Why is calculus important? │ The History of Mathematics with Luc de Brabandère

Calculus was one of the most important theories ever developed in mathematics. But why do we need it? 

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Mathematicians sometimes love to push things to the limit and to see what happens. For example, one of the fields of their research is series. If you take the series 1+1/2 + 1/3 + 1/4 + + +, you go to the infinite. The series doesn't converge. Strangely enough, if you take the series 1 + 1/2 + 1/4 + 1/8, you don't reach the infinite, you reach a limit. 

Again, it's this beautiful opportunity to show it graphically. You take a square; a beautiful square and the side is length 1. If you cut it into two equal pieces this is a half, 1/2. Now let's take this piece, and again you cut it into 2 pieces. This square here is 1/4. The upper square, the same style. Again, you divide into 2 pieces. Each is equal to 1/8. And you can go up to the infinite and you will get the whole square. And the square is 1, the surface of 1. 

So, it shows, it's proof there is a limit to this series: 1/2, 1/4, 1/8, etc. etc. If you try to reach the limit, you sometimes find fascinating things. And one of the most famous examples is this one. 

Let's take (1 + 1/X )^X. How far does it go? Is there a limit? Yes, there is a limit. Let's take this 1, it makes (1 + 1/1)^1, this equals to 2. Now let's take X equal to 2. It's (1 +1/2)^2, which is 2.25. And if you go to the infinite, you finally get a number 2.71… etc. which is E, another magic number, exactly like Pi, like the Golden Number.

So, if you love mathematics you will love to push things to the limit and you maybe will surprised by extraordinary results once more. 

Join us next time to find out how nothing happens by chance. 

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