What is pi?
A circunference is the set of points in a plane that are at equal distance (the radius) from a single point - the center. So a circunference is a closed line with a length we call perimeter. We can also define the diameter wich is just the double of the radius. (see picture below)
The interesting property of a circunference is that we only have to know a quantity (a number) to be able to draw one. Give me a radius and i will draw one. Instead you can give only the diameter. It is also possible to make a circunference knowing only the perimeter. So a circunference is a number and a rule - the rule that all points are equidistant of a center.
So it must not seem strange the fact that for all circunferences the relation between the perimeter and the radious is the same. This means that if you pick a circunference and divide its perimeter by its radious you get always the same number. This could look amazing but remember that you only need one quantity to define the figure. If i we have a radius, there can be only one perimeter correspondent to it. So
and we are free to chose the name of this constant. We can call it Potato, Glass, 3 times BlaBla, etc. But let's define
Then we can measure perimeters and radius of several circunferences and compute the value of pi with the precision we want (not that easy!). In fact, there are other ways to do that only with more or less heavy mathematics and computation but i want to keep this simple. pi value is known for a long time (see here a nice history about pi but remeber to see other sources). You probably know it is something like 3.14...
We have now a definition:
On the other hand we have -- now that we know the value of PI -- a way to compute the perimeter knowing the radius:
This is a linear relation. A double radius gives a double perimeter; one third of a radius gives one third of the perimeter; and so on...
There are many interesting facts about this important number and it's easy to find information about it.
The interesting property of a circunference is that we only have to know a quantity (a number) to be able to draw one. Give me a radius and i will draw one. Instead you can give only the diameter. It is also possible to make a circunference knowing only the perimeter. So a circunference is a number and a rule - the rule that all points are equidistant of a center.So it must not seem strange the fact that for all circunferences the relation between the perimeter and the radious is the same. This means that if you pick a circunference and divide its perimeter by its radious you get always the same number. This could look amazing but remember that you only need one quantity to define the figure. If i we have a radius, there can be only one perimeter correspondent to it. So
and we are free to chose the name of this constant. We can call it Potato, Glass, 3 times BlaBla, etc. But let's define
Then we can measure perimeters and radius of several circunferences and compute the value of pi with the precision we want (not that easy!). In fact, there are other ways to do that only with more or less heavy mathematics and computation but i want to keep this simple. pi value is known for a long time (see here a nice history about pi but remeber to see other sources). You probably know it is something like 3.14...We have now a definition:
On the other hand we have -- now that we know the value of PI -- a way to compute the perimeter knowing the radius:
This is a linear relation. A double radius gives a double perimeter; one third of a radius gives one third of the perimeter; and so on...There are many interesting facts about this important number and it's easy to find information about it.
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