Hey, I am Doctor Shah. I was the National Lector Competition winner in 1989. And I am the maths master in Mathscool. Now, ready for a new word in math? Circumference of the circle. So imagine you have a cape tin, and you want to line the cape tin with greaseproof paper. To start with, you can cut out that circle that goes at the bottom, simply by tracing around it on a greaseproof paper. What about the band that's going to go around the inside here? To do that, we need to know the circumference of the circle. The circumference of the circle is the length, all the way around the outside of the circle. That's ripping around the outside of the circle. And then, cut it to the length of the circle so that you have a strip that is the same length as the circumference of the circle. What you notice if I compare to the diameter of the tin, is one lots of the diameter, two lots of the diameter, three lots of the diameter, and a little bit. Three and a little bit, times the diameter. What is that little bit? While actually the circumference is 3.14 times the diameter, 3.14 being an approximate answer for what that little bit is. It's actually more accurately 3.14159265 and it goes on and on and on. And that number is called Pi. It is given the Greek letter Pi. And you can find that number on your calculator. So, to work out the circumference of my circle, I'm going to first of all, measure the diameter of the cape tin which is 18 centimetres and then I am going to multiply that diameter, 18 by pi, 3.14. We can check into a calculator. On a scientific calculator, I'll type in 18 times pi. Now, most scientific calculator nowadays, it gives you the answer exactly as 18 pi because it knows once it goes decimal, it is not going to be completely exact. But there is a decimal button to turn it into decimal. It tells me the answer 56.54866. But I am going to call that 56.5 for my purposes here. So I know the circumference is going to be 56.5 centimetres all the way around this circle. So if I cut my greaseproof paper to that land, it should fit exactly. I then, I am just going to try around the cape tin to see how well I have worked the circumference of the cape tin. And you can see it's pretty much perfect. So this number 3.1415926, roughly 3.14 seems quite like random. Seems, if it is being made up by mathematicians. But actually, this was known from a long time ago. We know the Egyptians knew about the number pi because, if we look at their pyramids, pyramids were being built sort of in that shape. The ratio of the parameter of the base. If you take the parameter of the base, and you decide it by the height of the pyramid, the answer turns out to be twice pie, 3.14, pretty accurately. So effectively, what that means is they were trying to build their pyramid as if they would fit perfectly inside a circle. And then, they would have done that if they knew pi was 3.14. .

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