Search found 868 matches

by LucasBrown
Sat Dec 26, 2015 1:47 am UTC
Forum: Mathematics
Topic: Counting tetris arrangements
Replies: 2
Views: 1862

Counting tetris arrangements

So I received this lamp for xmas... https://www.thinkgeek.com/images/products/zoom/f034_tetris_stackable_LED_desk_lamp.jpg It consists of the seven Tetris pieces; the long one plugs into the wall, and the other pieces can be pushed up against it to light up. Their arrangement must be coplanar, and t...
by LucasBrown
Thu Dec 17, 2015 3:36 am UTC
Forum: Science
Topic: Wendelstein 7-X
Replies: 43
Views: 7925

Re: Wendelstein 7-X

If the helium and the neutron carry equal kinetic energies, then their momenta will have different magnitudes.
by LucasBrown
Tue Dec 15, 2015 3:49 am UTC
Forum: Science
Topic: Unbihexium density?
Replies: 11
Views: 3060

Re: Unbihexium density?

Incidentally, where did you get tungsten in that purity / shape? I've been looking for some in a spherish sort of form with a purity in the range of 99%, but all I can find is ultra-expensive precision-machined stuff.
by LucasBrown
Sat Nov 28, 2015 8:12 pm UTC
Forum: Mathematics
Topic: Record High/Low
Replies: 3
Views: 1666

Re: Record High/Low

But if the distribution shifts, then the probability of a record is increased in the direction of the shift, with the net result being an increase in the total number of records — for example, the planet is warming up, so we can expect (and in fact we do observe) an excess of record highs and a dear...
by LucasBrown
Mon Nov 16, 2015 7:13 pm UTC
Forum: Forum Games
Topic: Count to a Million
Replies: 85243
Views: 5942083

Re: Count to a Million

2 × 3 × 29 × 359
by LucasBrown
Fri Oct 02, 2015 12:08 am UTC
Forum: Mathematics
Topic: Factoring numbers of the form p^x+q^y
Replies: 3
Views: 2005

Re: Factoring numbers of the form p^x+q^y

If both exponents are powers of 2, then we're looking at generalized Fermat numbers . If p=y and x=q , we have ourselves a Leyland number . If both exponents are 4, we're dealing with quartan numbers . I am not aware of any term that encompasses all numbers of the form you're discussing, so I'll ana...
by LucasBrown
Mon Jun 22, 2015 2:41 am UTC
Forum: Coding
Topic: Happy bases
Replies: 12
Views: 3325

Re: Happy bases

That appears to be correct, but it's been several years since since I (briefly) studied quadratic fields, so I wouldn't go so far as to give it my seal of approval.
by LucasBrown
Sun Jun 21, 2015 9:56 pm UTC
Forum: Mathematics
Topic: A Diophantine equation related to happy bases
Replies: 3
Views: 1451

Re: A Diophantine equation related to happy bases

I should have included the clause "in a nontrivial way" in the original claim. I'll edit that now.
by LucasBrown
Sun Jun 21, 2015 8:02 pm UTC
Forum: Mathematics
Topic: A Diophantine equation related to happy bases
Replies: 3
Views: 1451

A Diophantine equation related to happy bases

In a thread in the coding section , notzeb stated with incomplete proof that there is a number n >1 with happy b ( n ) = n if and only if b 2 +1 is composite, where happy b ( n ) is the sum of the squares of n 's digits when written in base b . It is fairly simple to show that any solution to happy ...
by LucasBrown
Sun Jun 21, 2015 1:33 am UTC
Forum: Coding
Topic: Happy bases
Replies: 12
Views: 3325

Re: Happy bases

notzeb wrote:This might help: ... b^2+1 can be written as the sum of a square and an odd square in a nontrivial way if and only if it is composite.


