JovialJman - Special Numbers (And Other Interesting Mathematical Anomalies)

Numbers can make your head hurt, but they are everywhere.

Numbers are somethings that many people tend to hate working with during their High school career, but their are really strange things that can happen with them that are seen to be cool. Let us talk about that.

There is am amazing YouTube channel that is dedicated to all things mathematical, and the videos are really informative. A fair bit of the content of this blog may be found on Numberphile, links will be present where I can fit them in as well. Then there is Vi Hart which is just as awesome. If you have never heard of these people before, I would suggest go and look at their channels and if you like what you see, please show your support and subscribe to their channel.

If I say think of a big number, what would you say? one thousand, or a million? well there is a number so big there is no way to write it in one line. This humongous number is Graham's number. For an easy way to find out how big the number is look at this video. If you cannot watch the video, I hope I can explain it well enough. So Graham used a notation as arrows pointing upwards. Now 3↑3 is 3 to the power of three which equals 27. With one arrow it does not mean much but when we get to to or more arrows things get a bit interesting. Now 3￪￪3 is 3￪(3￪3) which is 3￪(27) which is 3 to the power of 27 this equals 7 625 597 484 987. With more than one arrow, the number before the arrows is raised to one less arrow so many times, this amount of times is the number after the arrows. This means that 3￪￪2 is 3￪3 which is 27 while 3￪￪4 is 3￪(3￪(3￪(3))) there is 4 threes and this translates to a tower of 3's four high.

When we get to 3 arrows thing are really big, so 3￪￪￪3 is 3￪￪(3￪￪3) and 3￪￪3 is that 7 trillion number. So 3￪￪(3^27) has a tower of 3's 7 625 597 484 987 digits high. now the answer to this has over about 3.6 trillion digits. The scientific way to write it, (since I will fill a few pages writing normally), would be 1.258 * 10^(3 638 334 640 024). This is a really big number as it is, but we are not even close to Graham's number yet. So now we have 3￪￪￪￪3. this will be 3￪￪￪3￪￪￪3, just try and picture that large numbers ... got it? me neither. Well now lets just call the answer to 3￪￪￪￪3 is G1, (quick note before I blow your mind, you see how adding one arrow escalates things, well we are about to add a jetpack to it.)

Ok so now we have G1, now this is the amount of arrows in the next one so 3(G1's￪)3, and this is equal to G2. Then repeat to have 3(G2's ￪)3 to get G4. Now you carry on with this until you get to G64 and you have arrived at Graham's number. So we have this really ... really big number, (do you need a new pair of pants like me?) and this is not even the biggest number anymore, there are some that are bigger. I would try and explain them but I don't even know how to explain them.


This video show some of the big numbers

So now that we have experienced large numbers, lets talk about some numbers that some people know about. Pi is one that a lot of people know about but not many know of its properties. Pi is the ratio of a circle's circumference and it's diameter, and it is roughly 3.14, which many people know, but it has a string of digits after that, that is never ending and never recursive. This means that it goes on for every and you will never know what it will be after a point where you stoped calculating it to be. Since there is this strange fact people have been calculating digit after digit, and as of 8 October 2014 13,300,000,000,000 digits have been calculated. it took 208 days to computat on a home computer, now supercomputers have gone to 2,576,980,377,524 decimal places on 29 april 2009, and this took 29.09 hours.

There is a day that is celebrated once a year for this magical thing dubbed Pi day. It is celebrated on March the 14th since it is 3/14 the first first 3 digits of pi. Next year is something special though. on
3/14/15 at 9:26:53 mathematicians all over the world will be up in awe since this precise second will be the first 10 digits of pi and somewhere in this second will be a point in time that will contain all the digits of pi. So then, on this you day, you should grab a pie and chow down on it and celebrate this wonderful day.

There is many other things that I can talk about, but that is for another day. If you have any opinions on anything I said, or would like to tell us anything, please do so in the comments below, and/or on our official TCSA Facebook page, and on Twitter as we here at TCSA love to hear from you. If you know of anyone who would like to know stuff about pi or that you just want to blow their mind with maths, please share this post with them as I am sure they would really like to thank you afterwards. Do you want to see more post as they come out, please like us on Facebook and/or follow us on Twitter using the associated buttons on the bar to the left. Thank you for taking the time to read today's post, and I hope you have/had a wonderful day.

Stay frosty.