Here’s something I made yesterday! (Note, I strongly suggest watching it fullscreen, in HD if you have the bandwidth for it.)
Can you figure out what’s going on? The source code for the animation is here; I was inspired by Jason Davies’ visualization which was in turn inspired by this.
Reblogged this on nebusresearch and commented:
The Math Less Traveled has a lovely video here, animating the Sieve of Eratosthenes, one of the classic methods of finding all of the prime numbers one wants. I suppose it won’t eliminate writing out and crossing off numbers for extra credit on a math test. I actually remember that being one test I had in, I believe, seventh grade, for reasons that I don’t think I ever got. Possibly the teacher wanted to have an easy time grading, or was giving everyone a break from too much computation by shifting to evaluation of our crossing-out abilities.
Could you take a look at “Sloppy Computing” and give your opinion ? Specifically, does this form of computing dramatically increase computer power for math programs (Like simulators) ?
Yes, I think “sloppy computing” is a very cool idea. Ultimately, I think it’s primarily more about reducing power usage than it is about increasing speed — as computers get smaller, power consumption and heat dissipation are becoming major limiting factors. Sloppy computing could indeed be very useful for certain types of computations such as simulation.
I love it. Gorgeous, and gives a lot of feel for the sieve.
Is there anyway to add a counter in the lower left – to show what number you’re at?
Oh, a counter in the lower left is a good idea!
This gave me the idea to form the infinite product . The primes will be those integer where .
The infinite product you give converges to zero for every value of x so f(x) = 0 identically.
So f'(x) = 0 identically.
Thanks, I actually suspected that. Can you find a way to account for this by for example defining a sequence of functions and setting so that the sequence converges?
Cn = (n!)/(pi^(n-1) x^(n-1)) .
Of course… For large we will have and taking will compensate for those factors.
Have you studied what the limit function will look like?
It should say .
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