Friday, May 4, 2012

Famous Mathematical Constants I

Pi (not pie) is usually attributed to Archimedes. In any case, it's been around for a long time. And we use it in a lot of places (more on that later).

But first - what does pi represent?

In order to answer this question, I need to remind you about a tiny piece of geometry - about circles.

The measurement around the rim of a circle is called the circumference. The measurement across the centre of the circle (from edge to edge) is called the diameter.

Now at some point someone started investigating the relationship between the circumference and the diameter of the circle. Something like I did (and you can do it too if you don't believe me), except they did it a lot more times and probably a lot more accurately.

Draw a circle using a compass or other circle drawer. Measure the circumference of the circle with a piece of string.

Measure the piece of string.

Draw and measure the diameter.

Calculate circumference divided by diameter (called the ratio between circumference and diameter)


You see, if you do this accurately enough (which I definitely didn't) then you find that ratio is always the same. In fact it's always roughly equal to 3,14159... an irrational number which we call pi!

Now the first (and I think the most important use after all this fiddling around with string) of pi is to find the circumference of a circle more efficiently than measuring it with a piece of string!

Knowing just the diameter (or radius - half the diameter), we can use pi to calculate the circumference!

C = dπ = 2πr

And then we can also use pi to calculate the area of a circle (you might notice that the circumference is the derivative of the area :-) )

Here are some alternative ways of writing pi. As you can imagine, each one is linked to a very special and mostly very advanced branch of Mathematics. Here are some super awesome everyday applications of pi.

That's all from me for today...we'll tackle e next time!

1 comment:

  1. you could put a ~ on top of jj instead of dots and what would you get?