Hey, after all of my assignments (not only 236 but 2 other classes as well) I can finally get back to my slog (Hence why it took till today). I think today will be my last update tomorrow is the day the slog's are due.
Question: SpaceSplicing.
Anyway. Here is a chart that I made up on photoshop after I cut up a square multiple times.
Now I guess the goal is to find a pattern for this.
I kind of figured out a pattern...but I am not really sure at how to get a proof out of this. Every time the number of straight lines increases (Let n = Number of straight lines) then the number of max number of regions (let m = max number of regions) increases by the value of the difference of previous n values max number of regions plus one.
Below I have posted my rough work on getting a function that works for this problem. I used photoshop (since I tend to make a lot of changes during my rough work).
To make it more readable, I will probably post this up re-written on Latex tomorrow. For a full proof this function would need unwinding, to get a closed form. Then prove the closed form using induction.
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