Hello prasadcad Originally Posted by

**prasadcad** Hi Grandad,

Thanks a lot for the solution. It absolutely works fine.

But I need to understand how can we make it more generic. I had given some constant values like 500 mm X 500mm. If we consider the length of each side of Rhombus A is L1 and it is divided into P and small rhombus length is l1.

In the question I had posted the values I had given were L1 = 500mm, P = 2500 and l1= 10.

I would like to know how these values were used to deduce the equations? And how we can use it make it Generic equations?

Please excuse for my little knowledge about geometry.

First, note that $\displaystyle L_1, P$ and $\displaystyle l_1$ are not independent. The number of small rhombuses, $\displaystyle P$, will be the square of the number that will fit along one edge of the large rhombus. In other words:$\displaystyle P = \left(\frac{L_1}{l_1}\right)^2$

and, of course, if $\displaystyle P$ is to be an integer, then $\displaystyle L_1$ will have to be a multiple of $\displaystyle l_1$.

The formula for the number of the small rhombus containing $\displaystyle (x,y)$ that I gave you, $\displaystyle 50(n-1) + m$, will then become:$\displaystyle \frac{L_1(n-1)}{l_1}+m$

and the formulae for $\displaystyle m$ and $\displaystyle n$ will become:$\displaystyle m = \left\lfloor\frac{x\tan\theta-y}{2l_1\sin\theta}\right\rfloor+1$

and$\displaystyle n = \left\lfloor\frac{x\tan\theta+y}{2l_1\sin\theta}\r ight\rfloor+1$

Grandad