# Maximising shelf space in a given room

d3mm
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.

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.

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

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

d3mm
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.

enosis_
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.