OS X, like most modern operating systems, uses a virtual memory system for managing memory. Among other purposes, this allows the operating system to treat the computer as having an unlimited pool of memory. To achieve this, the OS will page unused parts of RAM out to a disk store known as the swapfile.
Of course, RAM is not unlimited, so OS X groups RAM into four categories: wired, active, inactive, and free. Wired memory is required by the operating system, and can never be paged out of memory. Active memory is memory used by currently-running programs. Inactive memory was used recently by programs which have now been terminated (or haven't been unused in a long time). Free memory is, as the name suggests, RAM that is not being used.
When you launch a program, it gets loaded into active memory. When you quit a program, however, it doesn't get removed from RAM; rather, it gets bumped into inactive memory. This is why it is often faster to re-launch a program -- it is still in RAM (try this with a big program like Firefox).
Once all your memory is used (free memory is 0), the OS will write out inactive memory to the swapfile to make more room in active memory.
If a program gets paged out to the swapfile, and you re-launch it, it'll get pulled from the swapfile into active memory.
So in short, you actually shouldn't care if your free memory is low. In fact, you want it to be low -- free memory is wasted memory (as the OS isn't using it for anything).
When examining how much memory your computer is using, you actually want to pay attention mostly to Swap used, which tells you the size of the virtual memory swapfile, and Page ins, which tells you how often the OS has to pull memory from the swapfile into active memory.
I have found, on my machine, that Mac OS X is a little slow to page the right things out.
Whenever doing anything particularly memory hungry, I will often quit a few applications to help it out. Safari is a huge memory hog if it has been running for a while and is top of the list of applications to quit. In my case this was when I tried to run VMWare Fusion without quite enough actual RAM.
You probably know this but here are a couple of links to Apple documentation which describe memory usage and virtual memory on OS X:
http://support.apple.com/kb/ht1342
http://developer.apple.com/library/mac/#documentation/Performance/Conceptual/ManagingMemory/Articles/AboutMemory.html
Here is the explanation that is given: The inactive list contains pages that are currently resident in physical memory but have not been accessed recently. It's hard to get an exact definition of what this means but is seems to include a file system cache as well as actual inactive memory.
Inactive memory is probably a difficult thing to handle on an interactive GUI driven OS where a user may choose to switch to any running application at any time and providing responsiveness in this sort of situation is important.... but the flipside of that is that in a situation like yours the OS doesn't quite know what the right thing to do is.
It is possible to purge (some of) the inactive memory by using the purge command. This may need to be installed by installing the CHUD tools but you may already have that installed. I haven't tried using the purge command so YMMV...
I've rambled on a bit and may or may not have answered your question. After writing all this out, I found another question on this site which much of the same info that might also help.
Best Answer
Apple documents the lowest levels of the Mach Kernel and the virtual memory subsystem fairly well on the web as part of it's developer documentation.
Since that kernel was developed by Carnegie Mellon University, you can find dozens of papers describing it quite easily.
If that is too low level for your paper, we have easily 10 or more good questions covering more of a non-programmer's view of OS X memory management. You'll probably have to do the synthesis of how OS X compares to the other two OS as I haven't seen that answered here to date.
Focus on the virtual-memory and os-x tags for the best results in your searching:
By the sheer number of "inactive memory" questions, you can focus on the part of OS X's memory management that is most puzzling to people and hence gathers the most questions here looking for explanations.