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Complex Fibonacci Numbers?

Stand-up Maths
1.32M subscribers
1.1M views 5 years ago
Huge thanks to Jane Street! https://www.janestreet.com/join-jane-... Check out Ben Sparks's GeoGebra files. Binet formula 2D complex output: https://www.geogebra.org/m/twvvzpga 3D imaginary output of Binet formula: https://www.geogebra.org/m/z6dy9cj5 3D plot of absolute output of Binet formula: https://www.geogebra.org/m/pb7hmxyd My four-part series on Numberphile videos about Fibonacci Numbers (from 2014) starts here.    • Brady Numbers - Numberphile   Here is me going on about the square root of five (Numberphile 2018).    • Lucas Numbers and Root 5 - Numberphile   This was the Fibonacci puzzle video from Matt Parker's Maths Puzzles.    • MPMP: The 1 Million Bank Balance puzzle   Read a whole bunch about "Generalized Fibonacci Sequences and Binet-Fibonacci Curves". https://arxiv.org/pdf/1707.09151.pdf The zero I found was at -9.14202391817 + 2.80064954276i and you can see the exact form here: https://www.wolframalpha.com/input/?i... Try …...more
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Complex Fibonacci Numbers?
41KLikes
1,112,667Views
2020Jul 2
Huge thanks to Jane Street! https://www.janestreet.com/join-jane-... Check out Ben Sparks's GeoGebra files. Binet formula 2D complex output: https://www.geogebra.org/m/twvvzpga 3D imaginary output of Binet formula: https://www.geogebra.org/m/z6dy9cj5 3D plot of absolute output of Binet formula: https://www.geogebra.org/m/pb7hmxyd My four-part series on Numberphile videos about Fibonacci Numbers (from 2014) starts here.    • Brady Numbers - Numberphile   Here is me going on about the square root of five (Numberphile 2018).    • Lucas Numbers and Root 5 - Numberphile   This was the Fibonacci puzzle video from Matt Parker's Maths Puzzles.    • MPMP: The 1 Million Bank Balance puzzle   Read a whole bunch about "Generalized Fibonacci Sequences and Binet-Fibonacci Curves". https://arxiv.org/pdf/1707.09151.pdf The zero I found was at -9.14202391817 + 2.80064954276i and you can see the exact form here: https://www.wolframalpha.com/input/?i... Try it for yourself and put the Binet Formula (((1+sqrt(5))/2)^n - ((1-sqrt(5))/2)^n)/sqrt(5) in the Wolfram roots calculator: https://www.wolframalpha.com/widgets/... This site has everything you'll ever need to know about Fibonacci Numbers. http://www.maths.surrey.ac.uk/hosted-... Buttercup - The original buttercupchallenge    • Buttercup - The original #buttercupchallenge   CORRECTIONS This was a long video and in hindsight there are a few things I wish I had phrased better. Here they all are:
  • I misspoke around 01:13 when I said "negative one, zero" as it is clearly "negative one, one, zero".
  • At 07:53 I mean the negative values -5 to 0. I said it a weird way.
  • My language at about the 1D input to 2D plot from 09:17 is a bit sloppy. The real values going into the Binet function are not the horizontal axis shown; the plot onscreen is solely the output.
  • I say "axis" when I mean "plane" or even "complex plane". The big flat thing.
Let me know if you spot anything else! Thanks again, as always, for Jane Street being my principal sponsor. https://www.janestreet.com/ Thanks to my Patreon supports who do support these videos and make them possible. Here is a random subset: Loren Thomas Richard Dickins Barry Salter Susan Moury Sarah Gerweck Ulrich Kempken Piotr Gary Martin Euler Daniel DeJarnatt Support my channel and I can make more videos:   / standupmaths   Filming and editing by Matt Parker Music by Howard Carter (excluding Buttercup) Design by Simon Wright and Adam Robinson MATT PARKER: Stand-up Mathematician Website: http://standupmaths.com/ US book: https://www.penguinrandomhouse.com/bo... UK book: https://mathsgear.co.uk/products/5b9f... Nerdy maths toys: http://mathsgear.co.uk/
1:13
I misspoke around.when I said "negative one, zero" as it is clearly "negative one, one, zero".

Stand-up Maths

1.32M subscribers
1:13
I misspoke around.when I said "negative one, zero" as it is clearly "negative one, one, zero".
7:53
At.I mean the negative values -5 to 0. I said it a weird way.
9:17
My language at about the 1D input to 2D plot from.is a bit sloppy. The real values going into the Binet function are not the horizontal axis shown; the plot onscreen is solely the output.