Irrational numbers cannot be represented in the real physical world, I’ve been told. So my question is: if I have a one meter by one meter square of wood, which is a perfect square precisely to the atom, is its diagonal length not sqrt2?
In: Mathematics
Irrational only mean that the number is not a fraction of two integers. Not that is not real
The more common example of a example is the circumference of a circle that it to Pi time the diameter.
You could measure it the other way and make a square with a diagonal of 1m the side would be 1/sqrt(2) meters long
Units we use is arbitrary and you could define one as a foo where a foo is defined as sqrt(2) of a meter. The in foo the previous irrational sides are know rational and the the previous rational is irrational.S
You could never build something that was exact a meter squared do to atomic level because atoms are discreet object.
There is also the plank limit of measurements.
The size of a atom is not well define and to quite wikipedia
>The atomic radius of a chemical element is a measure of the size of its atoms, usually the mean or typical distance from the center of the nucleus to the boundary of the surrounding shells of electrons. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Three widely used definitions of atomic radius are: Van der Waals radius, ionic radius, and covalent radius.
So you could not make something exact one meter there is always a margin of error. So the the 1m and sqrt(2) m will be that withing margins of error
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