Cookie Shapes!

so you're mean you're finally done with traveling in conferences for the season finally moved into your new office finally finished and submitted a paper involving four-dimensional symmetry groups and monkeys and now finally you get to rest you've got a whole free saturday ahead of you you're gonna take a break from math do anything but math yes you're going to hang out with your friends and bake so you go to your friend gwen fisher's house who makes her living making mathematical beadwork like this and designing instructions and exploring the theory but cookies aren't beadwork so you're probably safe from math there then there's ruth of sweet spy ruth who knows how to make a good sturdy shortbread and even though she's well versed in math there should be no problems because baking and only baking is the focus of the afternoon also andrea huxley is going to join and sure she's a software developer who creates mathematical art in her spare time but come on we're just speaking cookies what could go wrong wait what's that two-dimensional ruler doing there is that a square root of two rhombus no i'm sure it's just because omnom rhombus i mean even if you're trying to relax and avoid math cookies still need to have some shape right um as long as we have these extra little rhombus cutouts might as well stick them together but that's when disaster strikes our natural senses of symmetry color patterns infinite tilings on the euclidean plane we have to have color symmetry no gwen why why do you torture us so no living thing deserves such torment oh there we go nice save andrea tension resolved we extend our tiling just a little bit enjoying how they look like cubes in perspective finishing with a nice symmetric section i got to pay gwen back for the color pattern thing by focusing on this fingernail mark i'm focusing on that fingernail mark right now and after baking the cookie we all got to torment walter the walter dog by eating our delicious shortbread ruining symmetry good batter what was the joke you had short gray short breaks short braids oh yeah right let's make a short break braids they're short braids shirts um short braids well maybe we'll just do one little short braid as a test i mean anyone with a passing interest in mathematics and symmetry probably can't help liking braids i've done stuff with them and so has andrea and ooh gwen has some cool designs involving them on her beadwork table right now and wait andrea happens to have an unusual five strand braid she made us a necklace in her bag well we definitely need to learn from her how that works oh and of course you can't talk about braids without talking about knots and links and gwen wrote a paper involving those and has made a bunch of cool ones and look sections of infinite polyhedra must resist we're only going to make a nice simple linked cookie with obligatory discussion of the bruneian property of course which normal braids have as well as the bromine rings care if something's vernian or not that was useful well now i'm seeing how it's useful i mean right because this says i always have the blue on top of the yellow so i don't have to fiddle with that and then i can just i don't know that this is going to look good when i'm done but i'm not going to let that stop me from it'll still doing it'll still taste blue yellow and pink they're the same kind of braid and yeah but one of them got to be a ring the other one's jealous no this is this is a branch of the infinite ring look what do you think it looks delicious what do you think he's not going to appreciate the art he appreciates that that's delicious rooney and cookie so the yellow is completely on top of the red the red is completely on top of the blue and the blue is completely on top of the yellow which completely just is very counter-intuitive and if we flipped it over it would still be broonian and walter would still want to eat it no back to simple shapes like hexagons i feel like they're much more foolproof than our rhombic dodecahedron or trichometer idea like rhombuses hexagons also tile the plane though an aperiodic tiling would be much more fun how about the classic kites and darts we can make our own cookie cutters out of cardstock using the correct proportions and then tile them following the matching rules so many kites so many darts where am i i like to eat these kinds of cookies aperiodically after an aperiodic tiling the simple hexagonal tiling would be so boring so the only reasonable thing to do is glue together the cookies with chocolatish stuff in 3d to form a truncated octahedron i mean for any regular polyhedron that is made out of triangles if you truncate it those triangles turn into hexagons and we made this octahedral jig that brings four hexagons together at the correct angles but we're not sure if our two halves are going to go together yeah no there's a theorem that doesn't quite apply here it needs to be like differentiable continuously differentiable it's rigid enough that you can get pick it up i would drop it i wouldn't try and squeeze it you could play fetch with walter but you wouldn't bring it back since the truncated octahedron actually worked andrea starts work on a truncated icosahedron while i make a cardstock jig for holding together cookies at the correct angle for a rhombic dodecahedron while the edible glue hardens yes no wonder we made a square root 2 rhombus because square root 2 is a diagonal of the square which is what you need for this octahedral symmetric polyhedron though i suppose if we made golden rhombuses we could have gone for a rhombic tricontahedron but anyway the rhombic dodecahedron is working and then yeah no problem don't drop it inside i know there's a reason oh oh no beautiful quick before anything changes for some reason reminds me of stained glass yeah it's the play-doh coloring i'm just i have tried making polyhedra out of stained glass and it's again the thing where it doesn't quite fit you just fill in the water this is going to taste a lot better than the solder did it's also thinner than pure chocolate if you use regular chocolate would be a lot thicker this is gonna work i think that worked we're done nope obviously we need to make every shape possible so we're never really gonna be done somehow andrea comes up with jigs that work for the truncated dicosahedron a familiar shape sometimes known as a soccer ball or buckyball except this one is for eating and not for kicking though it is made out of molecules and meanwhile gwen is making an army of tiny tetrahedra because sometimes she makes a pinsky tetrahedron out of beads or baseball bats so of course she has no trouble bending cookies to her mathematical will they're right on top she's just gonna sit right there on top oh that looks very well that actually worked way better than i thought it was going to serpents cookies [Music] that is so beautiful that's the most delicious soccer ball i've ever seen but in the end we accidentally left walter alone in the room for one minute and he ate them all and does not regret it one bit

Channel: Vihart

Views: 1,300,252

Keywords: cookies, baking, braids, knots, polyhedra, tilings, aperiodic, octahedron, icosahedron, truncated, geometry, rhombus, math, mathematical, food

Id: _n1126GoxbU

Length: 7min 5sec (425 seconds)

Published: Mon Mar 03 2014