Can you explain the pattern? @MathVisualProofs

Uploaded September 2024 | Updated September 2026, 2 weeks ago

This enumeration shows all the tilings of a circular grid divided into n pieces from n = 1 to n = 8 using tiles that cover one or two cells. Can you tell the pattern? Can you prove why or how the Lucas numbers appear? If you are looking for more information about this, I recommend the wonderful textbook Proofs that Really Count: The Art of Combinatorial Proof from Arthur Benjamin and Jennifer Quinn: bookstore.ams.org/dol-27

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If you enjoy this enumeration, check out the longer form: youtu.be/4S85bHkmM_Y
or check out a Fibonacci tiling video : youtu.be/AFAcKDTmYXI

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#dominotilings #fibonacci #lucas #circulargrid ##countingtiling #count #mathvideo #math #mtbos #manim #animation #iteachmath #mathematics #discretemath #combinatorics #enumeration #synthwave

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