Measuring π

@marblerunsushe1

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Why it worked

The video effectively visualizes a complex mathematical concept (approximating pi) using a simple, iterative animation. The increasing number of sides on the polygons and the corresponding numerical output provide a clear and satisfying demonstration of convergence.

Summary

The video demonstrates how approximating a circle with polygons of increasing sides leads to a value closer to pi. Various polygons are shown inscribed within a circle, with a numerical value displayed that approaches pi as the number of sides increases.

Structure

1Introduction of the concept of measuring pi
2Demonstration with a triangle
3Demonstration with a square
4Demonstration with a pentagon
5Demonstration with increasing sided polygons
6Approximation of pi as polygon sides increase

On-screen text

Triangle Measuring pi 2.598076 square 2.598076 Pentagon 2.8283095 Hexagon 2.938842 Heptagon 2.999917 Octagon 3.037096 Nonagon 3.0613673 Decagon 3.078942 Hendecagon 3.0900746 Dodecagon 3.0989594 Tridecagon 3.1057422 Pentadecagon 3.1151974 Heptadecagon 3.1213484 Icosagon 3.1272018 Heptacosagon 3.133868 Hentetracontagon 3.1382678 Hexapentacontagon 3.1397886 Henheptacontagon 3.140442 Hexaheptacontagon 3.1407816 Henhectogon 3.1409892 3.1411054 3.1411917