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### 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 [2 of 3]

Part 1: http://youtu.be/ahXIMUkSXX0Part 3: http://youtu.be/14-NdQwKz9wMore on Angle-a-trons: http://www.youtube.com/watch?v=o6W6P8JZW0oNote: Beautiful spirally non-Fibonacci pinecones are very rare! If you find one, keep it. Created by Vi Hart.

## Want to join the conversation?

• What is Phi really?
• Phi is the positive solution for the equation x + 1 = x². Phi is a Greek letter and it looks like this → φ. It equals (1 + √5) / 2

Phi is also the limit of F(n) / F(n - 1) in Fibonacci sequence which is defined as follows:

F(n) = F(n - 1) + F(n - 2), F(0) = 0, F(1) = 1
or as follows:
F(n) = [φ^n - (-φ)^(-n)] / √5

Phi is also known as "the golden ratio". Phi is used as a ratio between different parts in art, and is found to be of great beauty.

In addition, as Vi mentions in the video, many plants grow with the angles between their parts being 360°/φ, or τ/φ radians (τ=2π, Vi also talks about tau) to catch more sun-light.
• What is Phi? I don't really understand Vi Hart's definition. Something about integers?
• Phi is a number that represents "the golden ratio", a pattern that many Renaissance artists and architects use. It is also connected to the fibonnaci series, as Vi mentions. I found a lot of information about phi and Phi on this website:
http://www.goldennumber.net/what-is-phi/
• How many mathmatical symbols are there again? 4 right?(T-I)
• The 4 basic ones, (plus) (minus) (multiply) (divide) are just the beginning. There are logarithms, and trig functions, and factorials, and integrals, and limits, and transformations, and radicals, and ...
• Can anyone tell me what Phi is?
• //pushes you in the direction of meera.kurup's question//

the awesome people answered that one better than I could
(1 vote)
• why are the Fibonacci numbers added with each other why not multiplied? I also wonder if are body's have Fibonacci in them?
• If they were multiplied, since you start at one, and one times one is one, the numbers wouldn't be more than one. If you started at two then you have 2, 4, 8, 32, 256, 8192.... The numbers get way to big way to quickly. I'm not sure what a spiral with these numbers would look like but it would be HUGE. It just doesn't work multiplying the numbers.

One place that Fibonacci numbers appear in animals is in the spiral of a snail's shell. Here is a site some more animals with Fibonacci numbers and the golden ration: http://jwilson.coe.uga.edu/emat6680/parveen/fib_nature.htm
• How do you do it? You make it look so easy.
• At , Vi Hart, mentioned an Angle-A-Tron. What is that?
• It's a special protractor made to make angles.
• Is phi represented by φ or ϕ?
I found both used on the internet, but on Wikipedia they represent different numbers.
(1 vote)
• The upper case phi looks like the second one you show, but larger. The two you show here are variants of a lower case phi. You can use either one, but if it's not clear from the context what the value represents, you should define it.