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 - 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.

JovialJMan - Tutoring

"JovialJman is so cool, he teaches people by folding his arms and ignoring them. Or by letting the lady behind him that you probably didn't notice deal with it." - OddballGreg

Teaching people things is a difficult thing to do. Sometimes because the person doesn't want to learn, or because what they're trying to learn is hard to understand. In my experience, learning to teach people what they need to know to do something correctly is both difficult and necessary for their success. Let's talk about that.

I have always been that guy who helps people out when it comes to maths, and I have found that oftentimes people don't understand the things they are doing in maths, but try to do it anyway so they can get it done and out the way (Rather than serving detention). Since realizing that, I started teaching people maths in a way that helps them to understand what it is that they are actually doing at school and now (for a fee) and I enjoy it.

Two years ago, I would never have said that I would ever enjoy teaching but when it comes to maths it has turned out to be something I quite enjoy. The only problem being that I have a bit of a low tolerance to people that don't really listen. (A rather big problem if you have many people asking you to tutor them.).

I have, so far, tutored two people this year, (and two while I was still in school),  and from what I could understand from them, is that I actually help them understand the concepts behind the maths which made it easier for them to do and easier to remember the steps as a result. My memory is something to laugh at but maths I can just do even though I don't always know how to explain it to someone. I can however do it because I understand the meaning behind what I am doing as I work towards the answer.

There are different ways to go about teaching, (which I found out while trying to learn how to teach, yes you have to learn to teach believe it or not, bachelors in education are not silly qualifications.). I tried to see where the person was at with their thought process and build on that and correct the errors; as starting from the beginning means a lot of time might be wasted on stuff they know really well already. After you have found out how they approach different problems you can get them to refine their actions and provide a more secure way of achieving the answer or become faster at the approach they are already using by improving their understanding of the methods and the reasons behind them.

Unfortunately, my overconfidence with maths did me from getting the matric mark I wanted as I did not concentrate on the different aspects of certain questions and, liking getting to the answer straight away, I left out crucial steps where in maths you have to show how you got to the answer to be fully awarded the makrs. This is really annoying in my opinion but it is something that they must keep in place. This allows the people that do not understand the different parts in maths too well to try and understand the steps and get at least some of the marks, instead of giving up hopelessly, (even though some still do that).

Despite all that, teaching is not as easy as I thought it might have been. I have had my struggles and downfalls, but I always managed to get it right in the end thanks to hard work, a good understanding of maths, and my humbling experience in the form of worse than expected school results. I will say thank you to all the teachers out there that may be reading this as you must put up with a lot from your pupils and yet you still go at it day after day. I commend you. So for those of you that cause mischief in the class, do remember that the teacher does what that they do for your benefit, not theirs. Without teachers, our regular lives would not be possible, so keep that in mind the next time you want to be painful in class.

In any case, that's all I've got for the topic of tutoring for now. Do you teach people and appreciate just how much it takes to teach properly, or are you a trouble maker in class for whatever reason, please let us know down in the comments or on Facebook/Twitter. If you enjoyed this post and would like to read the newest posts as they are published then please like us on Facebook and/or follow us on Twitter using the associated buttons on the bar to the left. Do you have any friends that would like to become a teacher one day, or a friend that causes trouble in class despite how hard these unfortunate teachers work; if so, please share this with them to show what teachers and tutors go through to help expand the minds of their students. Thank you for taking the time to read today's post, and I shall write again overmorrow.

Learn hard comrades.

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.