Picture this! is a very cool interactive thingy, made by Jason Davies, intended to get students (or anyone, really) thinking about some interesting math. Go play around with it and see if you can answer any of the listed questions (or any other questions you might come up with yourself). It turns out to be quite intimately related to something I’ve written about before—but I won’t spoil it by saying what (at least, not yet =).
The Math Less Traveled 
It seems to be limited to 200, making spirals using, say, 377 and 233 impossible. I discovered this when trying 355 and 113.
Yes, it seems you’re right. That is unfortunate.
OK, I’ve made a hacked version with a limit of 10000 which you can find here:
http://www.cis.upenn.edu/~byorgey/picture-this/picture-this.html
Of course once you get too big you can’t really see the smallest squares.
377/233 is a nice one. =)
So is 239/169, in a different way. I had hopes for 1264/465, but it got too small too fast. It looked better cut down to 799/465.
Neat! Also neat is the website that page is made for: http://nrich.maths.org/
There’s good math there for K-16.