Sir Isaac Newton was much more than a physicist. Some of his maths is amazing too.
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During our journey through mathematics we've already met
some geniuses. Pythagoras, Aristotle, Descartes, Galileo.
This video is about Newton. He said himself,
I built my science on the shoulders of giants. Newton of course is just another
giant. Newton is famous for his discovery of the gravity law and also details on
light. But those people were really multi-dimensional. And in mathematics
Newton wanted to solve, to find an easy way to calculate a + b to the power of
something. So let's start, a + b to the 2nd power, square. There is an elegant
graphic solution to that. Let's build a square. And each side is built with
a + b, a + b. You build the square and you can organise the square in four
pieces. A little square here, a square, a bigger square here, b square. And two
rectangles. The two rectangles have the same surface a x b, so the answer to
the question a + b to the 2nd power is equal to a square + twice ab
+ b square. Now let's do it for the 3rd square. There is no visual possible,
because you should do that in three dimensions. But believe me the answer a
+ b to the 3rd power will be something with a 3rd + +
b 3rd. And if you look at the coefficients,
you find 1 3 3 1. You remember the first was 1 2 1, now 1
3 3 1. And so Newton connected his problem, the a + b, to a triangle
named, I don't know why, Pascal's triangle. And the triangle is built this way. You'd
start with 1 and each digit is the sum, each number, is the sum of the two upper
digits 1 2 1, 1 3 3 1, 1 4 6 4 1. And this connection between Newton and Pascal
immediately gave a solution to his problem a + b to the nth power because you
just need the nth line. And this triangle has lots of properties. For example, each
line, if you sum the numbers of the line, you have a power of 2. Let's take line
number 4. 1 + 4 + 6 + 4 + 1 is equal to 16, and 16 is 2 to the 4th
power. And this formula designed by Newton was a tremendous breakthrough in
probability. Why? Because imagine an experiment with two outcomes, 3 chances out of
10 to get this result. 7 chances out of 10 to get that result. The sum of the
probability must be 1. 3 over 10 + 7 over 10 is equal to 1. Now let's take those
two numbers and you put in the formula of Newton and of course you have 3
over 10 + 7 over 10 to the nth power. 1 to the nth power is always 1 and
that's how you can easily connect this work of Newton to the science of
probability and what we call those distribution curves. Did you know that
it’s faster to travel in a cycloid than a straight line
Find out more in the next episode of our series 'The history of maths'.
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