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 [quote="Griffin"]Joe has a grid that consists of dots in rows and columns, place one unit apart. By connecting these dots, Joe can create a variety of polygons. In creating a particular polygon, Joe's pencil goes through [i]n[/i] dots. The polygon completely encloses [i]m[/i] dots. In terms of [i]n[/i] and [i]m[/i], what is the area of the polygon? Proof? [This message has been edited by Griffin (edited 02-25-2002 04:20 PM).][/quote]
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tigg
Posted: Tue Feb 26, 2002 1:39 pm    Post subject: 1

Glad to be a help, Griffin.
And nice job too, if you discovered it on your own.

You must like playing around with that stuff. Reminds me of me when I was in high school. I remember I discovered Pascal's triangle when I was in seventh grade, and I was all proud of myself. Some time later I was disappointed to find that Pascal discovered it several hundred years before. ("Hey- that's not Pascal's triangle. That's my triangle!") Oh well.

I'm 33 now and still think math is cool. Some things don't change.
Griffin
Posted: Tue Feb 26, 2002 3:10 am    Post subject: 0

Mith - When I come up with a good puzzle, I post it.

Anyway, thankyou tigg for the link. I had a feeling when I stumbled across this relation that it was probably a famous theorem of some sort.
tigg
Posted: Mon Feb 25, 2002 10:35 pm    Post subject: -1

Pick's Theorem
mith
Posted: Mon Feb 25, 2002 10:32 pm    Post subject: -2

Griffin, you should post more. I always enjoy your puzzles.
mith
Posted: Mon Feb 25, 2002 10:24 pm    Post subject: -3

maybe some sort of induction, but there's no way you are getting me to spend time writing it up

time for class
quercitron
Posted: Mon Feb 25, 2002 10:21 pm    Post subject: -4

yeah, mith has the same answer I do
quercitron
Posted: Mon Feb 25, 2002 10:20 pm    Post subject: -5

How about (n/2 + m - 1)

The proof is tricky though.
mith
Posted: Mon Feb 25, 2002 10:20 pm    Post subject: -6

(n+2m-2)/2 seems to work. Don't have a clue how to prove it though.
dethwing
Posted: Mon Feb 25, 2002 10:09 pm    Post subject: -7

i have no idea, but i'm wondering if he draws in straight lines, or can he do curves? Or does it not matter?
Griffin
Posted: Mon Feb 25, 2002 9:19 pm    Post subject: -8

Joe has a grid that consists of dots in rows and columns, place one unit apart. By connecting these dots, Joe can create a variety of polygons. In creating a particular polygon, Joe's pencil goes through n dots. The polygon completely encloses m dots. In terms of n and m, what is the area of the polygon? Proof?

[This message has been edited by Griffin (edited 02-25-2002 04:20 PM).]