Before hyperbolic geometry, mathematicians knew about two kinds of space Euclidean space, and spherical space.

So I found myself, in other words, constructing a geometry, a geometry of things which had no geometry.

Spherical aberration image correction plugin for digiKam

If it's circular, you make a spherical lens.

The puck of ice hockey is not spherical.

I have a straight line on my spherical surface.

CaRMetal interactive geometry

Interactive geometry viewing program

Extract geometry from the images.

But there is another possibility that you all know of spherical space.

Today we don't need one million light bulbs to create a spherical display.

They have a very rich, intertwined geometry.

The frilly crenulated forms that you see in corals, and kelps, and sponges and nudibranchs, is a form of geometry known as hyperbolic geometry.

We're just seeing the coarse scale geometry here.

The Greeks invented a theoretical model of geometry.

Africans can't possibly really be using fractal geometry, right?

So in Manghetu sculpture, you'd see this recursive geometry.

This is exploring geometry and the rhythm of shape.

I was thinking about mass produced spherical television sets that could be linked to orbiting camera satellites.

We use a modified inkjet printer, and we print geometry.

Geometry, fantastic. You know, quantum mechanics these are cool things.

So what is this hyperbolic geometry that corals and sea slugs embody?

This is the result of computational geometry, gesture recognition, and machine learning.

And primary visual cortex sees just simple geometry, just the simplest of shapes.

If geometry is the science of space, what is the science of time?

But it's reassuring that at the heart of this mathematics is pure, beautiful geometry.

This sort of geometry revolutionized mathematics when it was first discovered in the 19th century.

And then I went in, and measured all the geometry because I figured, hey, biomimicry.

And this cloud of matter is much more spherical than the galaxy themselves, and it extends over a much wider range than the galaxy.

I saw my geometry teacher in high school, Mr. Rucell's wry smile under his handlebar mustache.

The discovery of hyperbolic space ushered in the field of mathematics that is called non Euclidean geometry.

And where I was bad was algebra. And I was never allowed to take geometry or trig.

What physics tells us is that everything comes down to geometry and the interactions of elementary particles.

In May of this year, China s Five hundred meter Aperture Spherical radio Telescope China s Eye of Heaven, installed the world s first 19 beam L band receiver.

The first ingredient is materials and geometry, and that needs to be tightly coupled with the energy source.

And the power of mathematics is often to change one thing into another, to change geometry into language.

And a surprising aspect of it is that very often, the rules of this geometry are extremely short.

And as I looked at it, it kind of tucked its arms under it, raised into a spherical shape and turned chocolate brown with two white stripes.

Gigantic mistake I'm finding a lot of kids who need to skip algebra, go right to geometry and trig.

The toroidal geometry made for a very efficient building every beam in this building is the same radius, all laminated wood.

Together with quantum mechanics, the geometry of this shape could describe everything about how the universe works at the tiniest scales.

Talking about geometry and everything, if you take the circle and you split it in half can you run S Curve music?

The problem, as we see it, has to do with a single, simple word space, or a single, simple phrase real world geometry.

And this gives us a tangible model of the three dimensional protein and how it folds and all of the intricacies of the geometry.

We print geometry where we can make industrial design objects like, you know, shoes, leather belts, handbags, etc., where no sentient creature is harmed.