let's just say, this sliver.

So let's say I had some sliver.

And if I wanted to draw my sliver,

That thin sliver you see here, that's Africa.

If I know the area of any given sliver, what if I multiply the area of that sliver times dy?

So what would be the volume of that sliver?

But we took this sliver, and this sliver as we learned in previous calculus, the width of this little rectangle is dx.

So if this is a sliver, it's width is dx.

Now imagine taking that sliver and rotating it around the y axis.

That little sliver of liquid sustains human life on Earth, it literally holds up civilizations.

It's that little green sliver on the horizon, which makes them very nervous about rising oceans.

The effect of forces in the scene are computed for this sliver of time and objects are modified.

These eyes, having seen too much of the world, can no longer grasp even a single sliver of hope.

You can just see a little bit of North America up here and a sliver of Australia down there.

The volume of that sliver will be this function of y times dy, or this whole thing times dy.

If you give me a y, I can tell you the area of the sliver that corresponds to that y.

If I multiplied this area times a small dy, then all of a sudden I have a sliver of volume.

We've actually taken a sliver of the ocean, put it behind glass, and we together have put bluefin tuna and yellowfin tuna on display.

A tiny little sliver call themselves libertarians, or socialists, or some other small third party, and the largest block, 40 percent, say they're independents.

This would give us an expression so that I would know the area of this kind of sliver of the volume, for any given value of y.

And so we are in the middle of this thing that's completely linked, down to every object in the little sliver of a connection that it has.

But in just a tiny sliver of the Earth's history, the last one millionth part, a few thousand years, the patterns of vegetation altered much faster than before.

And because nothing is more important to us than survival, the first stop of all of that data is an ancient sliver of the temporal lobe called the amygdala.

So every item, every artifact that we make, will have embedded in it some little sliver of Web ness and connection, and it will be part of this machine, so that our environment kind of in that ubiquitous computing sense our environment becomes the Web.