Walking city streets: Catalan Closed Form (visual proof from lattice paths)

In this video, we show how to provide a closed form for the number of northeast lattice paths to the point (n,n) that don't pass below the line y=x. The number of such lattice paths is counted by the famous Catalan numbers. For other videos discussing lattice paths (and those mentioned in this video), check out 1)    • Pascal's Triangle from Lattice Paths (synt...   2)    • The Binomial Recurrence from Lattice Paths...   3)    • Catalan Numbers Enumeration of Lattice Pat...   If you like this video, check out my others and consider subscribing. Thanks! #catalannumbers #catalan​ #manim​ #math​ #mtbos​ ​ #animation​ #theorem​​ #visualproof​ #proof​ #iteachmath #mathematics #binomialcoefficients #latticepaths #discretemath #combinatorics #enumeration #closedform This animation is based on the well-known interpretation of Catalan numbers as counting restricted lattice paths. I recommend the Wikipedia site or the books Enumerative Combinatorics I and II by Richard Stanley for someone wanting to know more about Catalan numbers. To learn more about animating with manim, check out: https://manim.community _________________________________________ Music in this video: Cylinder Two by Chris Zabriskie is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/... Source: http://chriszabriskie.com/cylinders/ Artist: http://chriszabriskie.com/