In many cultures around the world, circles have been used as images of harmony, completion, perfection.
I have a vague recollection of a teacher once telling my that this is because circles are so sweetly symmetrical, though I honestly don’t have the expertise to tell you why the circle is so revered.
Perhaps, though, what I find most beautiful about circles can be seen in a force-diagram.
That is to say, what I find beautiful is the answer to the question, why does something travel in a circle?
Circular motion, you see, is the result of two perpendicular forces. One force, inertia, pushes an object in motion to continue in a straight line. Another force, say, gravity or the tension on a string, pulls the object inwards.
One force points towards the center of the circle, the other points tangential to the circle. And it is the conflict and synergy between these perpendicular forces which causes the circular motion to form.
It’s important to note these forces aren’t opposing. An object affected by a force pointing in one direction and an equal force pointing in the opposite direction would go nowhere. It would appear static despite the two very real forces pushing on it.
But circles form from perpendicular forces. At each moment, the object moves a little bit this way and a little bit that way, at the whim of two forces which, perhaps, seem to have little in common at all.
But the object in question traces out a beautiful, perfect arc.
Symmetry from different forces.