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Pi is not a faction

The number pi, that indicates the ratio between the circumference and the diameter of a circle, can not be written as a fraction

π =   circumference 
     diameter 

But surely this is a fraction?

 


Explanation

Yes, that's right. But if you want to determine the value of π this is not possible with a fraction. That seems absurd. Imagine you put a rope around the circumference of a circle. Now you want to cut a piece of that rope to get the diameter. That can not accurately be measured. A fraction for π only gives an approximation. That may very well be usable in practice. You write it usually as

Nowadays everyone has a calculator, and there you get

π = 3.1415…

A trillion decimal places have already been calculated, and there never occurs a pattern that repeats itself. Mathematicians have shown that this does not happen, and therefore call it a transcendental number. One of the best-known formulas for π is

There are many other formulas, all of which are very impressive. That seems to be hocus pokus. But that is how nature works.

 


Additional information

The German-Swiss mathematician Johann Heinrich Lambert (1728 - 1777) proved that π cannot be written as a fraction.

 


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