irrational number and the diagonal of a square

[33user]

seriously, due to the pythagorean theorem, how it's possible to describe a perfect square to exist in the real world, because it's diagonal must be an irrational number. now, how could it be that the distance between its two vertices are an irrational number? isn't distance in the real world always an irrational multiple of some rational unit?

or, could you imagine in real life an irrational amount of time? like 2^1/2 seconds, for example?

it's really bothers me, hoping someone would take the trouble and shed some light....

thanks in advanced
Andrew

 

[Deleted member 4993]

seriously, due to the pythagorean theorem, how it's possible to describe a perfect square to exist in the real world, because it's diagonal must be an irrational number. now, how could it be that the distance between its two vertices are an irrational number? isn't distance in the real world always an irrational multiple of some rational unit?

or, could you imagine in real life an irrational amount of time? like 2^1/2 seconds, for example?

it's really bothers me, hoping someone would take the trouble and shed some light....

thanks in advanced
Andrew

You are raising an old philosophical problem. This has been discussed in detail - do a google search.

This is exactly why Greek mathematicians did not believe in "irrational" numbers - for a long time. Incidentally, \(\displaystyle \pi\) is also irrational which comes from the circle geometry.

My conclusion is that the subject of geometry is for irrational people.