calculating ratios to find optimal grid layout

[madscijr]

I have no idea what this is supposed to do.

I type in: 5 Items

It matches a 16:9 ratio, with a 5x1 grid.

A 5x1 grid isn't a 16:9 ratio.  

What exactly is this supposed to be doing here?

For example, say you have 15 pictures. You might want to lay those out to fit a picture frame in vertical orientation. Say the ratio of horizontal to vertical is 3:5. 
So the pictures would be arranged as a 3x5 grid, like 

01 02 03
04 05 06
07 08 09
10 11 12
13 14 15

If you wanted a horizontal orientation, the ratio now becomes 5:3, a 5x3 grid, like 

01 02 03 04 05
06 07 08 09 10
11 12 13 14 15

If you had a square frame, you would arrange them in a 4x4 grid: 

01 02 03 04
05 06 07 08
09 10 11 12
13 14 15 XX

where the last space is empty. 

Depending on the # of pictures that need to be arranged, that number is going to more evenly fit into some picture frames' aspect ratios better than others, i.e., a perfect fit would mean no spaces are left empty, but 1 space left empty is better than 2 or more. 

So what this program does is, given a count representing the # of pictures (or items), it displays how evenly that many items are going to fit into different aspect ratios, in order of the best fit (least empty spaces) to the worse (most empty spaces).

As a tool it helps you decide what aspect ratio picture frame to get to display a given # of pictures, or if the frame or screen size's aspect ratio is already determined, it lets you know how many pictures you would need to add or remove for a perfect fit (if needed).