Simple Addition Connects Crazy Math Concepts | Pascal's Triangle

Why is Pascal's Triangle so cool? It's formed using basic addition, yet reveals SO MANY other math concepts that are somehow all connected. In my opinion, this is one of those topics that really shows the beauty of mathematics. I hope you find this as fascinating as I do. :) I wanted to include a variety of topics of different complexities, so feel free to skip around to what you find interesting! TABLE OF CONTENTS 0:00 Introduction 0:27 What is Pascal's Triangle? 1:22 First Diagonal & Symmetry 1:54 Natural Numbers (Diagonal 2) 2:16 Triangular Numbers (Diagonal 3) 3:16 Tetrahedral Numbers (Diagonal 4) 3:40 Fibonacci Sequence 5:13 Powers of Two 5:49 Powers of Eleven (& Decimal Expansion) 8:31 Sierpinski's Triangle (Odds & Evens) 9:07 Binomial Expansion Coefficients 10:38 Combinations 12:10 Conclusion 13:24 Nerding Out Additional Resources: Ted-Ed: https://www.youtube.com/watch?v=XMriWTvPXHI Numberphile: https://www.youtube.com/watch?v=0iMtlus-afo Math is Fun: https://www.mathsisfun.com/pascals-triangle.html Tipping Point Math: https://www.youtube.com/watch?v=J0I1NuxUcpQ Whether you're already a lover of mathematics, or you're someone who thinks math is the farthest thing from "cool", I hope you stick around, learn something new, or just find something to appreciate about the mathematics all around us. Tell me what other proofs or videos you'd like to see on my channel!