Areas of Regular Polygons and the Shrinking Sides Problem [Geometry]
Regular polygon areas are given a new perspective in this video through a geometry problem: the shrinking sides problem. In this problem, you start with a triangle with sides of length 1, and decrease the side lengths by some factor as you add additional sides to your shape. The question is: Does the sum of our shapes' areas go to infinity? Is our sum a convergent series or a divergent series? To solve the shrinking sides problem, we will use the concepts of limits, infinite sums, trigonometry, and geometry. In doing so, we will discover a beautiful connection between geometry and calculus.
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