Hello! Today I'm going to show you a
useful application of math and why it
works. It involves the Fibonacci sequence
which is a list of numbers that starts with
0 and 1, and to get the next one you add the two before it so then we get 1, 2, 3, 5,
and so on you get this list and in this
video and generally we call the nth
Fibonacci number F_n. Now, Fibonacci
numbers have this interesting property
where if you graph the ratios between a
Fibonacci number and the one that comes
before it you get this sort of zigzag
and as the Fibonacci numbers get bigger
the ratios get closer and closer to this
line which is this number, about 1.618
also known as the golden ratio.
Now, another related fun fact is that one
mile equals about 1.609
kilometers. There's that golden ratio again
(more or less). So then we can write... 1.6 is approximately equal to a Fibonacci
number divided by the one that comes before it. The closer these two are the more
accurate this whole calculation ,is but
generally for F_n that's five or bigger
everything works out. So then we can do a little bit more algebra
and we get F_n kilometres is equal to F_n-1 miles so basically if you have a distance that's
a Fibonacci number of kilometers, to find
the same distance of miles you go to the
Fibonacci number that comes before it. So for instance say I have a friend who's
gonna run a 5k but I can never remember
how long five kilometers is. So what I
can remember is that five is a Fibonacci
number and the one that
comes before it is 3, so 5 kilometers is about three miles it works
the other way to. You have a distance and miles you go one
Fibonacci number up to find the same
distance in kilometers. Say you're a
Canadian and you use kilometers but
you're talking to an American car
salesman who of course uses miles. He says he has this really fast car it goes up to 90
miles per hour. You remember that 89
which is pretty close to 90 is in the
Fibonacci sequence so 90 miles per hour
is about 144 km/hr. Huh, it's not that fast!
Maybe you shouldn't buy that car. So I
hope I've convinced you that the
Fibonacci numbers are useful, thanks for
watching!
