[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 102

 
MetaDriver писал(а) >>

Can you be more specific? Can you give me the full formula?

Yes, it doesn't work that way, but it has another way - 2^k1 : 2^k2, where k1,k2 < N

It's nice too :-)

 

Here's a geometry lesson:

Two circles and a point are given. Construct a segment whose ends lie on the given circles, and whose middle is at the given point.

2 Yurixx: I suspected that the solution is not singular.

 

Nope, there's something wrong with the condition. It's easy to specify situations where it's not possible. And there are countless of them.

2 Mathemat

Ponatno. But MetaDriver called me to the barrier. :-)

 
Yurixx >>:
Неее, тут что-то с условием не так. Запросто можно указать ситуации, когда это невозможно. И их бесчисленное множество.

Mm-hmm. Come on, Alexei, elaborate.

 

Yurixx писал(а) >>

Ponatno. But MetaDriver demanded to the barrier. :-)

;)

I don't see any other solutions even now. Only WHOLE and moreover DIFFERENT ones are allowed.

Is it fulfilled?

Or I am slowing down something.

 

And how to use a compass and a ruler to draw a tangent to two arbitrary circles. The circles are not one inside the other.

 

I'm confused. What problem are we talking about? I'm copying the conditions from the book as they are.

Well, yes, there are impossibilities in the segment problem. So there should be an analysis of when you can and when you can't.

 
MetaDriver писал(а) >>

I still don't see any other solutions. The condition states that only WHOLE and DIFFERENT ones are allowed.

Have you got it fulfilled?

Well, there are degrees of two in the denominator. Therefore the numbers in the proportion I suggested will always be reduced and both last numbers will be of the form 1/M1, 1/M2
 
Mathemat писал(а) >>

I'm confused. What problem are we talking about? I'm copying the conditions from the book as they are.

Well, yes, there are impossibilities in the segment problem. So the solution must also include an analysis of when you can and when you can't.

The analysis is for a fee. :-)

 
Yurixx >>:

А как с помощью циркуля и линейки построить касательную к двум произвольным окружностям. Окружности не находятся одна в другой.

Both radii at the touch points are perpendicular to the common tangent. What's next on your own?

Reason: