FREE CHOCOLATE!

Recently, I have seen a video in which it was told how to "get free chocolate", I was amazed about that paradox, so I started to investigate for myself, then I realized that it could be a good idea to post what I learnt about the subject, so here I bring you a bit of information about the "Chocolate Paradox".

In the video we can see that a man cuts a chocolate bar in two parts, but one different from the other, he starts to cut in the second  square in the left, and finishes in the third one from the other side. Then he cuts a vertical row from the left side, and finally, he cuts the last square of this row. Then he put the right piece on the left, and the cut row on the right, and there you have it! One "new" square of chocolate!

GIF that shows the cuts from a different way!

This of course has an explanation, because of course we are not creating chocolate from nothing! It seems that the chocolate bar, once we cut it, is the same, but with each cut we do, the bar decreases a little, just a few millimetres from each square of the last horizontal row. This image explains very well what is happening:

This peculiar phenomenon is part of the Geometric Paradoxes of Mathematics, where you can find another interesting paradoxes of shapes, surfaces and areas...

Hope you enjoy the video and the info given!

Euler number (e)

For my first post, I bring to you some information of one of the most famous special numbers on Mathematics, the number of Euler, most known as number e. This number appears many times, mostly of them to makes our lifes more difficult, it´s scary when you see it, because that means that the problem will turn a little bit more difficult, but once you´ve practice with it, it can be your friend when resolving a problem.

The number of Euler is a mathematician constant, it´s discovery was credited to Jacob Bernoulli, but the constant then was symbolized with the letter b. Was Leonhard Euler who started representing it with the letter e.

It has infinite decimals, as it is irrational, but the first decimals are easy to remember, here you have a little trick. The first three numbers are well known (2.71). Then you have the number 1828 that it appears doubled and finally you have the angles of a Right-angled isosceles triangle, which are 45º, 90º, 45º. Then you´ve got: e=2.7118281828459045…

An interesting property of the number e, if you divide a number into parts, and then you multiply those parts together, you´re going to get a number, but, did you know that the closer that number is to the e number (2.71), the bigger the final number is? Let´s demonstrate it with an example:

                -We have the number 12 for instance, then we divide it into equal parts: 20/4=5, then we do five to the power of four: 5x5x5x5=1024. But if we want the highest number that that formula could give, we have to divide our number (20) with a number that gives as result of the division a number close to the Euler number:

                                               20/8=2.5

                                               2.5^8=1525.87…

But if we, instead of 8, we divide 20 by for example 9, we´ve got 2.22…

                                               Then 2.22^9=1309.715

I hope you found these info at least interesting or useful!

WELCOME!

I welcome you to this blog, where you will find interesting info about Maths, or other subjects related with Maths, this blog is part of a project of the UE(Universidad Europea)´s calculus class. I will post several information and it will be as well as in video format or as links, interviews and images. Hope you´ll enjoy it as I do!