Dude, I think that you are less intellectually rigorous than you strive to appear, and rude to boot.
Did you look at the paper that the visualization cites? It provides both the semicircular version and a sine-wave version. The paper does some mathematical analysis on the sine wave version, and putatively comes up with a way to transform the series of sine waves for a Sieve of Eratosthenes of a finite size into a single function that is close to zero for composites and significantly non-zero for primes.
I assumed on first sight of the visualization that the semicircles were standing in for sine waves, and I was right. I assumed that semicircles were used because they are easier to draw, or because it's easier to see the Sieve of Eratosthenes in it, or that it was necessary to make this adjustment in order to perform well. Or maybe just that it was prettier. But it was clearly alluding to sine waves. Looking at the paper demonstrates that I was correct on this assumption.
By the way, you do know that any periodic function can be expressed as a sum of sine waves, don't you? Even a wave form made out of repeating semicircles. What I didn't know before this is that Fourier transforms are used in number theory, and now I know, thanks to this visualization. And best of all, this visualization let me intuit that fact on my own. I can't imagine a visualization that could provide anything better than that!
Did you look at the paper that the visualization cites? It provides both the semicircular version and a sine-wave version. The paper does some mathematical analysis on the sine wave version, and putatively comes up with a way to transform the series of sine waves for a Sieve of Eratosthenes of a finite size into a single function that is close to zero for composites and significantly non-zero for primes.
I assumed on first sight of the visualization that the semicircles were standing in for sine waves, and I was right. I assumed that semicircles were used because they are easier to draw, or because it's easier to see the Sieve of Eratosthenes in it, or that it was necessary to make this adjustment in order to perform well. Or maybe just that it was prettier. But it was clearly alluding to sine waves. Looking at the paper demonstrates that I was correct on this assumption.
By the way, you do know that any periodic function can be expressed as a sum of sine waves, don't you? Even a wave form made out of repeating semicircles. What I didn't know before this is that Fourier transforms are used in number theory, and now I know, thanks to this visualization. And best of all, this visualization let me intuit that fact on my own. I can't imagine a visualization that could provide anything better than that!