Euler's triangulation of a polygon | Famous Math Problems 8 | NJ Wildberger скачать в хорошем качестве

Euler's triangulation of a polygon | Famous Math Problems 8 | NJ Wildberger

In 1751 Leonhard Euler, the greatest mathematician of modern times, posed the problem of counting the number of ways of triangulating an n-gon. When n=3, this is 1, when n=4, this is 2, when n=5 this is 5, and when n=6 this is 6. The sequence C_n, defined as the number of ways of triangulating an (n+2)-gon, is called the Catalan numbers, and appears in many different guises in combinatorics. In this lecture we derive Euler's formula for C_n, and describe just a few ways in which this fascinating sequence appears, as well as connecting it to Newton's binomial expansion for sqrt(1-4x). This lecture has quite a few smaller problems inside that you might like to think about. ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист   Here are the Wild Egg Maths Playlists (some available only to Members!)    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист   ************************