Poncelet porism

Imagine you have a big box of different shapes - triangles, circles, squares and more. Now, let's say you take one of those shapes, let's say a triangle. You draw another shape that perfectly fits inside that triangle - it could be a smaller triangle, or a circle, or any other shape that fits just right.

Now, here's where things get interesting. You take that second shape, the one that fit perfectly inside the triangle, and you draw another shape that perfectly fits inside of it. You keep doing this, drawing new shapes that perfectly fit inside the previous shape, over and over again.

Eventually, something really cool happens. You end up with a bunch of shapes that all perfectly fit inside each other, like a set of Russian nesting dolls. And, no matter what shape you started with - a triangle, a square, or anything else - you always end up with the same set of shapes nested inside each other.

That's basically what Poncelet Porism is all about. It's a concept in math that deals with drawing shapes inside each other in a very specific way, so that you always end up with the same set of nested shapes no matter what the original shape was. It's named after a guy named Jean-Victor Poncelet, who figured out the rules for how to make this happen.

It's a really fascinating idea, and it has applications in lots of different areas of math and science. But at its heart, it's just about drawing shapes inside each other in a really cool and predictable way.