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The Mystery of the Fibonacci Cycle

A video about the mysterious pattern found in the final digits of Fibonacci numbers. It turns out, if you write out the full sequence of Fibonacci numbers, the pattern of final digits repeats every 60 numbers. What’s up with that? Watch this video and you’ll find out! (My apologies to any viewers who have calculated the Fibonacci sequence all the way up to the term one trillion, five hundred and forty-eight billion, eight million, seven hundred and fifty five thousand, nine hundred and twenty.) The first video in Vihart’s series on Fibonacci:    • Doodling in Math: Spirals, Fibonacci,...   The final animation, without my waffling over it:    • The Mystery of the Fibonacci Cycle   Writing: Andrés G-C and the enigmatic Assistant Visuals: Andrés G-C Camera Footage: Assistant Editing: Andrés G-C Music: www.bensound.com 00:00 Introduction 01:32 The Mysteries 05:13 Decimal Numerals 07:13 Honeycomb Numerals 07:51 Brazilian Tallies 09:04 Counting with Honeycomb Numerals 10:34 Inventing Minidecimal 16:36 Using Minidecimal 18:00 Solving the First Mystery 23:20 Intermission 24:31 Minihoneycomb 26:58 Introducing Rings 27:33 Ring Products (and Notation) 30:11 The Theorem 33:34 The Honeycomb Fibonacci Cycle 40:38 Solving the Second Mystery 45:22 Outroduction 45:45 After-Credits Rambling and Animation My submission for SOME1.