What You Thought You Knew: Geometry contains a shape called a “circle,” a line forming a closed loop where all points are equally distant from the middle.
What You Didn’t Know: In the 15th century, Nicholas of Cusa was a big fan of this geometric creature we call “the circle.” In fact, he loved it so much that he just couldn’t stop thinking about circular things — balls, plates, earth, anything he could find.
Since he spent so much time fantasizing about circles, it’s no wonder that he started to notice some strange things. The amount of curve around a circle decreases as a circle gets bigger. Make sense?
Think about it — if I have a tiny little circle and a big circle next to each other, the tiny one has a much tighter curve than the big one, right? The big one curves in a long, lazy way, and the tiny one is like, “Whoosh! I’m done!”
In other words, the bigger one is closer to being flat.
Nicholas first noticed this trend when he viewed the earth — the earth is so big, in fact, that the horizon looks flat even though we all know it is curved as part of a sphere. So then, we now know that the bigger the circle, the less it curves. By that logic, an infinite circle (one that is infinitely large) would have the greatest decrease in curve. An infinite circle is a shape that has the least amount of curve — a straight line! And we all know that straight lines are not circles. What gives?
Now You Know: that a circle can be composed of a straight line and is, therefore, not a circle. So do circles even exist?