Kind: captions
Language: en
if you want to understand what Infinity
can do we're going to need pizza
yes there's a science to making pizza we
don't typically
with infinity
so how can New York City's most famous
food
help solve one of the most elusive
mysteries of early mathematics
[Music]
so Steve how is this pizza gonna help us
understand Infinity huh I would say it
the other way infinity and the pizza are
going to help us understand one of the
oldest problems in math what's the area
of a circle which is not intuitive no
you know what's hard about it you might
think a circle is a beautiful simple
shape but actually it's got this nasty
property that it doesn't have any
straight lines in it right ancient
civilizations didn't know how to find
the area of a shape like that
[Music]
how to find the exact area of a circle
isn't obvious
for a square or rectangle you just
multiply the sides
but what do you do with a circle
so what do they do well they came up
with an argument that you can convert a
round shape into a rectangle if you use
Infinity so we're basically going to
kind of deconstruct this pizza make it
into a rectangle beautiful and then
we're going to know the area that's it
so I'm going to start with four pieces
okay
to do that I'm going to go one point up
and one point down and then one point up
and one point down
and yeah like that
how'd you do in Geometry
you don't think that looks like a
rectangle it's not close to you no it's
not it's not but come on I'm only using
four pieces if I use more I can get
closer okay so we got to cut these
babies in half let's cut them
let's rearrange them same trick
alternating point up and point down
one up and one down
[Music]
one up and one down
that is looking a lot better
what do you think is that a rectangle
um it's it's not quite a rectangle but
it's getting closer it is right yeah
in both the four piece and eight piece
versions
half the crust sits at the top and half
at the bottom
but with eight pieces The Edge becomes
less scalloped closer to a straight line
so we need to go at least a step further
let's go more we gotta do sixteen
so we have to just change every other
one am I going to mess this up I mean
that's that's a parallelogram that's
aspiring to be a rectangle that's got
aspirations
from four slices
to eight slices
[Music]
to 16 slices
and even 32 slices there's a clear
progression towards a rectangle with one
piece out of 32 cut in half to create
vertical sides the rectangle is almost
complete except for the wavy top and
bottom
but as the number of slices increases
the straighter and straighter those
edges would become
and the argument here is that if we
could keep doing this all the way out to
Infinity so that this would be
infinitely many slices infinitesimally
thin this really would become a
rectangle yeah and we can read off the
area it's this radius
that's the distance from the center out
to the crust times
half the circumference which is half the
crust half the curvy stuff and that's a
famous formula a half the crust times
the radius one half CR that's what this
is usually see for circumference but you
could see it's crust so at the limit
once we got all the way out there it's
gonna look like it would be a rectangle
and that is actually the first calculus
argument in history like 250 BC to find
the area of a circle who knew you could
learn so much from Pizza