Hello. Today I want to show you how to draw a perfect egg using geometry. Okay,
so what I'm mixing is formal geometry with nature, and isn't nature wonderful?
So what I've got is five dots here which I've already mapped out to make a pentagon.
If I threw it away it would be a penta-gone,
but it's here. And inside the pentagon I'm gonna form a pentagram. The pentagram was used by the
Pythagorean cult in southern Italy; the followers of Pythagoras. And they felt it was magic,
just magic. And in a way I agree with them. So a pentagon and a pentagram you need to join
opposite corners. Wonderful thing about the pentagon is all these lines are divided by
golden ratio. There's two things you can measure: you can measure that distance there short distance
to the side, or the long distance across there. Divide that into there you always get the golden
ratio. But even when you split it up again - divide that into that - golden ratio. And it's
it's just absolutely beautiful; but how am I going to form an egg? Something that's natural,
something that has a natural shape in nature. Well, a few more lines. Okay, first of all,
through this point here parallel to the base I'm going to draw another line. Now two more lines:
one of them there, the end of that one to there, and one from here to there
and all my line drawing is complete. Now for the egg. A hen is a production line of eggs;
there are nine in the process, from the very smallest to the one that's going to be delivered
today and it's the one that's delivered today that I'm going to show you now.
First of all I'm going to ask you, which end of an egg comes out first? The thin end or
the thick end? Did you know? Well I'll tell you the answer is the thicker end.
Why? And I'm going to explain that. What I'm going to do now is draw a semicircle. It's going to go
from this point here down here. Now it nearly coincides with the bottom line but it doesn't,
it overlaps it slightly. What I'm drawing shows you just how the hens egg is laid, because when
it's laid the shell is soft and as it's soft the egg inside has been more or less a perfect ball.
And as it begins to be laid it's pushed out just like a water bubble coming out
from the bath; a perfect hemisphere, a perfect heart sphere - and that's what I've drawn here,
and that's the bottom of the egg. As it's- - (Brady: Does it grow Johnny? Because it
doesn't come out-)
(Presumably the hole in the chicken's not that big so
it comes out thin and then balloons-) The hole- the hole
stretches perfectly to cope, right? And it allows it- and of course the pressure
inside the body is pushing it out, but it acts just like water forming a perfect
hemisphere right. When it's half out already it's beginning to solidify
but the rest has to be thrown out, and the rest is forced out through the pressure
inside. But now I need some more curves. So I'm going to take the end line- end point there
and stretch that out to here and draw that, that's it I've got it going now. And from the other end
I draw that right on the point, and there it goes, and we've nearly got our egg. Now we've got
one more curve to make and that's the top of the egg; and for that you need a centre here on the
leg there. And now I turn that around it should complete the top of the egg like that. And there
we have our perfect egg. And if you don't believe me, if I bring this to the towards the camera-
(I'll give you that) - My dad used to say 'I've got an egg here,
fresh. I caught it dropping.'
So that means it would- the shell wouldn't have been solid because it only solidifies once it's
out and the air gets to it and it's a reaction with the air. But it's very beautiful. I don't
know any more mathematics that goes with this at all other than the thing is beautiful and it links
nature to geometry and I love them both. Cheers. - If you'd like to go even deeper into
the mathematics behind egg shapes, this reasonably recent paper may maybe of interest.
They were chasing a universal formula for egg shape. Now for chicken eggs it looks like this,
but for more pear-shaped, so-called pyriform eggs, you need this one. Meaning the universal
egg formula - well it's this whopper. The four parameters are the egg's length,
breadth, shift of vertical axis, and the diameter at one quarter egg length. if you'd like to check
it out, read all the details, we'll include a link to the paper in the video description.
And over on our extras Numberphile2 channel you can see an interview I've just done
with a Ukrainian poultry engineer who helped create the formula. That's worth a look too.
The principles of evolution, yeah, to deduce another more complicated formula so it
it appeared to be very complicated. It appeared to be awful from from my point.