Search found 3664 matches

by PM 2Ring
Sat Feb 07, 2009 3:53 pm UTC
Forum: Mathematics
Topic: Can I have your prime number?
Replies: 30
Views: 4807

Re: Can I have your prime number?

There's a nice prime counting formula, due to Riemann IIRC, that uses the (ordinary) zeta function. I coded this formula in C years ago. Here it is, in case anyone's curious. /* * R I E M * * A function found by Riemann for Pi(x), the number of primes <= x. * * These are the formulae, using a modif...
by PM 2Ring
Sat Feb 07, 2009 3:43 pm UTC
Forum: Coding
Topic: anything fundamentally wrong with...?
Replies: 26
Views: 2210

Re: anything fundamentally wrong with...?

Berengal wrote:Asserts are usually conditionally defined, so in release code it's nothing.


Exactly. So thinking of them as C's version of try...catch is somewhat misleading.
by PM 2Ring
Sat Feb 07, 2009 3:35 pm UTC
Forum: Science
Topic: Organic Vegetables
Replies: 73
Views: 4406

Re: Organic Vegetables

http://www.dhmo.org/ Welcome to the web site for the Dihydrogen Monoxide Research Division (DMRD), currently located in Newark, Delaware. The controversy surrounding dihydrogen monoxide has never been more widely debated, and the goal of this site is to provide an unbiased data clearinghouse and a ...
by PM 2Ring
Sat Feb 07, 2009 10:58 am UTC
Forum: Mathematics
Topic: golden ratio proof
Replies: 15
Views: 4368

Re: golden ratio proof

Are the colors in there due to colored lights, or has POV-Ray gotten sophisticated enough to model prisms? POV-Ray has been able to model dispersion for a while now, but it does slow down rendering a bit, as it has to trace more rays, so I rarely use this feature, and when I do I don't use many dis...
by PM 2Ring
Sat Feb 07, 2009 10:15 am UTC
Forum: Coding
Topic: anything fundamentally wrong with...?
Replies: 26
Views: 2210

Re: anything fundamentally wrong with...?

Asserts should not be active once the program has been released. They should only be active during the development phase.
by PM 2Ring
Wed Feb 04, 2009 12:01 pm UTC
Forum: Coding
Topic: anything fundamentally wrong with...?
Replies: 26
Views: 2210

Re: anything fundamentally wrong with...?

is there anything fundamentally wrong with using commas to string together what would otherwise be separate statements and ending the "block" with a semi I'll admit I was tempted to do this a few times, when I was young & foolish. :) And lived to regret it... I recommend avoiding this...
by PM 2Ring
Tue Feb 03, 2009 2:11 am UTC
Forum: Mathematics
Topic: golden ratio proof
Replies: 15
Views: 4368

Re: golden ratio proof

You may enjoy playing with the "Phibonacci" sequence Whoa... there's a part of me that wishes I did maths instead of physics... that is a very cool sequence. Now I'm trying to prove that the ratio of two adjacent Fibonacci numbers F(n)/F(n-1) approaches phi for n->infinity, but I am not s...
by PM 2Ring
Mon Feb 02, 2009 5:57 pm UTC
Forum: Mathematics
Topic: 1 + 1 = ?
Replies: 44
Views: 5648

Re: 1 + 1 = ?

I believe 1+1 was proven to be 2 around 1900 by Bertrand Russel. It was. I have a picture of his original work. Its a halarious paper long proof. He also spent a few hundred pages just laying the groundwork for it. Sort of. Russell & Whitehead were attempting to formalize mathematics, from the ...
by PM 2Ring
Mon Feb 02, 2009 5:42 pm UTC
Forum: Mathematics
Topic: Life and math
Replies: 21
Views: 2296

Re: Life and math

I reckon you ought to include as part of your presentation the Life form that generates the primes as a sequence of gliders. Another nice one is the recursive "unit cell": a Life form that simulates Life. It's probably more exciting than a simple Turing machine (although it pains me to say...
by PM 2Ring
Mon Feb 02, 2009 5:29 pm UTC
Forum: Mathematics
Topic: golden ratio proof
Replies: 15
Views: 4368

Re: golden ratio proof

You may enjoy playing with the "Phibonacci" sequence: \varphi^0 = 1 \varphi^1 = \varphi \varphi^2 = \varphi + 1 \varphi^3 = 2\varphi + 1 \varphi^4 = 3\varphi + 2 \varphi^5 = 5\varphi + 3 etc (Sorry about the poor formatting. I'd better learn some LaTex, I guess.:)) EDIT: This pic features ...
by PM 2Ring
Mon Feb 02, 2009 5:01 pm UTC
Forum: Mathematics
Topic: One of those questions on the philosophy of mathematics
Replies: 18
Views: 2556

Re: One of those questions on the philosophy of mathematics

The physical world can be modeled (to an extent) by mathematics. But conversely, the mathematical world can be modeled (to an extent) by physical objects. That doesn't mean that one is inherently more "real" than the other. To argue further, we need to define reality... It appears that man...
by PM 2Ring
Thu Jan 29, 2009 7:34 pm UTC
Forum: Science
Topic: Phase of one molecule
Replies: 14
Views: 1270

Re: State of one molecule

Temperature is usually defined as proportional to the mean kinetic energy of a whole bunch of molecules, so the temperature of a single molecule isn't well-defined, either. But I agree with the OP that the main issue is with the lack of intermolecular forces.
by PM 2Ring
Thu Jan 29, 2009 7:29 pm UTC
Forum: Science
Topic: Most silly "constant of nature"
Replies: 64
Views: 7161

