[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 283

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Yeah, the problem is not stereotypical at all.

P.S. Nobody said it had to be differentiable or even continuous...

And the angle of rotation must be commensurate with Pi - otherwise it could be rotated by any angle.

 
Mathemat >>:

Ага, задачка совсем не стереотипная.

P.S. Никто не говорил, что она обязана быть дифференцируемой или даже непрерывной...

А угол поворота должен быть соизмерим с Pi - иначе ее можно было бы повернуть на любой угол.

I don't know of one. I'm still stumped.

 

Every time I get to the middle of a solution, it turns out that it has already been solved.

People, for the third time, please give me the answer to the problem with 7 cigarettes. I've solved 6, but I can't solve 7.

I don't remember which page it is on :)

 
f(x) = x ? one variable, when you need two variables for the graph, as above y = f(x). f(x) = x - why this notation, I do not understand?
 
yuripk >>:
f(x) = x ? одна переменная, когда для графика нужны две переменные, как и есть выше y = f(x). f(x) = x - к чему такая запись, не врубаюсь?

f(x) = x - in this case it is an equation, not a function.

 
Mathemat >>:

Ага, задачка совсем не стереотипная.

P.S. Никто не говорил, что она обязана быть дифференцируемой или даже непрерывной...

А угол поворота должен быть соизмерим с Pi - иначе ее можно было бы повернуть на любой угол.

Matemat, if you are referring to the problem from Quantum 1987, it seems that the angle of 90 degrees is specified.

Here, have a look, number 1059.

 
alsu >>:

Matemat, если имеется в виду задачка из Кванта за 1987 год, то там, кажись конкретно указан угол 90 градусов

Вот, полюбуйся, номер 1059

She is, I swear.

--

1059. The graph of a function y = f (x

), defined on the entire number line, passes into itself when rotated by 90° around the origin.

a) The equation f (x) = x

has exactly one solution.

Prove it.

b

)

Give an example of such a function

. That is, I can't think of an example.

You don't have to

prove anything.

 
So what function can you translate into yourself when turning 90?
 
f(x) = x and f(x) = -x, hence x = 0. If such a function exists and
 
There is no such function. Well, except y=0. That's my back word. :)
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