My number theory course has recently moved on to things that are a bit more technical and esoteric than our earlier fare, so I haven't felt they would make good blog fodder. If you need a quick math fix (and who doesn't?), you can have a look at this guest post I wrote for the Oxford University Press blog. It contains a few musings about pi, inspired by a recent satirical post over at HuffPo. Enjoy!
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Oh dear. A one point you state that 0.25 is the only way to represent 1/4. Surely we haven't forgotten that terminating decimals have two representations as decimals, and 1/4 is also 0.24999999... :-)
And I can't let a pi post go by without my favorite pi fact, that proves that pi is strictly less than 22/7: int_0^1 x^4(1-x)^4/(1+x^2) dx = 22/7-pi, and the integrand is nonnegative.
oh well ... already posted this comment to the wrong entry : Prof. Rosenhouse : Was wondering if you had ever heard of the Chudnovsky brothers (or met them?!), written about in the book "Panic in Level 4: ... Journeys to the edge of science". They are two russian born geniuses who built a supercomputer in their apartment in New York with the aim of finding the order in Pi. Believe they won the Macarthur prize (?). It's a great story!
Stephen --
What blog post did you read? I didn't say that the only way of representing 1/4 is .25. I said that if you divide one integer by another the resulting decimal either terminates or repeats. I used 1/4=.25 simply as an example of one that terminates.
ftfkdad --
I'm afraid I'm not familiar with the folks you're talking about. :(