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.

JovialJman - The Beauty Of Mathematics

"Maths stuff. Brain hurts already. Sadface." - OddballGreg

Do you find things really beautiful and don't know why? Do you hate this torturous subject at school that we call... dare I say it; "Maths"? Well they are actually related strangely. Lets talk about that.

In school, most students really hate that time of day when they have to go to their maths lesson. ("Trust me, I was one of them." - OddballGreg) They say it is tedious and that they will never use these things in real life. I agree that it does get rather monotonous, although, that can be down to the way it is taught, rather than because of the subject itself. There are so many ways in which maths can be really easy, useful and maybe, just possibly, even fun (ugh).

Most teachers in primary school tend to use the rote method to teach maths, which means that you will have to do it over and over until you know what to do. It is useful only if it paired with method teaching, which tries to get you to understand what it is that you are doing and why. (Notice that it should be together." The first thing is understanding that one mathematical concept can be written in multiple different ways eg, 1 + 2 = 3. In this case; what is on the left is the same on the right which is rather simple but you must understand that in order to do more advanced mathematics.

After you understand that these mathematical concepts can be written differently, you can start to manipulate larger numbers with far more ease, despite it all just being fancy ways of counting. Vihart on YouTube did an awesome video about it which is below this paragraph. I urge you to look at her channel as it is awesomely amazing. (Awesomely is a word right?) So if it is all fancy counting and you know how to count then you can do maths, (or at least some of it anyways).

Then there are ways in which maths can show us the beauty in things, and is part of the reasons that the beauty is there to start with. For instance there are pine-cones. Why is it in a spiral that looks so cool? How is it a spiral and is there maths involved? Well, since the pine-cone's scales need to grow in such a way that allows the previous and next scale to grow, it does so in a specific mathematical ratio. This allows each scale to have the optimal amount of space to grow without interfering with the other scales and results in the the spiral shape after multiple layers.

The one further back looks like a peacock. The peacock cone was taken from here.

Then there is this fancy thing mathematicians call the golden ratio. It is the ratio of 1:1.61803... This just means that you take a measurement of one thing and it will be 1.62 times smaller or bigger than the next measurement. People have found that the human body is largely comprised of this ratio with regards to beauty, such as the distance from your feet to your belly button, then from your belly button to the top of your head should be 1:1.62 if you are average, proportional person, along with the first digit of your finger to the second and second to the third.

Because everyone is a mathematician. Image gotten here.

Maths also has uses in every day life; if you want to know how much the dinner you just had is going to cost you, or if you want interest on your money at the bank. There is even cases that can help with happy hour in the bedroom, (you know ... when you are doing your homework). 

So if you want to check if you are beautiful by mathematical standards, (beauty is of course in the eye of the beholder though), or if you need to check how much those groceries costed you, remember maths is always there to help. If you liked this post or have any comments/suggestions on how to improve it or future posts, please leave a comment in the comments section down below, or write to us on Facebook/Twitter as we here at TCSA love to hear from you. Do you have any mathematicians as friends or friends that like to confirm they are beautiful, please share this with them as I am sure they will appreciate it. If you would like to show your support or want to see the latest posts as they come out, please like us on Facebook or follow us on Twitter with 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 really good day and I shall speak again overmorrow.

Stay beautiful my friends.