How to pronounce “euclid” in English

And Euclid says, these two parallel lines will maintain a constant distance forever.

And Euclid's theorems come from India.

And Euclidean geometry, you may have heard, is based on postulates or axioms.

So Euclidean space is a flat space.

Geometry is formalized by Euclid 2,300 years ago, it was highly influential and transformative.

There are flaws in "Euclid's Elements," as you might know.

And in Euclidean geometry, we can measure the distance along a path.

It's part of Euclidean geometry.

The real thing about Euclidean geometry is not that he derived brand new results because most of his results had already been derived by other people.

And I think that-- was it Euclid or Euler who thought that there didn't even exist Graeco Latin squares beyond a certain single digit

I had never actually read "Euclid's Elements."

And if you are familiar with "Euclid's Elements," the beauty is that you have both a construction and proof.

Why should the strange laws of non-Euclidean geometry, which were originally conceived of as a thought experiment in the 19th century, turn out to be the exact mathematics

This was the beginning of non-Euclidean geometry, which turns out to be very, very useful for Einstein.

Because Gauss knew about this non-Euclidean stuff, but he knew there was still a lot of work to do, the general problem.

Pythagoras' theorem helps you do it for Euclidean geometry.

You have Pythagoras' theorem for Euclidean space, and you have Minkowski's equation for relativistic spacetime.

How do we move from this Euclidean idea?

So all that quantification was achieved through Euclidean geometry tools, whereas the arithmetic number-based tools

It was only around 2,000 years after Euclid when people, such as Galileo and Newton came along, and fully integrated time and dynamics into physics.

It was worked out in the way of Euclid's "Elements," with the axioms and proofs.

This minus sign is obviously different in Minkowskian geometry versus Euclidean geometry.

of indefinite ternary quadratic forms are identical to those of non-Euclidean geometry." So this is the comment of Poincare.

And his fashion is about trying to incorporate non-Euclidean surfaces into his fashion.

Hilbert's Hotel, it violates Euclid's principle.

He had read two of my books, "Euclid's Window" and "Feynman's Rainbow."

So you know, if you start with Euclid, you've got these five really simple postulates, and then the first few things you prove just feel blindingly obvious

had come to the modern conception of space-- the idea that space is Euclidean void that can be described by mathematics.

The tension between the Cantor-Hume principle and what could be called Euclid's principle, which is that the whole is always greater than the part, is a principle that Euclid

We really only started doing mathematics a couple of thousand years ago, with Euclid's Elements, and everything kicks off then.

in UPenn and then pretty early on was a venture capitalist in New York City at Euclid Ventures.

If you don't know this book, that's "Euclid's Elements."

Or if you're working on a tabletop or something like that, we have Euclidean geometry.

Well, remember, there's Euclidean geometry.

So analytic geometry treats geometric issues with equations, and Euclidean geometry treats it with illustrations and shapes.

And this led to "Antifragile," where I was explaining that architects always do a better job when they don't use Euclidean geometry,

That discovery introduced a revolution in mathematics, and ultimately led to the field of non-Euclidean geometry, which is the mathematics that underlies general relativity.

I have helped my kids learn this stuff all the way up and by the time you get to Euclidian geometry, a good problem might take half an hour to an hour to solve. The answer might

So what Galileo was troubled by was this tension between what we call the Cantor-Hume principle and Euclid's

infinitely many infinities adding up still to the very same infinity, which is a strong instance, a strong violation of Euclid's principle once again, right?

But if you look at it with the eye of an expert, you can tell that it's no longer Euclid.

The Translation Movement also renders many works of science, and even engineering, into Arabic, so you have works by Ptolemy, Euclid,

There is no other subject, of course, in which knowledge can last thousands of years, and the theorems of Euclid

For about 15, 16 centuries, people were building things and never heard who Euclid was.

in one way or another, apply point A to point B, kind of a Euclidean approach, that I'm going to say is not quite how it works.

And in fact, Dr. Taimina and her husband David Henderson, who is a great geometer, they indeed do use these models to teach non-Euclidean geometry

and other geometric forms behave in hyperbolic space, which is different to the way they behave in Euclidean space.

Well, it's an alternative to the two kinds of geometries you're already very familiar with-- Euclidean geometry or Euclidean space, and spherical space.

So he's learning very elaborate, and pioneering very elaborate means of pattern cutting that enable him to sew non-Euclidean surfaces