Archive for January, 2010

The Scarecrow and the Pythagorean Theorem

January 10, 2010

Ray Bolger, who played the Scarecrow (THE Scarecrow) was born 106 years ago today.  In his honor, here’s a clip from Youtube in which the Scarecrow gets a Doctorate of Thinkology and makes reference to the Pythagorean Theorem — sort of.  (The exact words of the Scarecrow are, “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. Oh, joy, oh, rapture. I’ve got a brain!”)

Ray, here’s to you!  And remember: 1062=562+902.

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So what’s interesting about 2010?

January 2, 2010

It seems (perhaps only to me) like it ought to factor nicely, because 20 is twice 10.  But once you factor out that 10 and that 3 you’re just left with a prime, since 2010 is just 2·3·5·67. (Speaking of four primes, did you know that you can get four prime New York Steaks for $132.95 on Amazon?  I was relieved to see that they were not available for Super Saver Shipping.)

Wolfram Alpha points out that 2010 itself is a factor of 296-1.  And  Number Gossip adds that it’s untouchable, which means that there aren’t any numbers whose proper divisors add up to 2010.

It can be written as 133122 in Base 4, which is kind of cool, and as 6, 3, 12 in Base 18; my favorite, however, is that it is 5, 10, 15 in Base 19.

Finally, it’s equal to:
669+670+671
400+401+402+403+404
127+128+…+141 and several others
[Hmmm…I can find a string for each of the 7 odd factors, but I’m not sure that exhausts all of the possibilities.]

While getting ready to post this, I noticed that MathNotations has a similar post from yesterday.   Whoops!

Happy New Carnival!

January 1, 2010

It’s a new year, maybe a new decade (I’m a plebian), and the perfect day for a new Carnival!  Though I can’t help but feel guilty that I didn’t mention the previous one, and not because it wasn’t good either — it was.  So here’s a summary of the carnivals and a chance to start the New Year off on the right foot!

There was Math Teachers at Play #20 back on its original turf at Let’s Play Math, with it’s regular assortment of lots of fun math.  Speaking of Let’s Play Math, Denise has her annual New Year’s post with the 2010 Mathematics Game; I remember thinking last year that I should get a head start on that, and didn’t, but we’ve got some mathy company coming this weekend so it’ll provide some good entertainment.

Then there was the Carnival of Mathematics #60 over at Σidiot’s Blog (heheh — I just got that).  That carnival appeared back on December 4, and had some neat modular origami and puzzles and National Math Blog Writing month and a portrait of someone who isn’t a mathematician.

Next came Math Teachers at Play #21 at Math Mama Writes in mid-December (and Sue also has  a recent post exploring Pythagorean Triples, which seem to come back again and again as neat things to think about).

And now we’re at Carnival of Mathematics #61!  It’s up at Walking Randomly today, with puzzles and statistics and many other good things.  There’s a mention of calendars at the end, which reminded me of the printable dodecahedral one that TwoPi mentioned two years ago.  Not that that is a calendar or anything, but at least it’s a dodecahedron.

And there we have it.  Happy New Year!