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  • Tadashi: So here's a mirror of sorts, it's curved.

  • And in front of this mirror, I put this rectangular sheet (with something drawn on it).

  • And when you put it in front of the mirror

  • and look inside the mirror

  • you see a cat.

  • You know, with pointy ears

  • and side protrusions that look like whiskers and everything.

  • So, I am very happy with this cat.

  • I'm proud of this cat.

  • A nice cat, I will say.

  • But when I show this to a mathematician

  • and theoretical physicist colleagues

  • Some people like this

  • because they have good taste.

  • But others say

  • So?

  • Well, that's really sad.

  • I hoped that they didn't say so.

  • But for those of us who'd like to say so: here's the thing.

  • In front, you have a mirror, indeed

  • but that's what we call a "convex mirror."

  • So it's bulging out towards us.

  • In the back, inside of the tube

  • there is a concave mirror.

  • Which is bulging away from us.

  • So now, I'm going to put

  • another cat inside

  • and look at what happens.

  • And if you look from the correct angle

  • you see another cat inside.

  • By the way, some people might wonder

  • how many reflections are bouncing off before it reaches our eyes.

  • But in fact it is just one reflection.

  • It's reflecting on the back side and then coming out.

  • So you have a cat on the inside.

  • Now, the slightly odd thing is

  • that cat on the inside

  • looks very much like the cat on the outside.

  • Although the cat on the outside is from a convex mirror

  • whereas the cat on the inside is from a concave mirror.

  • So convex and concave

  • I mean they are opposite things

  • and you might expect the distortion effects to be the opposite

  • but they look very very similar.

  • So that's quite interesting.

  • It's not much of a hint

  • but one thing that has to do with this effect is the following.

  • This arrow

  • is pointing from left to right.

  • And if you look at it's image reflection

  • in the mirror in front, the convex part

  • it's still pointing from left to right.

  • But let's look at it on the inside on the concave mirror.

  • It's pointing from right to left!

  • So that's quite interesting

  • it reversed it's direction.

  • So, it's a matter of

  • where the center of focus you are placing the arrow.

  • As I move the arrow inside, or according to the outside, move the mirror

  • you see the arrow changing it's shape

  • and

  • somehow it sort of blurs out

  • and eventually at the end

  • you come to the point where you see the real image next to the original arrow.

  • So you can do something like this

  • with a cylindrical mirror

  • and little rectangular sheets of paper.

  • When I first thought of this

  • you know I thought something like this might be interesting to try.

  • The major problem I faced was

  • where do you find a cylindrical mirror?

  • I mean, if you have

  • a flat mirror

  • you know, slightly bulging out or bulging in

  • so it changes the size of your image

  • and so in a way, you can find that in cosmetic shops

  • and so forth.

  • But

  • where do you find a cylindrical mirror?

  • A tube-like mirror?

  • And I thought and I thought

  • and finally

  • I went to the shopping center and I found one!

  • These are cookie cutters!

  • It's a cookie cutter, you know, where you

  • make the cookie dough and then cut the shapes.

  • So you can buy 1 for $1.

  • And, with that

  • you can make a cat in the mirror!

  • Brady: A cat in the cookie cutter?

  • Tadashi: That's right!

Tadashi: So here's a mirror of sorts, it's curved.

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リフレクトされた猫 - Numberphile (Reflected Cats - Numberphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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