So we have a visitor over at the house
talking about elliptic integrals and
p-adic functions and things like this
and it's all
derived from conic sections. And my wife
Pat and I are listening, we could make
some conic sections. We could not only
make some conic sections
we could bake some. We could make a cone
and slice it,
let's make a conic loaf of bread.
Let's bring it in the kitchen. - (Brady: Kitchen?)
The timing on this is a little delicate
so I got up at six in the morning to
make the dough but then we had to keep
it from rising too much until you got
here Brady so so now I'm hoping that
it's going to be okay. This is what it
looks like right now before it's baked.
This is
a funnel
with the bottom chopped off made of
borosilicate glass. Because
it won't balance on one end
Pat had the idea we'll put it in- - It's a
stock pot, a stock pot. - A stock pot, and- why don't
you grab that end. - I'm gonna go ahead and
put it in the oven and hope that it's
risen enough to be okay.
That's good,
I think it's still alive and kicking.
Curiously her first idea was
to make scones
in a
cone. To have
scone-ic, sconic sections. We'll
see about this in an hour.
(How's it going Pat?) - I think it's alive, I
think it's growing!
I'm afraid it'll go all the way up and
stick to the roof of the oven and then
we'll have a problem.
Yeah that's pretty good. - Sorry I almost
stabbed you.
We now have
a conical loaf of bread.
Perfect time to do conics! Right? Here's a-
First thing, let's draw an axes.
Here's the axes of the cone,
if I cut perpendicular to this
I should get a circle.
Hot damn!
Basic conic.
A circle, or really in this case a disc
because it's a filled in circle.
So if I want a sandwich, a circular
sandwich,
I could
start here and make another one.
Another disc!
Now,
if memory serves me right,
I ought to be able to make an ellipse by
slicing
the bread
at an angle,
so let's try
an ellipse.
Oh yeah I've got an ellipse right here!
I can make a steeper ellipse,
a more elliptical ellipse, by cutting
this way yes yes yes yes yes yes yes.
I now have an ellipse! I have an
elliptical slice of bread! Looks a little
circular but if you look here it's
elliptical.
So now,
let's start pushing things.
Now a parabola
is a conic section where it's cut
parallel to one of the sides. Let's start
here.
Here's a section of a parabola with a
bite taken out.
If I rebuild this,
had I cut along here this would have
been a parabola.
A slice that's parallel to this axis is
a hyperbola.
To get a hyperbola let's slice right
along here.
And there,
along here,
is a hyperbola.
Cut here -
without slicing my hand -
a hyperbola along here, pretty poor
hyperbola,
with a little bit of
homemade plum jam.
A hyperbolic jam sandwich,
can't ask for more.
Oh it's beyond elliptical! It's beyond
parabolic!
It tastes hyperbolic. It tastes like the
orbit of a comet
that's coming in from an infinite
distance. This is a sandwich
that's
made
in conic sections.
(Is that a circle?)
Yeah sort of. This is homemade plum jam.
off that tree. Brady is right now
having a circular
disc plum jam sandwich. - (It's pretty good.)
(It's very good.)
Come on, does it taste conical?
Does it taste extra good because it's a
homemade conic section?
I think- - Can you taste? Is it possible for
you to determine that every little yeast
body and every little grain
of of organic flour that's used in that
has-
you know is a conic section?
Yeah I think I think I think I can taste that.
...means you're going to figure this out
and do the experiment, you're going to
find your own equipment. If you don't
have a turkey around,
measure the temperature of lasagna!
Or measure the temperature of
chow mein.