Mark Chu Carroll over at the Good Math, Bad Math blogs has a fascination with bizarre bits of math as I do. Today, he had a post about something which I investigated quite a bit a number of years ago: so-called Egyptian Fractions. The ancient Egyptians had a peculiar way of representing fractional numbers. They always represented values as the sum of fractions with 1 in the numerator. Hence, if you were trying to represent 3/4, you’d instead write that as 1/2 + 1/4. Well, that doesn’t seem so hard. Let’s try to represent 2/3. A moment’s worth of thought might give you the expansion 1/2 + 1/6. How about 3/7?

It might take you a bit longer to come up with the expansion 1/3 + 1/14 + 1/42. Or maybe you got a different expansion, like 1/3 + 1/11 + 1/231. The fact is, these Egyptian fractions are a good deal more subtle than you might have imagined. There are numerous algorithms to try to generate interesting (mostly short) representations for arbitrary fractions: the best online reference that I’ve found (with plenty of code and information to chew through) is David Eppstein’s terrific page on Egyptian Fraction Algorithms.

[tags]Egyptian Fractions,Mathematics[/tags]

ESPN is reporting that Athletic slugger Frank Thomas could be about to sign an agreement with the Toronto Blue Jays. Sniff. I really hoped that the A’s might cough up the big bucks to resign Thomas, who was really the only bat in the lineup for the Athletics that any team took seriously. But the Jays are reportedly offering a two year deal potentially worth $30 million, so you can hardly blame the Big Hurt for looking toward greener pastures. Well, if you are on the way to Toronto, take my best wishes Frank. It was great to see a sure Hall of Famer swing the bat, you made a great impact on our season, and I’ll be sad to see you missing from the Oakland lineup.

[tags]Oakland Athletics,MLB,Baseball[/tags]