# Maximising shelf space in a given room

## Main Question or Discussion Point

How do I calculate how to do this?

I believe I need to maximise the perimeter of the units while minimising the area they take up, and also allowing access space for a human.

I will probably end up with a comb shape, but I am intellectually curious about the mathematics involved. No need for exact dimensions as I'm more interested in generic formula.

Let's discount the variable configuration units that slide out, since I want to view all my books at once.

Bacle2
If the shelfs are 2-dimensional (meaning you don't worry about their height) and

rectangular with sides w,d (width, depth) , then

you want to maximize the expression 2w+2d , while minimizing wd. But I imagine

width is more important than depth (since more depth will not, in general,

allow you to store more books), so maybe you just want to maximize w , and

choosing d large-enough to store the books.

How much human access space would you specify? Also, is overhead and underfoot space considered?

Btw - with the overhead and underfoot question I considered the viewable requirement achievable with mirrors on ceiling and floor between shelves.

There are lots of websites on maximising area with minimising perimeter but so few of the reverse!

Enosis, I am more interested in a generic solution, even though I do have a specific room to fit, i would like to understand the process. I'm not worried about exact details like the amount of space a human needs as it can be expressed as a variable in an equation.

Please consider this solution. Determine the size required for a single person and a folded ladder to reach the ceiling - perhaps 2 sq ft? If the space is an even number of sq ft - construct 2' square shelves (accesible from 4 sides) on casters and extending from floor to ceiling. Fill the entire room with these shelves except for the human space and 1 additional 2' square space - this will allow you to move about through the room and utilize the ladder.

Stephen Tashi
I am intellectually curious about the mathematics involved. No need for exact dimensions as I'm more interested in generic formula.
Only the simplest of real life situations can be solved by a single formula. Your problem is too complex for that. A practical way to approach your problem would be to write a computer program that tried a large number of configurations. You would have to specify the algorithms that determine if there is sufficient space for a human being to access the books conveniently and that is probably not a simple algorithm to write. You have to include other other practical considerations such as shelf length and shelf vertical spacing. Unless you are a metal worker, if you use metal shelves to have the advantage of the vertically thin shelf, you only find these made in certain lengths. If you use wood (or thin metal) you have the problem that a long shelf will sag. A clear space of 10 1/2 between shelves and a shelf depth of 10 inches is enough to accommodate most books but there will be a few bigger ones and if all your shelves have that spacing, the tall books would have to go on the top of the bookcase or on their sides.

Practical design problems are very interesting. Good designs are often compromises between several contradictory goals.

A practical way to approach your problem would be to write a computer program that tried a large number of configurations.
I tried to cut out out pieces of paper and move them about. I think you are correct that a computer is needed.

I can deal with vertical spacing because that is pre-defined by the books I have.