Fundamental group

How can we measure the "holes" in shapes?

Imagine you're walking around a park shaped like a circle. How many different ways can you start at one point, walk around the park, and come back to the same spot without lifting your foot off the ground?

Think of the circle as a loop. The fundamental group tells us how many unique loops we can make that can't be squished into each other. It's like counting different ways to tie a knot with a piece of string.

Example

If you walk around the park once in a clockwise direction and then in a counterclockwise direction, these paths are different loops.

Remember this

The fundamental group of a circle is infinite because there are infinitely many ways to loop around it.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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