eli5: What does it mean that you can’t “square a circle”? Couldn’t you just take a circle with diameter 2, and then a 2×2 square ?
In: Mathematics
The square will have a area of 2 * 2= 4 but the circle area is pi * 2^2 /4 = pi ~3.1415…
The problem of squaring the circle is to make a square with the same area as the circle or vise versa. The only allowed tools are a compass and a straightedge and a finite number of steps.
The square need to have sides of sqrt (pi) ~1.772… so you need to get exactly that length from the circle with just a compass and a straightedge. This have been frooven to be impossible in 1882. PI is what is called a transcendental number, that is not a root of a polynomial with rational cooeficents. It was know before that if pi was a transcendental number the problem would be impossible to solve, it was the proof that pi was transcendental that was from 1882.
You can create a approximation with the tools, the more steps you use the closer you get but to get the exact correct value you need a infinite number of steps.
You example is creating a square with the same side as the diameter of the circle and how to do that have been known since antiquity. Here are one method [https://mathbitsnotebook.com/Geometry/Constructions/CCconstructionSquare.html](https://mathbitsnotebook.com/Geometry/Constructions/CCconstructionSquare.html)
Latest Answers