method, but that is still completely impractical for these large numbers. What algorithms should I be looking at? The size of the matrices can be...

- Fri Dec 14, 2012 9:33 am UTC
- Forum: Mathematics
- Topic: tree growth / thingy problem
- Replies:
**21** - Views:
**3070**

- Tue Dec 11, 2012 12:31 am UTC
- Forum: Mathematics
- Topic: Probability that x/y > x^y
- Replies:
**10** - Views:
**2367**

### Probability that x/y > x^y

If you compute the number of all integer (positive and negative excluding 0) pairs (x, y) for x in range(-h, h) for y in range(-h, h) inclusive s.t. x/y > x^y vs total pairs, you get the following plot: http://imgur.com/lKrku

What number is this approaching as h -> infinity?

What number is this approaching as h -> infinity?

- Mon Dec 03, 2012 7:06 am UTC
- Forum: Mathematics
- Topic: How many functions are there over a given number of states?
- Replies:
**3** - Views:
**1601**

### Re: How many functions are there over a given number of stat

I guess that depends on what you mean by "general"... the sequence is given by the Euler transform of the CIK transform of the recurrence equation a(n+1) = (1/n) * sum_{k=1..n} ( sum_{d|k} d*a(d) ) * a(n-k+1) (I don't know what a CIK transform is).

- Tue Oct 23, 2012 11:36 pm UTC
- Forum: Mathematics
- Topic: probability of random walk bot getting stuck
- Replies:
**25** - Views:
**3255**

### Re: probability of random walk bot getting stuck

I'm getting an expected value of ~70 (var = 2500) for the 2d case in my simulation.

The number of steps goes up dramatically for the 3d case- usually in the thousands of steps, which makes it hard to do any kind of analysis.

code: http://pastebin.com/rxHmmypw

The number of steps goes up dramatically for the 3d case- usually in the thousands of steps, which makes it hard to do any kind of analysis.

code: http://pastebin.com/rxHmmypw

- Mon Oct 01, 2012 11:02 am UTC
- Forum: Mathematics
- Topic: Exponent of a two-by-two matrix
- Replies:
**3** - Views:
**2649**

### Re: Exponent of a two-by-two matrix

You just need to use the exponential power series (see http://en.wikipedia.org/wiki/Matrix_exponential). Of course actually computing this infinite sum isn't always easy and that's where your eigenvalues might come in.

- Thu Sep 27, 2012 11:12 pm UTC
- Forum: Mathematics
- Topic: Traffic load balancing... What's the probability model?
- Replies:
**3** - Views:
**835**

### Re: Traffic load balancing... What's the probability model?

Isn't this just a multinomial distribution? You might have to do some sums if you want the distribution of each link though.

- Thu Sep 20, 2012 7:38 pm UTC
- Forum: Mathematics
- Topic: Lottery Problem: "All or Nothing"
- Replies:
**8** - Views:
**7596**

### Re: Lottery Problem: "All or Nothing"

Call k the total amount of numbers to be picked, and n the number of possible numbers. There are n! / k!*(n-k)! combinations that can be picked. Only 1 of these matches exactly. There are (n-k)! / k!*(n-2k)! combinations that have no numbers matching, so n needs to be at least 2k. n = 2k is also whe...

- Thu Sep 20, 2012 1:15 am UTC
- Forum: Mathematics
- Topic: Parabola in 3 dimensional space/line passing through object?
- Replies:
**18** - Views:
**5373**

### Re: Parabola in 3 dimensional space/line passing through obj

You can find the equation of the parabola defined by 5 points by parameterizing the parabola (P(t) = [t, 0, a*t^2]), then multiplying by the appropriate rotation matrices (http://en.wikipedia.org/wiki/Rotation_matrix#Three_dimensions), and adding a translation vector. Then solve it like a system of ...

- Thu Aug 23, 2012 9:46 pm UTC
- Forum: Mathematics
- Topic: Conway's Game of Life: Collapsing Lines
- Replies:
**8** - Views:
**3193**

### Re: Conway's Game of Life: Collapsing Lines

Well you could start by writing a program to determine whether a line collapses or oscillates indefinitely. Here's a (slow) python script I wrote (http://pastebin.com/mXTYUXbB). I don't know whether it's possible for a line to produce a glider, which I haven't checked for and would result in an infi...

- Tue Jul 31, 2012 10:23 pm UTC
- Forum: Mathematics
- Topic: Frustrating Indefinite Integral
- Replies:
**16** - Views:
**5487**

### Re: Frustrating Indefinite Integral

http://math.stackexchange.com/questions ... -logarithm

Here's a stackexchange discussion on this integral if you're looking for more ways to derive f(1).

Here's a stackexchange discussion on this integral if you're looking for more ways to derive f(1).

- Sat Jul 28, 2012 12:11 am UTC
- Forum: Mathematics
- Topic: Frustrating Indefinite Integral
- Replies:
**16** - Views:
**5487**

### Re: Frustrating Indefinite Integral

otherwise: ((2 * log2(a) + 1) / (2a)) * ln^2(2)

Actually these are equivalent, so all you need is (-ln(2) * ln(2a^2)) / (2a).

- Sun Jun 10, 2012 1:58 am UTC
- Forum: Mathematics
- Topic: Seeming Coincidences
- Replies:
**1** - Views:
**1623**

### Re: Seeming Coincidences

I assume you've seen this comic?

- Thu May 31, 2012 5:33 am UTC
- Forum: Mathematics
- Topic: Fitting circles under a curve
- Replies:
**18** - Views:
**3985**

### Re: Fitting circles under a curve

Is there a closed form expression for the same scenario but with squares instead of circles? It's much easier to derive the equation (a(0) = 0, a(n) = W(e^(a(n - 1))) + a(n - 1)) but the sum seems to converge very slowly (maybe my implementation of the lambert W function is just inefficient). I get ...

- Wed Apr 21, 2010 9:21 pm UTC
- Forum: News & Articles
- Topic: Apple Employee Misplaces New iPhone
- Replies:
**24** - Views:
**2847**

### Re: Apple Employee Misplaces New iPhone

Oh sure, he just 'happened' to leave his phone in a bar...

Apple has done things like this in the past. It would really surprise me if this wasn't a deliberate leak.

Apple has done things like this in the past. It would really surprise me if this wasn't a deliberate leak.