Back when this video was making its rounds on the interwebs (it periodically resurfaces but its popularity seems to be dying out, perhaps behaving like a damped harmonic oscillator), I did a little project explaining the motions involved.
It appears something got wonky with the transparency options but everything else seems to work fine. If you click and drag on the animations you can rotate them in 3D. Try adding a bunch of extra pendula if your computer can handle rendering it.
Let’s see if the interactive stuff works this way…
cool, I guess I’ll have to just do it this way and supplement it with screenshots and explanation
The other day my friend noticed that for the first several pairs of consecutive integers, the difference of their cubes was prime. I investigated the subject and am posting the Mathematica file to test CDF compatibility with the blog.
Well wordpress.com is retarded and claims that embedding is not allowed “for security reasons”, so I guess I just have to link all my Mathematica work.
What it came down to, in case anyone was wondering, is explained by the graph above. The horizontal axis is in 100s of numbers, the vertical axis is the percentage of those numbers that are prime. The red curve corresponds to the percentage of the odd integers which are prime (up to the first 1,000,000) and the blue curve is the percentage of the numbers generated by the difference of cubes of sequential integers which are prime (up to the first 1,000,000). There doesn’t seem to be anything special about the difference of cubes of sequential integers with regards to primality. Further explanation is in the link.
In order to view interactive documents made in Mathematica, you will need the Wolfram CDF Player. It is available here http://www.wolfram.com/cdf-player/ or click on the link in the links section of this blog.