Farewell to 2011

As has become a tradition here at CatSynth, we present our end-of-year image.

[Click to enlarge.]

It was a bit of a challenge to decide what to put in, as there were so many this time. But I think these are particularly representative. And it’s also significant that it is more colorful than previous end-of-year images.

The first few days of this year were quiet and a bit dark. That changed quickly, with tumultuous events around the world, and new experiences close to home. It’s the year I finally had a photography show, and by the end of the year I had several. There were new surprising types of performances and the costumes to go with them. I deepened my connections back in New York with friends, music, art and the landscape. And I no idea what I would have the chance to participate in something like the Occupy movement . There were many sad moments as well, with the loss of friends.

In all, 2011 has been particularly rich and productive, if sometimes a bit chaotic. If one had told me at the end of 2007 or 2008 (or 2001 for that matter) that this is what life would be like now, I would have been pleasantly surprised. There is a sense, however, that the patterns of this past year are not sustainable. This will have to be part of the plan for 2012, in particular getting organized, staying healthy and trying to make good choices. We will see how that unfolds as the new year progresses…

Happy New Year and thank you for all the support and warmth from those who read these pages!

Properties of 2011

The number “2011” abounds with fun numerical and “visual-numerical” properties. Early into the new year, we experienced the time “1:11:11 on 1/1/11″. And this week, we had the even more auspicious “1:11:11 on 1/11/11″, at least with the date-writing convention we use in the United States. This week all the dates have been palindromes using the two-digit year convention, e.g., today is “1 14 11″, and if one uses the full four-digit year, this past Monday was “1 10 2011″, also a palindrome.

While text-based properties are fun, they are somewhat arbitrary and less interesting than mathematical properties of numbers. First, 2011 is a prime number, the first prime year since 2003. And from @mathematicsprof on twitter, we have this interesting coincidence:

“2011 is also the sum of 11 CONSECUTIVE prime numbers:

In other words, this is not just a series of prime numbers, but all the prime numbers between 157 and 211. I like that the last prime in the series happens to be 211!

The Republic of Math blog follows the consecutive-prime inquiry further, with the observation that 2011 can also be written as the sum of three consecutive primes “661 673 and 677″.

From The Power of Proofs, we have the property that 2011 is the sum of three squares:

2011 = 392 + 172 + 72

However, any number not congruent to 7 modulo 8 will have such a property. I.e., if you divide 2011 by 8, you have 3 left over. So really 7 out of 8 integers can be expressed this way. Finding the series of squares can take some time, though.

Please feel free to share any other mathematical or fun coincidental properties in the comments below.