Name: Earthquakes, Circles and Spheres - Numberphile
Uploaded: 2020-03-27T18:41:18.000Z
Duration: 16 min 26 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

we live in the three dimensional world a few times.

This time four dimensional world on this surface is two dimensional on some curve, lying can be one dimensional so forth.

Adverbs of degree

And we have a tendency to believe that low dimensional things are easier, certainly easier to visualize and highly mission things that mysterious some kind of buffalo because sometimes high I dimensional objects are easier on dhe.

A problem can be solved by lifting the academician coming down to the dimension.

In point to the beginning of the slow re draw three circles R B three circles, but different sizes and different positions.

Let's say they're all overlap with one another.

You have three of them large, middle on small sizes.

Any pair of circles, for example, large on middle intersect in two points here, here, and you can connect those two points by a core.

So like that on because they're three pairs of circles, you can connect all of them large on the middle.

Connect middle and small connect on snow on large connect, so you have three lines that appear now.

If you throw three random lines they just pass through each other, but they don't meet in the point any.

What are the chances that they meet exactly one common point village?

But in this case, if you start from three circles and if you do this construction, it turns out that those three course meeting in exactly one common point that is quite mysterious.

It happens for any three circles that the Intersect one another.

You draw those course automatically on forever.

Every eye in the university's happens, so there must be a reason you clearly have three circles on this sheet of paper, which is a two dimensional world.

But instead of thinking of these circles, let's lift them into the three dimensional space.

Think of these as pictures of steers a scene from above.

Let's suppose that you have a large sphere here on the medium size here, here and there, like bubbles, and they're so the magic spheres, which can enter each other.

They collide, but they can enter each other.

Let's say that their centers are all on the same height, so if two spheres and th other the Intersect.

They meet each other along some common circle like this, which is vertical and similarly, if there's 1/3 sphere, which is small, enters the middle and that's fears.

Then, in a small one meets the medium sphere on small sphere meets the large sphere along some circles as well.

So you have circular arcs along which those three spheres enter each other on intersect.

And if you take a top view of this, a bird's eye view the picture that you get well look like this, you can imagine three kind of bubble like spheres entering each other right on Dhe.

Remember, their centers are all on the same horizontal plane at the same height, so the kind of very nicely entering each other now, clearly, if you take a view from the top, those are circular arcs, which kind the move like this.

Like a long values like that on they die, all of them into a common dimple in the middle, and in fact, this is a bird's eye view.

But if you look at the whole thing from underneath, you see from underneath, those three arcs are coming up like that, and they'll meet at the dimple, which is pointing up like this.

So there's that the emperor at the top and import the bottom like this.

And if you take a view from the top of those to the the most look super pose and that's what you see.

And so you see those three lines, the actually projections.

Or, if you like, the apparent lines off the actual circular arcs, which meet at a single point.

If you imagine it, everything's transparent, you get back.

This picture in that was, those three circles are supposed to be actually spheres scene from the top on those two spheres meet along that circle, which looks like a line because we're looking at it straight down from the top.

Those two circles on those two circles meet, and they all sort of meat in a single point.

So by lifting the two members of a problem to three dimensional, so the more free ambient space where you can move around more freely and you can sort of go up and down, you simplify the program and infected improvement became easier and obvious.

In fact, there's no more problem can just see this experience has a very nice application.

I've recently moved from England to California.

Well, California is very sunny, wonderful people, and the weather is sunny and so are people, but also eat on earthquake territory.

That doesn't surprise me because I always come from Japan, another earthquake country.

The filming of an earthquake is a rare event, even in Japan, where such disasters are only too frequent.

California in Japan, both of them belonged to what is called the Ring of Fire that surrounds the Pacific on the Pacific Plate.

In all, directions are entering under continental plates On.

In doing so, they rub underneath and then suddenly everything vibrated.

That's why we're alone, full of earthquakes.

My wife, who's English, is not used to earthquakes.

And so she was very, very worried before we moved back in October, to be precise, attentive October 9 and 2017.

We were playing with a little child, that little baby in our living room, and then we felt an earthquake.

It was a small tremor, but very, very perceptible one.

I started counting one, 23 and my wife looked at it for her.

Puzzled by this and I count it up to six or seven.

I know this is not such a large earthquake, and the center is about 40 kilometers away.

We don't know which direction, but we're about 40 kilometers away on the fact that we've had only this.

That means that he was a small tremor, probably magnitude, I don't know, four or five at that distance and so forth, and she was very puzzled by this on dhe.

This was done because of the folding mechanism.

You probably are familiar with how, in a thunderstorm you see a flash of lightning and afterwards, a little late that you hear the rumble of thunder flash followed by rumble on.

By measuring the delay between the lightning on the rumble of thunder, you can estimate the distance to where the lightning struck.

Emitting light and light travels extremely fast.

It's not even its speed, but it's very, very fast.

It can go around escape of going around the earth, for example, or the whole of seven and 1/2 times per second, so it's very, very fast.

So for that kind of distance, you can recommit its basically infinite.

So you get the light from lightning insomnia.

The thunder takes time to travel because sound travels at what, three or 400 meters per second, that kind of speed.

So if you count the number of seconds that the sound is delayed with respected arrival off the right light, then multiply that by 300 or 400 meters per second will give you the distance to the lightening spot meters.

So you know you count for example three seconds one, 23 seconds and boom that.

Well, that means that you are probably 901,200 meters about that one kilometer away from where the lightning struck on.

So it's exactly the same with earthquake.

Absent the calculation, it turns out that when the earth shakes, that's the ass quick.

It sends out various kinds of waves all over the place, but they're two very prominent waves.

One of the waves works us like this say that this part is shaking on that part because it expands, compresses the next part off the earth and then bounces back because Earth is a little elastic on.

Then that bounce compresses an expert and expands complex, so you get this kind of compressive wave.

A pressure wave which travels like this on the shake is in the direction of travel like that.

That's called a P wave or pressure way for primary wave.

Another kind of wave, it's called she away for secondary wave on DDE.

That works because when the Earth is shaking, that kind of shake in trains also drugs the next part of the Earth and then goes like that and that shake.

So the shake is happening in a direction perpendicular direction of travel, where, as in the previous case, he was going along direction.

So that's called the S Wave on the 1st 1 has got a P wave P primary secondary on as prime on dhe on secondary indicate P wave travels faster, and that's kind of intuitive rate for something as strong and as robust as Earth.

Probably this kind of wave is much faster and this is a much softer mode.

So s wave travels slower the speeds off p and s waves very a lot.

In fact, they tend to increase as you deep into the going into the depths of the earth.

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Earthquakes, Circles and Spheres - Numberphile

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