Fibonacci of 3, it had to call Fibonacci of 2 and Fibonacci of 1, and then to do Fibonacci of 2 it had to call Fibonacci, it had to call Fibonacci of zero and Fibonacci of 1.

But why not ratios?

The Fibonacci sequence.

Fibonacci of 6 8.

21 a Fibonacci number.

Fibonacci, I can just

It's a Fibonacci sequence.

Your grandfather's Fibonacci sequence.

Over here, 3 is based on Fibonacci of 2 and Fibonacci of 1.

Welcome to the presentation on ratios.

There's nothing really difficult about ratios.

It is the Fibonacci sequence.

Well, that's going to be based on Fibonacci of 4 and Fibonacci of 3.

But I never really got logarithms, or I never really got trigonometry, or ratios...ratios killed me

And you can keep going! try fibonacci of 3! it'll work! because we know fibonacci of 0,1,or 2 works cuz fibonacci of 3 will boil down to fibonacci of 2 plus fibonacci of 1. we know that fibonacci of 2 is 1, fibonacci of 1 is 1 1 1 is 2 so it'll just keep working. now we could try it out

Fibonacci of N is strictly gt than Fibonacci of N 1, except right here at the start when Fibonacci of 1 and Fibonacci of 2 are both 1, so they're rather than lt .

I taught a lesson once on ratios.

Onto fractions and decimals, ratios and rates.

The Fibonacci sequence is strictly nondecreasing.

Is Fibonacci of 20 gt 1000?

Alright, so there's our Fibonacci sequence.

We're computing the value of Fibonacci of 2 and Fibonacci of 3 over and over again.

Fibonacci, just to calculate the Fibonacci of 3. and then eventually it gave me the answer.

The ratios of consecutive numbers also approach phi.

They have urban streetscapes, but suburban parking ratios.

They have higher mass to light ratios then

So ratios are just expressions that compare quantities.

Fibonacci numbers show up occasionally in nature.

The mass to light ratios reached levels of 100.

So what are their respective Price to Earnings ratios?

So, on average, the actual ratios are shown here.

When we were trying to compute Fibonacci, the Nth position in the chart corresponded to the Nth Fibonacci number.

let me do Fibonacci off 3 so notice, when it called, it called Fibonacci of 3, then to do

lets say you took the fibonacci of 2! or,then, n is not zero then you wont do this n is not one so you wont do this but you'll say return fibonacci of 2 minus 1 so thats fibonacci of 1 plus fibonacci of 2 minus 2 plus fibonacci of 0. but we know fibonacci of one, evaluates to one fibonacci of zero evaluates to zero so it'll be one plus zero, or, just one!

A true pineapple would have Fibonacci spirals, so

However, Fibonacci involves a huge amount of work.

Similarly, Fibonacci of 3 is called multiple times.

And one Fibonacci pine cone is one thing.

So there are Fibonacci numbers in pine cones.

But they're in spirals too of Fibonacci numbers.

And what are the terms and the ratios people use?

It's important whenever you talk about any of these ratios.

light ratios will be higher for the more massive galaxies.

Let's try to learn a thing or two about ratios.

It ended up being just on reserve ratios, this one.