I was doing a thought experiment and came across something that I'm going to term the Planck Circle Problem for the sake of naming it something. The logic is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

1.) All lengths contain an integer number of Planck Lengths.

2.) The radius and circumference of a circle are both lengths.

3.) Therefore, the radius and circumference of a circle must both contain an integer number of Plank Lengths.

4.) A circle cannot have both a radius and circumference with an integer number of units because pi is a transcendental number.

I asked a mathemetician about this problem and his response was that the concept of a fundamental unit of length is impossible. However, physicist are just as adamant in claiming that a universal unit of length does exist. What am I missing?

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# The Planck Circle Problem

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