Happy 2012!

Happy 2012! The above image (click on it) is from Jesse Vig’s geoGreeting site where you can enter a message and obtain a link which you could send in an email. It is also possible to send as an E-card. Jesse Vig noticed whilst working on a Google Maps project that a number of buildings looked like letters of the alphabet when viewed from above. and his website was born!

So to complete the new year greeting we need of course some number properties of 2012.
We could use Tanya Khovanova’s site: Number Gossip where we learn that 2012 is evil!

We’ll come back to the meaning of evil shortly! To take a look at the other properties, you will find that you can click on each for a definition.

Apocalyptic power:  a number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal). If we check the value of 2 to the power of 2012 – we can use WolframAlpha – we see that there is a string of three consecutive 6s.

2012 is a composite number because it is a number greater than 1 which is not prime.

2012 is deficient because the sum of all its positive divisors except itself is less than 2012.
1+2+4+503+1006=1516.

2012 is clearly even.

To understand the definition of evil requires a knowledge of binary, an evil number has an even number of 1s in its binary expansion. 2012 as a binary number is 11111011100 which we see has an even number of 1s (8). If you are interested in finding out more about binary, have a look at Math is fun on the subject.

Finally 2012 is an Ulam number. An Ulam number is a member of an integer sequence devised by and named after Stanislaw Ulam. The standard Ulam sequence begins 1, 2 … then subsequent numbers in the sequence are found by adding up two earlier ulam numbers. The number must be as small as possible and be the sum of two different earlier terms; but it can only be found in one way.
So if we start 1, 2  the next number is clearly 3, next we can have 4 because there is only one way of forming 4 from 2 earlier numbers: 1+3 (2+2 does not count as the two numbers must be different). We now have 1, 2, 3, 4… we cannot have 5 because that can be formed in two ways 1+4 or 2+3. The next in the sequence is 6 (2+4). The sequence carries on as follows: 1, 2, 3, 4, 6, 8, 11, 13, 16….. and if we carry on then 2012 is in there!

WolframAlpha can of course supply some number properties of 2012 or provide a calendar for the year …or even send us best wishes for the new year! Wishing all of you a great 2012!

By Colleen Young Posted in Number

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