Reflected Cats – Numberphile

Reflected Cats – Numberphile


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!

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  1. I'm a big numberphile fan but this guy has the WORST videos. They are the only numberphile videos I skip.

    I tried to watch this but after about 1:30 I had to stop.

  2. I like how the cookie cutter animation shows it cutting through cookie dough that doesn't need to be cut at all.

  3. This is the kind of Numberphile video where I see the title and instantly know it's got Tadashi in it.

  4. I keep thinking Godzilla is going to ruin his videos…
    Racist? Is it just me? Come on Godzilla…just smash everything already.

  5. It doesn't matter if it's concave or convex it will still be the same as it is pretty much symmetrical so there won't be a big change it will just flip.

  6. If you want a better mirror just go get a bit of steel tube take to a machinist to have the surface polished to highest quality they can and then take it to be chromed.

  7. Jacobite supporters used cylindrical mirrors to create crypto-portraits of Bonnie Prince Charlie. They had a hand-painted plate with what appeared to be just a colourful design. When they put the cylindrical mirror in the centre of the plate, the reflected image was a portrait of Prince Charlie. If English soldiers came to the door, they just had to remove the mirror and put it on a different shelf to hide their sympathies.

  8. Can you ask the Doctors is Pi a real number? Can you place Pi on Number line? For example 1,2,3,Pi, 4 and on and on

  9. Thank you for uploading yet another Tadashi Tokieda video ! I'm always fascinated by how he manages to take household objects and derive entire lessons in mathematics and physics from them, making the ordinary something special.

  10. I would love to see a video about a stick with negative length or circus with negative radius. And what is the differences between a line with -4 length and a line with -4i length.

  11. nice video , btw is there any pretty way to simplify (a+b)sqrt(n) , I mean n^(1/(a+b))
    with pretty i mean a way that allows you to do this also for n^(1/(a+b+c+…))

  12. Couldn't he hit the cylinder with a spoon just once? Only one time, we are simple people, that's all we fans want. Please.

  13. This is probably the most important thing I have seen in a number of years. I need to go sit down for a minute. If anybody has any stories on how they broke this news to their families, this is a safe place to share. Everybody keep it civil.

  14. then in side the cylinder, it is two reflection. not only one. but it can be one refelection when you move it close to one side enought.

  15. I like how you explained the difference between these effects a little with the outward and inward curved mirrors. I was a little confused on how the arrow likes to point in the opposite way when reflected in the inward mirror but I will try to do this at home if I can acquire a cylindrical mirror.

  16. Knowing Dr. Tokieda is an artist -> classical linguist -> mathematician, who knows NINE languages, I shat bricks.

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