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• So say you're ruining yet another batch of cookies because, who knows, too much butter?

• not enough flour? didn't chill the dough long enough?

• Could be anything, there's too many variables and this is why baking from scratch is hard

• and I'll stick with mathematics thank you very much.

• But I do know one delicious recipe that's hard to get wrong.

• And by the way this video is in VR180 so use a headset or look around by moving your phone

• or dragging the video because today we're making Monkeybread.

• in the 1970s to take advantage of pre-prepared refrigerated biscuit dough for an easy-to-make

• snack suitable for groups of children and/or adults with no plates or utensils necessary.

• I'll be making the dough bits round to better simulate properties of Voronoi diagrams, but

• the basic idea is that each ball of dough is like a little cell coated in cinnamon sugar,

• and large amounts of brown sugar butter.

• Lots and lots of butter.

• In the oven all these spheres of dough will expand and develop facets as they smoosh into

• each other, so they're more polygonal and no longer spheres.

• What kind of shapes would you expect the cells to form?

• Let's go back to my batch of cookie, and I'll use icing to draw the lines where the

• It looks a lot like a Voronoi diagram, which is a kind of diagram where you start with

• a bunch of points, or, cookiedough blobs, and then it's as if each point spreads out

• until it gets all the area that's close to it, or at least, closer to it than to any

• other point.

• If you started with points organized into a very efficient cookie packing like this,

• then the Voronoi diagram would look like a bunch of hexagons, except on the edges where

• technically the cell includes the slice of space going infinitely off the cookie sheet,

• not that I have enough dough for infinitely large cookies, which just marks another place

• where mathematical theory is better than the realities of baking.

• But for our more randomly placed cookie blob sheet, the Voronoi cells are irregular polygons,

• and these look pretty typical for 2D Voronoi cells.

• But what about 3D Voronoi cells?

• There's many theoretically perfect way to pack spheres together where they'd expand

• into perfectly fitting cubes or rhombic dodecahedra or other fun shapes, but when you toss all

• the dough balls randomly into a bundt pan we'll get more typical random Voronoi cells.

• I mean it's not quite mathematically Voronoi-y because of how dough works and physics but

• it's similar enough that our Monkeybread bits will have that distinctive Voronoi flavor.

• The Bundt pan, by the way, not only makes genus 0 baked goods into genus 1 baked goods,

• but the hole in the middle adds surface area, which is not only great for having lots of

• glaze or crust but essential for Monkeybread in particular so that more cells are on the

• surface.

• You eat it by just grabbing a cell and pulling it apart from the bread, and the toroidal

• shape means you can pick at it from all sides, including inside.

• Bundt pans also provide areas of both negative and positive curvature to observe, which helps

• better simulate a comparison to the formation of epithelial cells, hence the Scutoid connection

• (more about scutoids next time).

• Altogether, Monkeybread is quite the mathematical snack.

So say you're ruining yet another batch of cookies because, who knows, too much butter?

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B2 dough butter genus bread diagram baked