system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: In mathematics, why are squares of numbers used so prominently in formulas?

I mean, why the square so useful?
gpt
In general, because that’s how geometry works.

A square is a common and easy shape. A right-triangle is half a square. A circle is related to a square via π, or to a right-triangle via sin/cos. Coordinate systems are either based on squares or circles.

Almost every 2D geometry formula will involve a square. And a huge number of physics problems will have squares in for the same reason.