A circle has infinite corners
A circle can be understood as a polygon with infinite sides, a paradox that illustrates how calculus uses limits to mathematically describe curves and change in the world.
From a mathematical view, a circle can be seen as a polygon with endless sides, giving it infinite corners—or, paradoxically, no corners at all! This idea reveals the power of calculus. As a polygon gains more and more sides, it gets closer to becoming a perfect circle. Ancient Greek mathematician Archimedes used this concept to estimate pi by calculating the perimeters of polygons with increasing numbers of sides. Calculus, developed by Isaac Newton and Gottfried Leibniz around 1670, formalizes these limiting processes. It's how we describe motion, growth, and change, underpinning all modern physics, engineering, and technology.