Planar

Circuit NPN Transistor

Circuit PNP Transistor

This is a planar graph.

Unlike Gertrude Stein's roses, it's not the case that a transistor is a transistor.

Puzzle game involving untangling planar graphs

The transistor was only for experts.

Here's an example of a planar graph.

Here's a planar graph on five nodes.

We had a planar graph. amp gt amp gt About the planar graphs. amp gt amp gt Yup.

Processor performance on Intel chips, the average price of a transistor 1968, you could buy one transistor for a dollar.

The invention of the transistor introduced a new era.

The invention of the transistor marked a new era.

I just won a small, little transistor Philips radio.

A transistor is nothing more than a wall switch.

Here's a planar graph a bunch of nodes and edges.

The devices that computers use are what's called a transistor.

They can be planar formations, they can be three dimensional formations.

I don't know what every transistor in the connection machine does.

We can build any planar graph by iteratively adding nodes and edges.

To do that we're going to need another concept about planar graphs.

For any planar graph, n m or is equal to 2. Really?

This picture is the working part of every computer. It's the transistor.

So the second layer of simplicity was the transistor in the Internet.

There's no way of predicting the Internet based on the first transistor.

What about coloring a graph with four colors if its a planar graph.

You could have made it in the 1890s you wouldn't have the transistor.

Let's think about the colorability of planar graphs. In particular, here's a decision problem.

There's going to be some graphs that can't be drawn as a planar graph. If we add this edge between this node and this node, the resulting graph is no longer planar.

And if you're thinking of the brain as a computer, this is the transistor.

The most common form of transistor today is built on what's called a chip.

Look at this graph here.You could buy one transistor for a dollar in 1968.

So maybe it's about the equivalent of 1947 when this was invented, the transistor.

And that means that a transistor corresponds to about 12 ion channels in parallel.

So, since the transistor is so simple, you can put lots of them together.

As you can see here, they collapse from a three dimensional formation into planar formation.

We're also going to now talk about a notion of regions in a planar graph.

Any lines drawn across co planar surfaces can be erased to form one larger surface.

We're given a graph G and a number K. Is planar graph G K colorable?

So probably one of the most important inventions of the twentieth century is the transistor.

Another category of graphs that are very important and come up a lot are planar graphs.

Now, the explorers of the world of the atom did not intend to invent the transistor.

What I mean that is the, lower down layers and the implementation technology, like the transistor technologies.

But if you look at computing in general across, this, this is all across transistor based technologies.

A three coloring of planar graph isn't any easier than three coloring in general graph, it's NP complete.