Why Does This Sequence Keep Appearing?
What is the pattern in these Domino tilings? And how can we use them to prove things by "double counting"? Related links: This truly excellent video by @ericseversonmath does an equivalent thing using a combination of 1x1 squares and 1x2 dominoes. One of my all time favourite math YouTube videos (seriously!) • Secrets of the Fibonacci Tiles - 3B1B Summ... @AnotherRoof video about determinants in counting • Why Do Determinants Count Trees? @Mathologer video about domino tilings and the arctic circle theorem of the Aztec diamond • The ARCTIC CIRCLE THEOREM or Why do physic... @physicsforthebirds video about rhombus tilings • Random Rhombus Tilings My marimo notebook for generating random aztec domino tilings using the shuffling algorithm (press show app view to hide the code!) https://marimo.app/?slug=1mvs3h Chapters 0:00 The problem 2:17 The solution 4:58 Writing it in math notation 5:56 A double counting problem about Fibonacci numbers 10:46 Bonus sneak peek on more domino tilings
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