Falando pelos Cotovelos

nice!!! ^_^

Pi is a finite number, and this method is just an approximation of pi. Consider a perfect wheel (in real life there is no such thing as a perfect wheel that I know of, but most wheel also approximate to the perfect circle) with a radius of 1 centimeter. If you roll out this wheel, you will measure pi cm on the floor, but you cant measure this distance exactly to 3.14159... cm, because there is always some deviation in the measurement or the instrument. Each instrument has a certain resolution which defines what the smallest value that is distinguishable on the instrument. If you take out a ruler, this will mostly have a resolution of 1 millimeter, if you try to measure something 0.1 mm, you can't use this instrument. Another parameter is the range of an instrument: this defines what the largest value is that one can measure. So take you standard ruler again and its range will be 0 to 15 cm in most cases.

In our measurements, let's say we have a measuring instrument that can measure to 1 µm (10^-6 meter) and has an infinite range (so we can measure from 0 µm to several light years with just this instrument). So if we take our wheel with diameter of 1 cm, we can measure (in the ideal case) 3.1415 cm on the floor. But if we take a wheel with diameter of 1 meter, we can measure 3.1415926 meter on the floor. We could repeat this experiment with wheels getting bigger and thus the approximation getting better.

Of course, pi is just a mathematical symbol, in real life its millionth digit will have no real life purpose, as what we know in physics and other nature sciences is limited by mathematical approximations we make: a wheel is not a perfect circle as it may contain cracks, also, if a force is applied to the wheel and the floor is not perfectly frictionless, the wheel will somewhat slide while rolling, so the distance will not be perfectly pi; and on molecular scale: the atoms don't make it possible to get a perfect circle). But the millionth digit can be calculated by using this method mathematically in some sort.

But in the beginning I stated pi is a finite number this is true, but it is a finite number with an infinite number of digits. Pi is what one calls an irrational number, this means that you can't take a fraction (a / b) and get pi when a and b are whole numbers. But here also, one can approximate pi by different fractions: a common one is 22/7 (which is 3.14285 in stead of 3.141592...).