Circle packing in a square

Imagine you have a big empty square that you want to fill up with small round circles. The goal is to fit as many circles as possible in the square without any of the circles overlapping or going outside the square.

To do this, you start by placing one circle in the middle of the square. Then, you add more circles around it, making sure each circle touches the circles next to it, but doesn't overlap with them.

You continue adding more circles in this way, always making sure that they are touching other circles, until there is no more room to add any more circles without overlapping.

This process of filling up the square with circles in such a way that they don't overlap is called circle packing in a square. It's used in many different fields, like computer graphics, design, and even in the study of crystals!

Overall, it's a fun way to challenge yourself and see how many circles you can fit in a square without breaking the rules.