Re: Most silly "constant of nature"

As long as we're being pedantic.... ... you can as easily have a mole of Carbon atoms as a mole of ping-pong balls... I doubt that. :) In theory, there is no difference between theory and practice. In practice, there is a huge difference between theory and practice. According to Wikipedia, the stan...
by PM 2Ring
Thu Jan 29, 2009 7:03 pm UTC
Forum: Mathematics
Topic: Favorite mental math tricks/shortcuts
Replies: 61
Views: 9546

Re: Favorite mental math tricks/shortcuts

(x^2 - y^2) = (x + y)(x - y) Very useful for the 10th graders I teach. I usually use this in the opposite direction. 17*13 = 15^2-2^2 = 221 Me, too. If you memorize the squares up to 25*25, and use a few other formulas, like (50 + x)^2 = (2500 + 100x +x^2) and (100 + x)^2 = (10000 + 200x + x^2) so ...
by PM 2Ring
Thu Jan 29, 2009 6:29 pm UTC
Forum: Science
Topic: After the big bang, where did pi, e and the rules originate?
Replies: 53
Views: 5362

Re: After the big bang, where did pi, e and the rules originate?

e, on the other had, is more "abstract" in the sense that we can't measure e like we measure pi. We can easily give a geometric definition for e. Draw the hyperbola xy = 1. The area under the branch in the ++ quadrant between x=1 & x=e is exactly one. And so is the area between x=e &a...
by PM 2Ring
Thu Jan 29, 2009 5:58 pm UTC
Forum: Science
Topic: Rapidly rotating wire
Replies: 52
Views: 3816

Re: Rapidly rotating wire

Alternatively, the problem can be analyzed in a rotating frame of reference centered on the wire's midpoint Can we? According to the OP: Lets say you have a long wire out in space, and you start spinning it very quickly around one end, so it looks sort of like a rope with a weight on the end being ...
by PM 2Ring
Thu Jan 29, 2009 5:39 pm UTC
Forum: Mathematics
Topic: objects that we'd like to hold, but can't in this universe
Replies: 41
Views: 6108

Re: objects that we'd like to hold, but can't in this universe

It's quite easy to make a flat model of a Klein bottle from paper & adhesive tape. Sure, it still self intersects, but you can cut it into a pair of Moebius strips with a pair of scissors. And regarding the projective plane, there are programs around that let you play with hyperbolic tessellatio...
by PM 2Ring
Thu Jan 29, 2009 5:06 pm UTC
Forum: Mathematics
Topic: Interesting sequences (Catalan, maybe?)
Replies: 42
Views: 3238

Re: Interesting sequences

I second t0rajir0u's nomination of derangements. The concepts are fairly easy to explain, and you can show the connection between the total number of permutations of n items (= n!) and number of derangements (= !n) and their relationship with e. I also like his idea of Beatty sequences, and not just...
by PM 2Ring
Thu Jan 29, 2009 4:38 pm UTC
Forum: Mathematics
Topic: Can I have your prime number?
Replies: 30
Views: 4807

Re: Can I have your prime number?

I think it's interesting to look at the primes from a complex POV. The Gaussian integers (complex numbers of the form a + bi, where a & b are both integers) have unique factorization. All the normal primes of the form 4n+3 are still prime in the Gaussians, all other primes have a Gaussian factor...
by PM 2Ring
Tue Jan 27, 2009 5:08 pm UTC
Forum: Science
Topic: Is consuming DNA safe? (not what you think. perverts.)
Replies: 39
Views: 5610

Re: Is consuming DNA safe?

You have to be really careful. Things labeled "75% ethanol" often contain methanol, which you definitely don't want to consume. That depends where you live. Some denatured ethanol does contain methanol, but it's pretty rare in Australia these days, and only used in certain applications. M...
by PM 2Ring
Tue Jan 27, 2009 4:37 pm UTC
Forum: Mathematics
Topic: x - cos(x) = 0
Replies: 36
Views: 10282

Re: x - cos(x) = 0

Prof. Dottie Fixed and I think that's probably part of why the name is what it is. And my high school colleague never published his result, so his chance of glory was lost. Thus is the lot of the 'umble amateur. :) Speaking of iterating cos, Julia sets of complex trig functions can look quite prett...
by PM 2Ring
Tue Jan 27, 2009 4:25 pm UTC
Forum: Mathematics
Topic: Can I have your prime number?
Replies: 30
Views: 4807

Re: Can I have your prime number?

From Wikipedia: In number theory, Skewes' number is any of several extremely large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x for which π(x) > li(x), where π(x) is the prime-counting function and li(x) is the logarithmic integral ...
by PM 2Ring
Tue Jan 27, 2009 4:08 pm UTC
Forum: Mathematics
Topic: Triangular Numbers
Replies: 9
Views: 1111

Re: Triangular Numbers

if we take the ratio of successive triangular squares, it converges to 17+12sqrt(2). How curious! Anyone familiar with the continued fraction of sqrt(2) will recognize 17/12 as a handy approximation of sqrt(2). Or for those who are more geometrically inclined, a 12, 12, 17 triangle is an isosceles ...
by PM 2Ring
Tue Jan 27, 2009 3:56 pm UTC
Forum: Mathematics
Topic: x - cos(x) = 0
Replies: 36
Views: 10282

Re: x - cos(x) = 0

You can also just do n2 = cos(n1). No calculus needed. Certainly! But it takes ages to converge. If we use Newton's method, it converges rather rapidly. After the first couple of iterations, the number of correct digits doubles at each step. I tried this a few days ago using bc & was most impre...

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