Search found 33 matches

by nadando
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.
by nadando
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.
by nadando
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...
by nadando
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?
by nadando
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.
by nadando
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.
by nadando
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
by nadando
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)?
by nadando
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.
by nadando
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...
by nadando
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 ...
by nadando
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.
by nadando
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?...
by nadando
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...
by nadando
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).
by nadando
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 ...
by nadando
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...
by nadando
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))
by nadando
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...
by nadando
Fri Dec 14, 2012 9:33 am UTC
Forum: Mathematics
Topic: tree growth / thingy problem
Replies: 21
Views: 3070

Re: tree growth / thingy problem

I haven't proven this, but I believe the probability that the tree is dead after n steps is given by A167424 / A058891.
by nadando
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?
by nadando
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).
by nadando
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
by nadando
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.
by nadando
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.
by nadando
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...
by nadando
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 ...
by nadando
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...
by nadando
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).
by nadando
Sat Jul 28, 2012 12:11 am UTC
Forum: Mathematics
Topic: Frustrating Indefinite Integral
Replies: 16
Views: 5487

Re: Frustrating Indefinite Integral

If a is not a power of 2 the formula is: (-ln(2) * ln(2a^2)) / (2a)

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


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

Image
by nadando
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 ...
by nadando
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.

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