[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 501

 
Mathemat:
Yeah, don't explain 0.1 yet. Let the others suffer.

Sadist.

The root of one tenth squared is exactly 1/10.

 

I've been playing around with colouring books. I coloured a cavadrat.


 

I see, now thanks to your colouring in, everyone will know the solution. But why (root of 0.1)^2 is unclear. The colouring book was enough for me...

There's another problem on the previous page.

 
Mathemat:

I see, now thanks to your colouring in, everyone will know the solution. But why (root of 0.1)^2 is unclear. The coloring was enough for me...

On the previous page is another problem.

I'm actually intuitive. Here in the picture below you can see that the shaded square is slightly smaller than the one in the middle highlighted.

And since allocated = 1/9, so a smaller one would be 1/10.

Does it make sense?


 

Makes sense, of course. But less than 1/9 could be 1/11.

Although if you don't know numbers over 10, 10 is just right, right.

 
Mathemat:

Makes sense, of course. But less than 1/9 could be 1/11.

Although if you don't know numbers over 10, 10 is just right, right.

О! Exactly.
 
Mathemat:

Why (root of 0.1)^2 is unclear.

How so! The root of one tenth is the length of the small side. You have to multiply it by the square to get the area. You're not confusing me!
 
Place several point electric
charges in space so that at rest the system of these charges is
in equilibrium. You can choose the number, magnitudes and coordinates of the charges yourself
. You must check that the sum of electrostatic
forces acting on each of the charges of your proposed
is zero.

of the system. There must be more than one non-zero charge in the system.

2010

Strange, I thought that was impossible. Somewhere I saw some theorem about it. But now I strongly doubt it.

 
A pyramid with a different charge in the centre is greater than the angular ones modulo ? I don't want to write out an equation.
 

Nah, three charges on one line is enough - one positive in the centre and two negative on the edges symmetrically (charges 4 times bigger). Everything there is elementary and simple - you don't even have to think about it.

I realised what was bothering me. There is such a theorem by Irnshaw. I just forgot that it's about the stability of the system of charges, not about its existence in principle.

Reason: