A analysis of brownie division algorithims

[nminusone]

Or "What to say when your kid asks why they need to learn algebra"

The other day geekchick and I had a pan of brownies. She prefers edge pieces and I prefer middle pieces, but after cutting it up in a fairly typical way, (3x6 or so) I realized there were a lot more edge pieces (14 out of 18 for 3x6). Driven by my love of math and chocolate, I set out to

Comments

[boadiccea]

Ow! Heady hurty with the maths.

I'd just eat the damn brownie already. Don't care which kind. ;)

[geekchick]

You should've heard the complaining when I cut into the brownies without having done the appropriate math first! ;)

[boadiccea]

LOL!

[brian1789]

It was all my fault! Although it made for a yummy breakfast, this morning.

[geekchick]

My calculations imply that the number of brownie middle pieces available at this moment either equals or is rapidly approaching zero, is that correct? ;)

[nminusone]

It reached zero last night. I ate an edge piece or 2, then in desperation sliced an edge piece lengthwise to make a new middle piece. Unfortunately this made a long, skinny middle piece, which is by definition brownie abomination. So I had to eat it, and never speak of it again.

And then I had a dream about waiting in line for like 2 hours to buy some brownies. Once I finally got near the head of the line the guy in front of me somehow got me to shove like a quarter pan of brownies into my mouth at once. I wath tafkin life thiff!

[brian1789]

Forgot to ask... does Gateway eat brownies, and does he prefer edges or middles? That might affect the optimal balance numbers.

[geekchick]

He doesn't get chocolate. Even if I wanted to give it to him, he seems uninterested in brownies once he gives it the obligatory sniff.

[geminigirl]

Round. aquariumgirl's husband, after hearing about my feeling on brownies (I'm with you on the middle thing, no crusty edges for me) has come up with a way to make "edgeless brownies" which satisfy the desire for all soft, squishy edges.

[nminusone]

I've gotta see that, do you have a link?

I was thinking that people who like edge pieces are in luck. They could make a brownie pan based on the Hilbert Curve, which would give them lots more edge pieces.

[geekchick]

http://www.bakersedge.com/

[geminigirl]

I don't have a link, but I know it involves a round cake pan and Magic Cake Strips.

[dcseain]

Fair enough, but one could just as easily trim some centre from edge bits, no? I, as an edge-preferer, would be fine with that.

[nminusone]

I'm not sure if it's what you have in mind, but I briefly mentioned one approach that sounds like it might be:

... cut a rectangle in the middle which is sqrt(2)*X by sqrt(2)*Y units. This works, but makes it harder (impossible?) to get equally-sized pieces.

Is that basically the same thing?

[dcseain]

Similar, i was envisioning squares surrounded by rectangles. Some would argue that would be sacrilige, as the double rectangles around the edge, ignoring corners, would be shaped wrong for some who believe all must be equal. Basically, halve the side edge bits from the 1st round of cutting.

[nminusone]

Ah ok. In my post I specified a preference (not requirement) for all equal sized pieces, but that was mainly to make the math more fun. I don't personally care that much, since I'm very likely to sub-slice pieces depending on how hungry I am at the moment.