How many n square can fit into a square of side N Suppose we have n small squares of equal sizes that has area w.
Suppose we have a fix square S of area A such that for area A, one area w < area A.
If square S's area A, length, and width are given, 
and if the n small square length, width and area w is given,
and if n small square has to be placed in area A such that n small square has to be space equally, 
then I want to know how many n small square I can placed into square S?
A simple formula.
This type of problem came from an engineer question. 
Space equally means: 
Suppose I have small square A, B, C, D.
If I place A and B inside square S, the distance between them is d.
If I place C inside square S, I want the distance between B and C to be e such that e=d.
If I place D inside square S and it is underneath A, I want the distance between A and D to be f, such that e=d=f.
I will repeat pattern into Square S is filled.
Furthermore, What if I replaced the n small square, with n small circle or rectangle.
But for now let just focus on n small squares.
IS there a area in mathematics that explore this problem? 

I'm going to assume that all the squares are aligned (that is, each side of each square is vertical or horizontal), that the small squares are not to overlap (except possibly at their boundaries), and that the centers of the small squares are meant to form a square lattice (this takes care of the "equal spacing" requirements. 
The small squares have area $w$, so side length $\sqrt w$. The big square has area $A$, so side length $\sqrt A$. So the number of small squares we can put in a row is $[\sqrt A/\sqrt w]$, where $[x]$ means the greatest integer not exceeding $x$ (e.g., $[\pi]=[3.14159\dots]=3$). The number of rows we can get is also $[\sqrt A/\sqrt w]$, so the number of small squares is $$[\sqrt A/\sqrt w]^2$$ 
For example: if $A=10$ and $w=2$, then $\sqrt{10}/\sqrt2$ is between 2 and 3, so $[\sqrt{10}/\sqrt2]=2$, and we can fit in $2^2=4$ squares. 