Could you explain that a bit more?
by LucasBrown
Tue Jun 16, 2015 10:37 pm UTC
Forum: Coding
Topic: Happy bases
Replies: 12
Views: 3325

Happy bases

A happy number is defined as follows: ⋅ Given a number n , repeatedly replace n with the sum of the squares of its digits. ⋅ This will eventually reach a cycle of numbers of at most 3 digits: the cycle will either be 1 --> 1 --> 1 --> etc, or consist of number(s) greater than 1. ...
by LucasBrown
Sun Jun 07, 2015 9:21 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 382
Views: 121333

Re: Math: Fleeting Thoughts

Do I sense a fellow TMLT reader?
by LucasBrown
Sun Jun 07, 2015 9:51 am UTC
Forum: Computer Science
Topic: Deliberately bad algorithms
Replies: 120
Views: 45424

Re: Deliberately bad algorithms

Could you explain that for people who don't know Haskell?
by LucasBrown
Wed Jun 03, 2015 3:48 am UTC
Forum: Computer Science
Topic: Deliberately bad algorithms
Replies: 120
Views: 45424

Re: Deliberately bad algorithms

Or you could just bogosort the list and then extract the middle element.

Elegantly bad: deterministic primality test via trial division implemented in regular expressions. Uses O(n2) time and O(n) memory.

Code: Select all

import re
def isprime(n): return not re.match(r'^1?$|^(11+?)\1+$', '1'*n)
by LucasBrown
Wed Jun 03, 2015 3:36 am UTC
Forum: Computer Science
Topic: How efficient is the H.O.W. solution?
Replies: 1
Views: 3485

Re: How efficient is the H.O.W. solution?

A more common name for the HOW solution is "right hand rule". You might have better searching luck using that, but you'll want to add "maze" or something similar to the search string lest you get swamped with results about vectors. There's some discussion of this solution and oth...
by LucasBrown
Mon Jun 01, 2015 2:57 pm UTC
Forum: Coding
Topic: Useful applications of recursion?
Replies: 19
Views: 4456

Re: Useful applications of recursion?

You mean the Euclidean algorithm? That's actually (IMO) more obvious to implement iteratively than recursively. For example, in Python we have def gcd(a, b): while b: a, b = b, a%b return a but now that I think about it, the recursive solution is a bit more elegant: def gcd(a, b): return gcd(b, a%b)...
by LucasBrown
Mon May 25, 2015 8:07 am UTC
Forum: Mathematics
Topic: "Late math"
Replies: 1
Views: 1197

"Late math"

I'm helping put together a math circle class targeted at high-achieving middle schoolers / high schoolers concerning mathematics that was "discovered late" in the sense that deriving it requires no recently-developed apparatus. Topics of this flavor include ⋅  The pigeonhole prin...
by LucasBrown
Tue Apr 28, 2015 2:03 am UTC
Forum: Mathematics
Topic: Real roots of polynomials with integer coefficients
Replies: 10
Views: 2376

Re: Real roots of polynomials with integer coefficients

... I'm an idiot. That was easy.
by LucasBrown
Tue Apr 28, 2015 1:27 am UTC
Forum: Mathematics
Topic: Real roots of polynomials with integer coefficients
Replies: 10
Views: 2376

Re: Real roots of polynomials with integer coefficients

quantropy: You mention at the bottom of your page that we can ignore squarefree polynomials, but I'm not convinced that your argument for ignoring them is valid. Sure, we can divide by the repeated factors until the polynomial's squarefree, but it's plausible that the result of this division could h...
by LucasBrown
Sat Apr 25, 2015 6:04 am UTC
Forum: Mathematics
Topic: Sum of sin^2(pi/n)/n
Replies: 2
Views: 1528

Re: Sum of sin^2(pi/n)/n

Wolfram|Alpha doesn't simplify it at all, so there's a good chance that if a closed form exists then it's rather ugly and quite hard to derive.

Incidentally, your sum has the wrong sign. It should be positive.
by LucasBrown
Sat Apr 25, 2015 2:09 am UTC
Forum: Mathematics
Topic: Real roots of polynomials with integer coefficients
Replies: 10
Views: 2376

Re: Real roots of polynomials with integer coefficients

>-): I am quite fond of sympy, but it's even slower than mpmath, and general formulas do not exist for degree 5 and higher. jaap: That is impressively elegant. jestingrabbit: ...that makes sense. Why did I not think of that? General plan of action moving forward: 0. Linear / quadratic: use the exact...
by LucasBrown
Fri Apr 24, 2015 10:02 am UTC
Forum: Mathematics
Topic: Real roots of polynomials with integer coefficients
Replies: 10
Views: 2376

Real roots of polynomials with integer coefficients

I'm writing some code to enumerate the real algebraic numbers. This entails root extraction, so I have a few questions in that direction. My code (Python) currently uses numpy.roots when I'm going for speed and mpmath.polyroots if I want to be precise. I don't like either package, so I'm researching...
by LucasBrown
Mon Apr 20, 2015 3:58 am UTC
Forum: Mathematics
Topic: Lagrange numbers and badly-approximable irrationals
Replies: 2
Views: 1021

Lagrange numbers and badly-approximable irrationals

Is there a general formula for the terms of the first column in the table at Mathworld's article on Lagrange numbers ? In other words, what is the sequence of irrational numbers that are badly approximable, in descending order of badness? The right column of that table is known and stated (just appl...
by LucasBrown
Thu Apr 09, 2015 11:28 pm UTC
Forum: Forum Games
Topic: The Incredible Changing Sentence
Replies: 5621
Views: 597396

Re: Dear Cthulhu Platonically Coveting a Rabbi.

Drat, the colorless kelpie, flashed, "my light relief!" from its belly button fabulously.
by LucasBrown
Wed Apr 08, 2015 4:11 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1509: "Scenery Cheat Sheet"
Replies: 77
Views: 13243

1509: "Scenery Cheat Sheet"

http://imgs.xkcd.com/comics/scenery_cheat_sheet.png Title: “At the boundary between each zone, stories blend together. Somewhere in the New Mexico desert, the Roadrunner is pursued by a tireless Anton Chigurh.” The Kill Bill bit is incorrect. The desert bits were all shot in California, as evidence...
by LucasBrown
Sun Nov 23, 2014 12:33 am UTC
Forum: Mathematics
Topic: [Resolved] Proving some inequalities
Replies: 2
Views: 1565

Re: Proving some inequalities

#1: Well that was distinctly non-obious.

#2: I am an idiot.

Thanks!
by LucasBrown
Thu Nov 20, 2014 6:56 pm UTC
Forum: Mathematics
Topic: [Resolved] Proving some inequalities
Replies: 2
Views: 1565

[Resolved] Proving some inequalities

I'm helping prepare a class on inequalities for a high-end high-school-level math circle. The class covers things like the Cauchy-Schwartz, Young's, Hölder's, rearrangement, Chebyshev's sum, isoperimetric, Bonnesen's, Jensen's, Bernoulli's, power mean, etc. Part of the materials will be a set of cha...
by LucasBrown
Sat Apr 19, 2014 12:51 am UTC
Forum: Coding
Topic: Approximate speed classes of programming languages
Replies: 33
Views: 47256

Re: Approximate speed classes of programming languages

It would be interesting to see where Python interpreted via PyPy falls. Is there any data on that?
by LucasBrown
Sun Apr 13, 2014 1:49 pm UTC
Forum: The Help Desk
Topic: Diagnose random freezes (Linux)
Replies: 9
Views: 4557

Re: Diagnose random freezes (Linux)

Concerning the video card: I will try switching drivers if it is not too complicated. By "move it to another machine and see if the crashes still occur" you mean "see if the first machine now does not crash" or "see if the second machine now crashes"? I'd find a proble...
by LucasBrown
Sat Mar 22, 2014 3:45 am UTC
Forum: Coding
Topic: [Resolved] [Python] Parallel, fully independent tasks
Replies: 11
Views: 4747

