Why is a circle important?

Answer 1

Historically, circles are important because they were one of the first geometric shapes that early mathematicians had the ability to study analytically; i.e. graphically and algebraically. Analytic geometry has since expanded greatly, and now provides some of the mathematical foundation for such fields as topology and general relativity.

Additionally, the symmetric nature of circles have influenced philosophers and certain religions throughout the ages.

Let's also not forget that, without circles, we'd be driving on square wheels!