JovialJman - More Special Numbers (And Other Interesting Mathematical Anomalies)

Numbery things again, I wonder if you can see it is an interest of mine?

Numbers can be a rather big interest of mine because with certian parameters it can be said for certian things will come up. Not many other fields can say the same. So let's talk about some of the mathy things.

So in the last post I talked a bit about Pi and things around it, well Brady on his YouTube channel Numberphile uploaded "Mile of Pi" as a thank you to his million subscribers. In the video they talked about some of the interesting things that are in Pi and have printed the first million digits of pi end to end and this is where the Mile of pi comes from. I would recommend watching the video and the extras in the second video as there is really fascinating things in each video.

I have talked a little about the Golden ratio in how things are beautiful and where it crops up in the human body, but I never really got into it. So now I am going to talk more about it. The golden ratio is a relation of 2 lengths. If you have length A and length B, the golden ratio is when you have (A + B) /A is equal to A/B. Now if you want you could go work this out, and find that it only holds true for the one ratio. The way you can work out the ratio is (1 + √5)/2. This is what gives the 1:1.618033... and many people have worked with it in many fields. There are links between this and the Fibonacci numbers. I shall urge you to try and do some research on this and see what you find. Google is your friend here.

I have recently found out an interesting thing about paper sizes. There is a standard way of measuring paper, and it is often referred to the A scale. It starts off with A0 and the area of this size paper is 1m^2. Now most people will know the A4 and A5 as these are the sizes of normal standard books used everywhere, (or at least here in South Africa anyway.) Now there is a cool thing about the A scale, if you were to fold the paper exactly in half along the long edge, you will get the next size paper in the sequence, but the ratio of the long side to the short side will always be the same. So if you fold a paper of A0 in half you will get A1, then if you fold A1 in half you will get A2, and so on and so forth. Now this ratio of these sides will only work like this with a ratio of √2. If it had any other ratio, it would not work at all.

Since we are talking about √2 I think I should mention this video where Numberphile talked about it, along with the paper example, and the maths behind it. Now √2 has had a tough time trying to get recognized, as since in previous times there were people that really acknowledged the works of mathematicians, and they really liked rational numbers. Rational numbers are and number that can be written in the form A over B, where A and B are integers. Now since √2 was not able to be written like this, these people did not like it and tried to dismiss it. By using the Pythagorean theorem you can get it by having a right angled triangles with the short sides being of equal length 1. The hypotenuse will the be √2.

Now we go onto a greek letter Tau. This greek letter, (it looks like this τ , it is like Pi but with one leg.) The main thing Tau is used for is another way to write 2 times Pi, and in some cases it would make equations a lot nicer to look at, and make some of the teachings easier, (as said by a few people), but there is a whole debate amongst people which is better and which we should use. Numberphile did a very entertaining video about it as well. 

Anyways, that is all I have fro today, I hope you have enjoyed reading today's post, which I might add to it later. Thank you for taking the time to read it, and if you know of anyone who would like to read this post, please share it with them, as we would greatly appreciate it. If you liked what you read, or have any questions or ideas, please leave them in the comments below, or on Facebook/Twitter. While you are there, can you please like our Official Facebook page, and/or Twitter account, and if you are not there, you can use the associated buttons on the bar to the left. I hope you have/had a brilliant day, and I shall talk again overmorrow.

Never stop learning.