Welcome to 300 BCE, where we are about to look in on one of my good friends, Euclid. Wow. Without this guy, my
favorite book, "Flatland" couldn't have been written. I mean, the whole thing is based off of the world that Euclid
introduced us to. And the movie to go along with it is just priceless.
Ah, 21st century graphics. They're beautiful. Oh, and there's the classic videos from the old days! You know, the
ones from Kahn Academy. Those were so helpful to me growing up. I think I can get the one about Euclid on my cellular
device here. Oh, here it is.
Goodness, how I get distracted. We're here in the 3rd century BCE and we're watching videos from the future. Let's see
what's around us. Oh my 6! We came at a perfect time, it looks like he's just writing out his proof to show that
the set of all primes is an infinite set. I love that proof. I'm glad in the 23rd century I am allowed to marry
that proof. It's been the happiest years of my life. This is one of my favorite explanations of that proof.
Doesn't that just show off the natural beauty of Euclid's proof? It's so elegant. I find it so fascinating that the ancient
mathematicians dealt so much with prime numbers, even though they didn't find an actual use for them until the 20th century.
The mathematicians of the day, Eulcid and especially the Pythagoreans loved to examine prime numbers and their properties.
It was a treasured pastime to discover a new prime number. They did all that research just because it was mathematics and cool.
Oh, I could spend so many millennia
just watching Euclid write that proof and learn about prime numbers, but we don't have the time for that. Goodness, I'm giving people the impression
that Euclid only worked with prime numbers. Euclidean Geometry is named after him for 28's sakes! Of course he did more than work with primes!
All of those shapes
you've learned about since you were born, they're all thanks to him. I especially love all of his axioms and postulates,
even that parallel postulate. Oh, things go crazy when the parallel postulate isn't assumed. This image shows some things that
happen in a world that isn't Euclidean.
All those things that you memorized in geometry classes isn't true in this case. The circumference of a circle is
greater than 2πr! The interior angles of a triangle are less than 180°. Holy 6's, the shortest distance
between two points isn't even a straight line anymore in this type of universe! We can also see that the parallel postulate doesn't
apply in this particular geometry.
Well, we better keep moving along. We've got lots of time to cover. Our next time leap won't be quite as long. We're
just going a few decades ahead to the time of ...
