Huge thanks to Jane Street! www.janestreet.com/join-jane-street/

Check out Ben Sparkss GeoGebra files.
Binet formula 2D complex output: www.geogebra.org/m/twvvzpga
3D imaginary output of Binet formula: www.geogebra.org/m/z6dy9cj5
3D plot of absolute output of Binet formula: www.geogebra.org/m/pb7hmxyd

My four-part series on Numberphile videos about Fibonacci Numbers (from 2014) starts here.
www.youtube.com/watch?v=D8ntDpBm6Ok

Here is me going on about the square root of five (Numberphile 2018).
www.youtube.com/watch?v=z1THaBtc5RE

This was the Fibonacci puzzle video from Matt Parkers Maths Puzzles.
www.youtube.com/watch?v=ILrqPpLpwpE

Read a whole bunch about «Generalized Fibonacci Sequences and Binet-Fibonacci Curves».
arxiv.org/pdf/1707.09151.pdf

The zero I found was at -9.14202391817 2.80064954276i and you can see the exact form here: www.wolframalpha.com/input/?i=(10*pi)/(pi + i*(log(sqrt(5) — 1) — log(1 + sqrt(5))))

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: www.wolframalpha.com/widgets/view.jsp?id=b858339e64fa997454dd12f77cb1ece1

This site has everything youll ever need to know about Fibonacci Numbers.
www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html

Buttercup — The original buttercupchallenge
www.youtube.com/watch?v=l17l_KTAVJ0

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.
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:
www.patreon.com/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: standupmaths.com/
US book: www.penguinrandomhouse.com/books/610964/humble-pi-by-matt-parker/
UK book: mathsgear.co.uk/products/5b9fa76f230ffa140094dc43
Nerdy maths toys: mathsgear.co.uk/