This right here is a

picture of Fibonacci, one of the most famous

mathematicians of all time, and he was a mathematician

in medieval Italy. And he’s most famous for

the Fibonacci numbers. And he didn’t discover them. They were actually discovered

several centuries before him in India, but he popularized

them, especially in the West. And the Fibonacci

numbers are super simple. The first two are

defined as 0 and 1. And every number after that is

the sum of the previous two. So what I’m

constructing right here is really a Fibonacci

sequence of numbers. So the next number

in the sequence is going to be 0 plus

1, which is 1, Then the next number after that

is going to be 1 plus 1, which is 2. Then the next number

after that 1 plus 2 is 3. 2 plus 3 is 5. 3 plus 5 is 8. 5 plus 8 is 13. 8 plus 13 is 21. 13 plus 21 is 34. And the Fibonacci

numbers, especially once you start getting into

number theories, tons of fascinating

things about them. But probably the

coolest thing about them is as you add more and

more terms to the Fibonacci sequence, and you take

the last two terms that you’ve generated, obviously

there is no really last two terms. You could keep going on

forever, get arbitrarily large Fibonacci numbers. But say we take these last two

terms over here, 21 and 34. If we take the ratio of

these two, 21 over 34, this is going to be pretty

close to the golden ratio. And I encourage you to look up

the golden ratio on Wikipedia and the internet. You’ll find all sorts of

fascinating and mystical things about the golden ratio. What’s cool about the Fibonacci

numbers, or the Fibonacci sequence, this gives

you an approximation of the golden ratio. You’ll get even a

better approximation if you add another

term to our sequence. So the next term over

here, 21 plus 34 is 55. So the ratio of 34 to 55 is

even closer to the golden ratio. So one way, if you

wanted to compute a really good approximation

for the golden ratio, you could really just get

super high Fibonacci numbers just adding the previous two

terms to get the next one. And you will get a pretty

good approximation, when you take the ratio

of the last two terms. Now that’s what the

Fibonacci numbers are about, and now I want to pose

a challenge to you. I want you to write,

since we’ve already done some examples

using factorial, I want you to write

an implementation of a function that generates

the n-th term in the Fibonacci sequence. So the function

will be like this. So if I call your function–

Let me make it a lowercase. Let me just give

you some examples. So if I take your function,

and I call Fibonacci– and you could really implement

this in any language you want, although we’ve been

dealing in Python, it might be simplest

to do it in Python– if I call fibonacci of

1, what I want this to be is the first term. And just to make things

clear, and you should always clarify this, especially

in computer science, because it’s not always

clear what the first term is. And I’m going to make

it clear right now. The first term is not going

to be this one over here. I’m going to make it

this one over here. I’m going to call

this the 0-th term. That’s the 0-th

term, and then that is going to be the first term. This is going to be the second

term, third term, fourth term, so on and so forth. And so Fibonacci of

1, the first term will be this right over here. It should return 1. So Fibonacci of 0

should return 0. Fibonacci of 3 should

return 0, 1, 2, 3. It should return 2. Fibonacci of 5 should

return 0, 1, 2, 3, 4, 5. It should actually return 5. And what I want you to

do is write a function so we could put in

any argument over here and it will return that third

term of the Fibonacci sequence.

def Fibonacci (towhich):

towhich=towhich-2

number=0

number2=1

for i in range(towhich):

temp=number2

number2=number+number2

number = temp

print(number2)

Fibonacci(input("enter the number of term"))

thanks!

f(x)=f(x-1)+f(x-2)

f(0)=0, f(1)=1; at least that is the way I've always learned to do it.

U_(k)=U_(k-2)+U_(k-1) ; U_0=0, U_1=1

Dynammic programming is the way to go.

the first example should be 34/21 which is closer to Golden Ratio 1,61… instead of 21/34. THANKS FOR YOUR VIDEOS HELP ME A LOT TO UNDERSTAND EVERYTHING IN MY UNIVERSITY, Typing from Cali, Colombia!

For anyone who doesn't have python or any other programing language implementation installed, and for some reason can't download one, check out ideone.com. Actually, I use it often even though I have several language implementations installed, because it's really convenient.

this was a test i received in my first job interview, haha.

btw, i think you should use R instead of python for your math lectures.

Or you can just use the fibonacci function =p

Man we are on infinite series and we came up on this in my Calc 2 class.

Visual Basic

Private Function fibonacci(ByVal term As Integer)

Dim value As Integer = 1

Dim prevalue As Integer = 0

Dim i As Integer = 0

Do Until i = term

value += prevalue

prevalue = value – prevalue

i += 1

Loop

Return value

End Function

the initial value of i is the first term, so in this case it starts at 0

Just to solidify what Khan was saying about the ratio being approx. = golden ratio

As F(n) -> inf

F(n)/F(n-1) -> phi

the golden ration is ~34/21 not 21/34 (1.62)

lol at all the incorrect answers, not a recursive function!!!

Does it really matter if we say 34/21 or 21/34 … the ratio is the same, just the result of the division is different.

I suggest a tuple in python. This was the line that took me a moment:

for i in range(term):

Careful not to let it trick you, remember range starts counting from 0. I'd paste my solution, but I don't wanna let everyone cheat. 🙂

My solution took 5 lines, so it's a relatively simple function to implement. Just careful about your order of assignments if you use separate variables for your terms. That's why I found a tuple easier.

@IceFurnace

It's the same ratio. It doesn't matter if you got 1:1,62 or 1,62:1.

@personkid20 shut up u douche

@personkid20

Right….

ur smart

Plz, use the CC function "Transcribe audio" and have fun wit the "Feminazi sequece" numbers and the "field nazis sequence"

that is the inverse of the golden ratio

Dude, "1,62" isn't even a ratio (1:1,62 or 0,62:1 would be).

Btw. do the math by your own definition: guess what (0,62+1)/1 equals (i. e. sum of two values divided by the larger of the two)? Guess what (1,62+1)/1,62 equals? Guess what (1+1,62)/1,62 equals?

he deserves one

SPOILER ALERT:

Look up Binet's formula:

Fib(n)=((Phi^n) -(-Phi)^(-n))/√5

I could prove it, but the comments section is too small.

Challenge accepted

This is the code ####

def fibon(number):

if(number == 0):

return 0

elif(number == 1 or number == 2):

return 1

else:

n = 0

m =1

l = m

for i in range(number-2):

m = n + m

n = l

l = m

return m

num = int(input("please inter a number : "))

print (fibon(num))

I got lost on fib (3) 🙁

1980

Hey Sal!

Can you make a video to Print all Prime Numbers in an Interval?

import math

def fibonacci(x):

phi=(1+math.sqrt(5))/2

term=lambda x:((phi^x)-(-phi^(-x)))/math.sqrt(5)

return term;

Is this correct?

Thank you, thank you, thank you, thank you!!!!!!!

WHAT FOR FORMULA SHOULD I USE TO GET 34TH TERM OF FIBONACCI SEQUENCE OR HOW DO I GET 34TH FIBONACCI TERM THANKS

theres no way anyone would have a clue how to write that by this point if their only experience was this tutorial

You already have a Video on golden ratio bro

13*2=26-5=21*2=42-8=34*2=68-13=55*2=110-21=89*2=178-34=144*2=288-55=233*2=466-89=377*2=754-144=610*2=1220-233=987*2=1974-377=1597*2=3194-610=2584*2=5168-987=4181*2=8362-1597=6765*2=13530-2584=10946. This pattern just keeps going. Can someone please explain why this happens? PLEASE?