Calculate Size of Small Rectangles to Fill Max Area in Encompassing Rectangle

[kleinma]

The issue at hand, is I will have a rectangle of size x. This rectangle will contain n smaller rectangles. Each of these smaller rectangles is the same size though.

I need to figure out how to calculate the SIZE that the smaller rectangles should be, based on

1) the size of the encompassing rectangle
2) the number of smaller rectangles that go inside it

so that I can fill the maximum area inside the main rectangle, without altering the height/width ratio of the smaller rectangles (ie they can grow in size, but they can't be sized in a way that it distorts their height/width ratio, so some area in the encompassing rectangle will not be filled in, and this is ok)

both these values are known when I need to do the calculation.


Here are a few images to illustrate this (note sizes of red rectangles in each image are always the same). Is there any specific geometric formula to do this?

 

[Alex48674]

I think you could fit an infinite number of rectangles in the larger, either the smaller shave to be infitly small or the larger infinitly big =]

 

[kleinma]

That wasn't what I was asking...

This is for a real world problem, so I need a real world answer.. not theoretical assumptions.

 

[ModernLogic]

Well, the "size" of rectangle is called area and its two dimensional. So let's call the rectangle's area L x W. And suppose we want to fit n smaller equivalent rectangles inside the big one.

The dimension of each of the smaller rectangles can be (L/sqrt(n)) x (W/sqrt(n)).

 

[Alex48674]

That wasn't what I was asking...

This is for a real world problem, so I need a real world answer.. not theoretical assumptions.

I was just joking around a bit =]

but I think you could go along the lines of the ratio of the original rectangle and then just solve alegraicly. such as

(L1)(W1)=x(L2)(W2)
where L1/W1=L2/W2

x represents the number of smaller rectangles you want
L1 is the length of big rectangle
W1 is the width of the big rectangle
L2 is the length of smaller rectangles
W2 is the width of the smaller rectangle

the L1/W1=L2/W2 should assure the proper ratios

I think this should be right if I read this right, but you said something about theoretically assumptions, and depending on what you want x to be, it could be infinitely small. But I g2g so I have to stop here.

 

[awvvu]

You're asking what are the different ways to arrange a bunch of videos onto a screen without changing their aspect ratios right?

 

[mubashirmansoor]

(L1)(W1)=x(L2)(W2)
where L1/W1=L2/W2

I think this should be right if I read this right,

Thats correct. I got the same results too...