Re: [Resolved] [Python] Parallel, fully independent tasks

concurrent.futures is actually really really good at things like this - in fact, it's basically what it exists for. It abstracts away the queue management you've coded manually (which wouldn't be needed if you didn't care about the results). I would code your case roughly like this (untested): from...
by LucasBrown
Thu Mar 20, 2014 2:14 am UTC
Forum: Coding
Topic: [Resolved] [Python] Parallel, fully independent tasks
Replies: 11
Views: 4747

Re: [Python] Parallel, fully independent tasks

@wumpus: Thanks! That was quite helpful. My code is now def multifactor(n): # Note that the multiprocessing incurs overhead to the tune of 0.1s. # This is generally negligible compared to the time to factor the sort of numbers this is fed # and the time already spent in the first two phases of the f...
by LucasBrown
Tue Mar 18, 2014 10:35 pm UTC
Forum: Coding
Topic: [Resolved] [Python] Parallel, fully independent tasks
Replies: 11
Views: 4747

Re: [Python] Parallel, fully independent tasks

Of course it gives parallelism! That's what the whole threading and multiprocessing modules are for!
by LucasBrown
Tue Mar 18, 2014 6:29 pm UTC
Forum: Coding
Topic: Suggest an open-source C/C++ IDE
Replies: 22
Views: 7247

Re: Suggest an open-source C/C++ IDE

What about Geany?
by LucasBrown
Tue Mar 18, 2014 11:39 am UTC
Forum: Coding
Topic: [Resolved] [Python] Parallel, fully independent tasks
Replies: 11
Views: 4747

[Resolved] [Python] Parallel, fully independent tasks

I'm writing a function in Python to factor large numbers by running several algorithms in parallel (Pollard's Rho algorithm, Lenstra's elliptic curve method, and the multiple-polynomial quadratic sieve. I've defined those as pollardRho() , ecm() , and mpqs() . Each takes the number to be factored as...
by LucasBrown
Sat Feb 22, 2014 3:33 am UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 382
Views: 121333

Re: Math: Fleeting Thoughts

The 48 known Mersenne primes have exponents 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036...
by LucasBrown
Thu Jan 30, 2014 2:44 pm UTC
Forum: General
Topic: You can't prove a negative : why, logically?
Replies: 25
Views: 5466

Re: You can't prove a negative : why, logically?

Or you could mix it with pastry and honey to get baklava.

There's a joke about balaclava in there somewhere, but I can't figure out how to structure it...
by LucasBrown
Fri Dec 20, 2013 5:46 am UTC
Forum: Coding
Topic: Bugs popping up only under optimization
Replies: 25
Views: 7487

Bugs popping up only under optimization

I've been around programming long enough to have heard horror stories of code that does exactly what it's supposed to when fed into a plain compiler but, when compiled with -O2 or -O3 enabled, starts misbehaving. I have not been around programming long enough to have actually encountered such code. ...
by LucasBrown
Thu Dec 19, 2013 5:26 am UTC
Forum: Coding
Topic: [done] Translating Mathematica to Python
Replies: 7
Views: 4713

Re: Translating Mathematica to Python

eta oin shrdlu wrote:I think your line

Code: Select all

            if a*x == r+y and a >= minden*x:

should be

Code: Select all

            if a*x == r+y and a >= minden:

But the original Mathematica code has minden * x instead of just minden...

... huh. That did the trick. I'm declaring this problem solved. Thanks!
by LucasBrown
Thu Dec 19, 2013 3:44 am UTC
Forum: Coding
Topic: [done] Translating Mathematica to Python
Replies: 7
Views: 4713

Re: Translating Mathematica to Python

divisors(1368857880324) takes less than half a second on my computer. I accidentally submitted my previous post after the first sentence. Here's the rest: Also---the code has now been more-or-less translated and simply laughs at the 4-minute benchmark (which was set way back in 1996), computing Egy...
by LucasBrown
Thu Dec 19, 2013 3:06 am UTC
Forum: Coding
Topic: [done] Translating Mathematica to Python
Replies: 7
Views: 4713

Re: Translating Mathematica to Python

I'll eventually submit this code to SymPy, so I'm using their built-in divisors method.

Go to advanced search