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Mathematics Weblog » 2005 » July

Summer Reading

Monday 11 July 2005 at 5:25 pm | In Articles | 7 Comments

I finally succumbed and bought Martin Gardner’s Mathematical Games: The Entire Collection of His Scientific American Columns. Of course, as it had to be sent from America, the postage wasn’t cheap and it locked up my computer when I first tried it. Turning off CD autorun solved that problem.

Now I can spend the summer reading all those articles I’ve never read or even only half-remembered. The ability to search all the articles is a real boon. Did you know, for example, pi is mentioned 5645 times in the books?

In Fractal Music, Hypercards and More… Martin Gardner refers to the e^\pi>\pi^e problem (which I’ve mentioned before) and says:

    Dozens of proofs have already been published. One of the shortest is based on the fact from elementary calculus that x^{1/x} has a maximum value when x equals e. Hence e^{1/e} is greater than \pi^{1/\pi}}. Multiplying each exponent by \pi^e and canceling yields the inequality e^\pi>\pi^e.

The perils of publishing mathematics 😕 Can you spot the error and correct it?

Getting help

Monday 4 July 2005 at 11:08 pm | In Articles | Post Comment

At the S.O.S. Mathematics Cyberboard there’s a nice example of how students can spend all day struggling with a problem, but with a little help they can see their way to solving it in seconds. Such forums are great for getting those little nudges in the right direction that are so crucial in mathematics.

The student was trying to solve:

    For a,b,x,y \in \mathbb{R} show that if |x-a|< \varepsilon and |y-b|<\varepsilon then |xy-ab|<\left(|a|+|b|\right)\varepsilon+\varepsilon^2

If you’ve had a go and would like the ‘nudge’ the forum provided then click here Continue reading Getting help…

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