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# 261

Batman Teaches Math - June 28, 2010
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Not really funny today but hopefully educational if you don't know Pick's Theorem.

I was talking to a friend yesterday about how we wanted to do some educational comics, and he said "Wait, are they gonna be funny?" It's hard to do both lol especially since people read webcomics to be entertained (usually) but I enjoyed this one for what it's worth.

Batman Teaches Math http://youtu.be/SmfE157qElw

dun na na na na na BATHMAN!, no wait sound stupids, um... maybe
dun na na na na na MATMAN! no that doesn't work either, I guess that's why Batman does math so rarely

dun na na na na na na na BATMATH.

(I went to the same high school as the guy who wrote that theme. I just like to say that.)

I get 203...

I get 180 + 90/2 - 1 = 224, but I had a hard time determining what were boundary points sometimes when the edge went between points.

Yeah, but I get 39 for the B/2 which is less than your boundary points (albeit, I only counted half of them, and used the symmetry of the polygon to know the rest).

(and it posted down there because I forgot a field, oops)

203 still seems pretty low. I recounted the border and got 41 for B/2. But then I also recounted the internal points and got 183 which is more than I had before. So that's 223, one less than I got the first time. I also only counted the ones on the left half in both cases, multiplied by two and then added the center vertical line.

Ok, re-did it :)
I get I = 87 * 2 (edges) + 11 = 185 + 39 - 1 = 223 so yeah, I concur now, not sure how I got 203 unless it was a mistype.

"Not really funny today but hopefully educational if you don't know Pick's Theorem"

Batman should/could/would totally say that line

I just taught a lesson this theorem a couple of weeks ago in a summer class I am taking. Talk about funny.

Does anybody ever wonder if Georg Pick was at a long, uninteresting math conference or just sitting in his office bored one day and he started doodling on a sheet of lattice paper and as he worked out of each shape he found, he made the correlation between the interior and the boundary points.

well supposedly a bunch of the laws of probability were discovered by a war prisoner who spent 5 years in cell flipping a coin over and over again (i'd appreciated if any one could tell if thats really true or just an urban legend)

Yes, that is true. It was twoface.

from the Wiki on Blasie Pascal "In 1654, prompted by a friend interested in gambling problems, he corresponded with Fermat on the subject, and from that collaboration was born the mathematical theory of probabilities. The friend was the Chevalier de Méré, and the specific problem was that of two players who want to finish a game early and, given the current circumstances of the game, want to divide the stakes fairly, based on the chance each has of winning the game from that point. From this discussion, the notion of expected value was introduced."

apparently schwarzchild worked out the singularity solutions for gtr while he lay dying in a field hospital of a skin disease (sauce: life of the cosmos lee smolin)

Yeah, but I get 39 for the B/2 which is less than your boundary points (albeit, I only counted half of them, and used the symmetry of the polygon to know the rest.

Only works on a square lattice. What if you use a triangular lattice?

(The answer and the proof are left as an exercise for the student...)

I got 224.

You forgot the (-1)

bmonk, you can modify Picks theorem to fit your shape. One of the theorems we did for my research project arose out of Picks theorem on a polytope with the convex hull {0,ell e_1, 2ell e_2, 3ell e_3} where ell is an integer. The integer lattice points in such configuration was P=(ell + 1)^3.

You've ruined me!
I was trying to find this theorem and i could only remember that it was called the batman theorem

This theorem is used way too much as a time-waster if you don't know it.

I know it, but finding it in the first place is probably the hardest part.

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