## Friday, October 3, 2014

### Interesting Numbers

I enjoy math.  I mean I really enjoy math.  Two of the main reasons I enjoy math is: (1) I only work on the math I want to work on, and (2) I don’t have to do it – if I am not enjoying it I can move on to something else.  I have to admit that I don’t enjoy all math (I can’t say I really enjoy differential equations), but there is enough math out there that I haven’t learned about yet that is enjoyable and interesting to me.  A lot of that math just does not appear in text books, or on math tests, or on the SAT.  You probably won’t see a lot of that kind of math on this blog.
My love of math is not understood by most people – but that’s OK.  I don’t always understand why other people are interested in collecting stamps, hunting, playing video games, or reading books on historical fiction.  We are different people – it is not logical that different people are all going to like the same activities.
Most of the stuff I blog about probably won’t help you raise your grade point average, or earn you a promotion or raise at work.  Me? – well I’m retired – I don’t have to worry about grades or work – I can do what I want to.  On this blog I can blog about the math that I enjoy and find interesting.  I hope that you will find my blog interesting too.
If you are still reading this then you are probably one of those people that enjoy math also – maybe not all math, but some math!
It is hard to say what makes math interesting to me.  What I think is interesting may not be interesting to others – even though we are looking at the same thing.
Take for instance the number 15.  It’s an odd number, it’s not prime, it is equal to 3 times 5.  Is that enough to make it interesting?  Probably not.  But have you ever noticed that 15 is equal to the sum of all the digits from 1 to 5?  15 = 1 + 2 + 3 + 4 + 5.  Well that is a little interesting.  27 has the same property: 27 = 2 + 3 + 4 + 5 + 6 + 7 (27 equals the sum of all the numbers from 2 to 7.  And 429 is equal to all of the numbers from 4 to 29.  That makes these numbers interesting to me.  They have a property that most numbers don’t have.  Which is also why I think 891,406,343,154,063 is an interesting number – it is equal to the sum of all of the numbers from 8,914,063 to 43,154,063.  I think that is astonishing.  The next smaller number that has this property is over 16 trillion less than this number.
Most people think 891,406,343,154,063 is just an uninteresting “big number”.  Math people know it is not a really big number (over 99.9% of numbers are larger than this number), and some math people know that it probably is an interesting number (but don’t know why – because not all math people have studied the same kinds of math).  But I know why it is interesting, and now so do you.  Next time you see your math teacher, math professor, or boss ask them why that number is interesting – they won’t know – but you will.
I also think the number 988,001 is interesting.  If I take the inverse of this number (turn it into a fraction 1/998,001) and write out the decimal expansion of this number it show an interesting result.  Don’t try this on your calculator – it can’t do it.  You either have to use long division (which you can do but it takes a long time) or a computer program.  I can write it out from memory to 3000 digits because I am good with fractions and I know a secret.  1/998,001 = 0.000,001,002,003,004,005,006,007,008,009,010,011,012,013, … ,996,997,999,…  (It counts from 0 to 997 without an error – then it skips 998, but includes 999.  It’s all done in 3 digit “chunks”.)  I also know how to make a number that counts to 999,997, or 999,999,997, or as high as I want it to (I’ll share that in a future blog.).
Will that help you get a promotion or a raise?  No.  Will it help you pass the final exam?  No.  Will it help you get a date to the prom?  Well, maybe – if you ask a “math nerd”.  (By the way, I do not like to be called a “math nerd”.  I prefer the term “mathematical badass”.)
I hope this explains what I want to do with this blog, and I hope that you will come back to see what else.

David.