Some mathematical videos

Some videos:

Meep's Math Matters is a new series of videos that look at some simple mathematics. (You don't see Meep; you hear her voice and see her writing on an imaginary "board".) The first two installments are available on YouTube, and embedded below. The first one looks at the standard trick for summing an arithmetic series, and includes one of about a zillion retellings of the Gauss 1 + 2 + ... + 100 = 5050 anecdote; if you want to read more such retelings go here.)



The second installment shows how to sum consecutive even and odd numbers:



From Science after Sunclipse: all of first-year physics (a ridiculously fast-pased explanation of derivatives and integrals, the basic conservation laws, and so on) in nine minutes! This is from Caltech's The Mechanical Universe, a series of computer animations by Jim Blinn.



and The story of π, from Caltech's Project Mathematics around the same time; the animation is supposedly due to Blinn, and the video is credited to Tom Apostol (the number theorist). From this, I learned that "one of the most practical uses of supercomputers is calculating a billion digits of π." Some other videos I found at Google Video include The Law of Large Numbers (which includes a wonderful animation illustrating the law of large numbers in terms of random walks, set to some sort of futuristic music...) and The Optiverse, by John M. Sullivan, George Francis and Stuart Levy, showing an optimal (in some energetic sense) way to turn a sphere inside out! More information is available here. Mostly it is good for the pretty pictures.