## We are somewhat amused

As the person who coined “JASE,” I’m amused.

Speaking of, I was invited into a game of Newton last night and after 10 minutes of point salady rules I bailed.

Open Thread — Newton: JASE or not?

Also — if any of my more mathematical readers has an explination as to how this works (note — I am assuming it does), that would be lovely.

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Not a proof (too lazy), but I think what is happening:

Given two points in the plane, create the 2 x 2 matrix from the coordinates (vectors). Its determinant (up to sign) is the area of the parallelogram. Half that is the area of the triangle formed by those two points and the origin. Now, continue around the polygon, each pair given a triangle area. I would think that completing the cycle causes cancellation of the areas outside the polygon.

A 2 x 2 determinate is just the product of one diagonal minus the product of the others. So the table just records that information.

Joe J. RushananJanuary 15, 2019 at 6:47 pm

I like Newton. It’s a JASE but a good one.

AnonymousJanuary 15, 2019 at 7:30 pm

Isn’t it a special case of Green’s Theorem?

Green’s Theorem can be used to compute the area of a planar region (under suitable conditions) as half of the integral of -y dx + x dy around the perimeter of the region.

Eric BrosiusJanuary 16, 2019 at 5:42 am

Yes, and looking at Green’s Theorem on Wikipedia led me to something new to me called the “Shoelace formula” which is has early connections to mathematicians Meister and Gauss. https://en.wikipedia.org/wiki/Shoelace_formula

bwingraveJanuary 16, 2019 at 8:57 am

Thanks. The proof on the Wiki page is precisely what I was too lazy to write out. Have to remember the name. I never think of Green’s Theorem (as a discrete mathematician, it rarely comes up).

Joe J. RushananJanuary 16, 2019 at 6:35 pm

I agree with Anonymous. Given its tenuous theming and almost complete lack of player interaction, I’d have to say that Newton is JASE. But my last play of it was probably my favorite session of a new game since Essen, so clearly its JASEness doesn’t bother me.

huzonfirstJanuary 16, 2019 at 9:19 pm

I’m confused, Larry! What does that have to do with Green’s Theorem?

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Eric BrosiusJanuary 17, 2019 at 10:06 am

I never play with Green. Only with Yellow!

huzonfirstJanuary 18, 2019 at 11:19 am