Huge thanks to Jane Street! [ Ссылка ]
Check out Ben Sparks's GeoGebra files.
Binet formula 2D complex output: [ Ссылка ]
3D imaginary output of Binet formula: [ Ссылка ]
3D plot of absolute output of Binet formula: [ Ссылка ]
My four-part series on Numberphile videos about Fibonacci Numbers (from 2014) starts here.
[ Ссылка ]
Here is me going on about the square root of five (Numberphile 2018).
[ Ссылка ]
This was the Fibonacci puzzle video from Matt Parker's Maths Puzzles.
[ Ссылка ]
Read a whole bunch about "Generalized Fibonacci Sequences and Binet-Fibonacci Curves".
[ Ссылка ]
The zero I found was at -9.14202391817 + 2.80064954276i and you can see the exact form here: [ Ссылка ]
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: [ Ссылка ]
This site has everything you'll ever need to know about Fibonacci Numbers.
[ Ссылка ]
Buttercup - The original buttercupchallenge
[ Ссылка ]
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.
[ Ссылка ]
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:
[ Ссылка ]
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: [ Ссылка ]
US book: [ Ссылка ]
UK book: [ Ссылка ]
Nerdy maths toys: [ Ссылка ]
