Math noob + graphic design 3 point grid numbers equence

[citizenzen]

First, my apologies ... my last math class back in high school, sophomore year geometry, many years ago. I am a graphic designer, but have discovered an interesting math problem and would like some help identifying what it is and how to better express and use it.

Thanks for any help!

And now, the issue. For the sake of simplicity, I am only concerned with the horizontal measurements.

Graphic designers can employ a number of grids to provide a unifying structure for laying out pages. I use Adobe InDesign and these are the grid components that I use ...

Document Grid - Like graph paper, a document grid consists of a "net" of vertical and horizontal lines that (can) evenly space out a page.

Margins - provide space on the left and right edges of the page before columns begin.

Columns - divide the page into equally spaced horizontal sections

Column Gutters - provide space between each column​

There are a nearly infinite number of ways for all of these components to combine, However, in some cases, there are times when all of the components "match" and fall into perfect alignment. I have found a mathematical sequence that makes it easy to find these instances and I've attached a table I've created that identifies them.

Now I could either spend a lot of time creating tables to find each of these instances for all the varying page sizes and document grids, or ideally I could find a single equation that I can plug in the variables and find the answer.

So I need some help. What realm of mathematics am I dealing with here? Can somebody help me come up with the equation that can solve this problem?

Below is the first of my tables. It applies to an 8.5" wide page (612 points) and assumes a document grid of 3 points. The gold blocks indicate that the margin offset could be zero as well as the number in the block. The red multiplier to the right of the column designation above the table indicates the margin width, which can be any product of that number. The margin offset needs to be added to that product to create the matching grid.

I hope that makes sense.

Thanks again!

 

[phinds]

Don't know if you can generate a formula for this but I do this kind of thing from time to time rather trivially in computer software such that I just stick in the parameters and the value I want pops out. SO ... what I'm saying is that an algorithm can be constructed to do it, but that may not resolve down to a single equation it may involve putting some of the constraints into tables for lookup.

If you have software folks in your organization it should only take one of them 15 minutes or so to do it for you.

 

[citizenzen]

If you have software folks in your organization it should only take one of them 15 minutes or so to do it for you.

I was thinking I might be able to come up with something using PHP. I've done enough work with that in the past to muddle my way through.