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
A circle with diameter 2 has an area of pi. A 2×2 square has an area of 4.
“Squaring the circle” means, using only a compass and a straightedge, constructing a circle and a square with equal area. (Not a square inscribed within or circumscribed around a circle.)
It turns out there is no way to manipulate angles, rays, arcs, and segments using compass techniques to convert between the side length and radius length that you need.
There are a variety of other tasks, like “Take one triangle and construct another triangle with the same area” or “Take a triangle, and divide it into two triangles with equal areas” that are possible with only a compass and straightedge. But “squaring the circle” is not one of them.
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