If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Math for fun and glory>Unit 1

Lesson 1: Spirals, Fibonacci and being a plant

# Doodling in math: Spirals, Fibonacci, and being a plant [3 of 3]

Part 1: http://youtu.be/ahXIMUkSXX0 Part 2: http://youtu.be/lOIP_Z_-0Hs How to find the Lucas Angle: http://youtu.be/RRNQAaTVa_A References: Only good article I could find on the subject: http://www.sciencenews.org/view/generic/id/8479/title/Math_Trek__The_Mathematical_Lives_of_Plants Book of Numbers: http://books.google.com/books?id=0--3rcO7dMYC&pg=PA113&lpg=PA113&dq=conway+phyllotaxis&source=bl&ots=-bTLzWkMtB&sig=XnbL9nRYQoWOCbvWdZPAlVa3Co0&hl=en&sa=X&ei=2afqTui9L6OUiAKapaC7BA&ved=0CCkQ6AEwAQ#v=onepage&q&f=false Douady and Couder paper with the magnetized droplets: http://www.math.ntnu.no/~jarlet/Douady96.pdf Pretty sane page on phyllotaxis: http://www.math.smith.edu/phyllo/. Created by Vi Hart.

## Want to join the conversation?

• Are there any types of number other than Lucas and Fibonacci numbers?
• at around , Vi is talking about Lucas and Fibonachi numbers, but there are other numbers. Google, "the real number system" you might want to memorize it, or at least try to understand it. It's basically a system that divides numbers into groups based on properties. The Lucas and Fibonachi numbers are patterns in nature and math that people discovered.
• What if you started with 2? 2+2=4+2=6+4=10+6=etc etc etc. What would that be like?
• Do the Fibonacci numbers just keep going on and on?
• Fibonacci numbers go on forever! The 1000th term in the sequence is:

43466557686937456435688527675040625802564660517371780402481729089555
54179490518904038798400792551692959225930803226347752096896232398722
471161642996440906533187938298969649928516003704476137795166849228875.
• (For Fibonacci numbers)Why do you need to start with 1+2=3 2+3=5 3+5=8..... not something like 34+65=?
• The short answer is because the start 1,2,3... Is how Fibonacci numbers are defined. If you were to go 34, 65, 99, 164, 229, 393 etc that would be a different sequence using the same rule but different seed numbers. For fun you can rewind the sequence to an origin of some kind via subtraction and see where it crosses into negatives, or math out 40 or 50 of this new sequence and find the ratio of consecutive numbers. Maybe it converges on something interesting.
• Why is it called Lucas angle a tron?
• Vi called it a Lucas angle-a-tron, because it is an angle-a-tron that forms Lucas numbered petals.
• this woman is a really fast talker i can't understand her.OMG
• Try using subtitles. Click the button marked 'CC'. It's next to the settings button which is next to the full screen button. However if you're watching this on YouTube, the subtitles are wrong sometimes. Hope you're a fast reader : )
• who came up with Fibonacci numbers? Fibonacci?
• There is a story about rabbits that contain Fibonacci numbers
• What are fibonacci numbers
• The Fibonacci series was explored by the Italian mathematician, Leonardo of Pisa, more commonly known as Fibonacci. He didn't originally study the series, however, his writing about them led others to refer to them as the Fibonacci series, the Fibonacci sequence or Fibonacci numbers.

This video is the third in Vi's series on the numbers and how they occur in nature. The sequence starts with 1 and 1, and then each successive number is determined by adding the two numbers that come before it. Check out the other videos for a much more interesting exploration than my dry, boring statements of fact.Source: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html