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Math Food for Pi Approximation Day

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July 22 is Pi Approximation Day because pi's fractional approximation is 22/7. To celebrate, here are some math foods Miss C rounded up last year.

Food is often used to illustrate shapes, and recipes are used to introduce children to measurement and proportions. But if you really care about your mathematics -and your food- there are ways to take the marriage of math and food to the next level!

Pi Pie

The simplest way to incorporate math into food is to bake a Pi Pie. Meg made this lovely Pi Pie to celebrate Pi Day in 2004. It's a normal fruit pie with the pi symbol carved into the top crust. Then the numerals of pi were cut from pie crust and added to the rim of the pie. Yummy!

Möbius Strip Bagel

George Hart, who I've run across before, has turned breakfast into a puzzle with a bagel that has been sliced into two halves that are linked together! The secret is that the cut itself is a two-twist Möbius strip. If you can't quite visualize that, there are explicit instructions for this project. This is sure to impress your mother-in-law, one way or another.

Sierpinski Carpet Cookies

Sierpinski Cookies-11

Lenore at Evil Mad Scientist Laboratories made cookies in the fractal pattern of the Sierpinski Carpet. These are made with butter cookie dough, a portion of which was colored with delicious cocoa powder. The dough is shaped, stacked, and stretched, then stacked and stretched again, and when the fractal is at your limit, the dough is sliced to make cookies. Illustrated instructions are included at the laboratory link.

Fractal Snowflake Cupcakes - 24

Lenore also gave us instructions for making this beautiful fractal cupcake in the Koch Snowflake pattern. This uses the same method of stacking and rolling out iterations of fondant, this time tinted blue or left white.

Menger Sponge Gingerbread House

This fractal gingerbread house resembles the Sierpinski carpet a bit, but a Menger sponge contains holes rather than cocoa cookie dough.

A Menger sponge is a 3D fractal that starts with a cube. In each iteration the surface of each cube is divided into 9 sections and the middle section is pushed out.

In the next iteration, you look at the smaller subcubes of the original cube and repeat the same process.

in the picture below you can see the same process. With this gingerbread fractal we'll be making a level 2 Menger sponge and using decoration to make it look like a level 3.

The actual making of the gingerbread is easier than the explanation of the fractal. Understanding fractals can be plenty intuitive when you've seen them built.

Sierpinski Hamantaschen

Hamantaschen is a Jewish holiday pastry that comes in a triangle shape filled with prunes, poppy seeds, or other sweet filling. Deborah Gardner took her family's traditional recipe and made "Sierpinskitaschen," or Sierpinski Hamantaschen. This is not pieced together like the cookies, but it begins with a large pastry which is then subdivided as may times as you can.

Apple Chain

Marius van Voorden enjoys food sculpting. He was inspired by Neil Fraser's soap carvings of links from a single solid, and decided to do the same with apples. You won't find step-by-step instructions, but I suppose it's about as difficult as cutting the bagel above.

Hyperbolic Dried Fruit

Vi Hart has a gift for making mathematics into something enjoyable, even if you can't keep up with the math. She wrote on The Hyperbolic Nature of Dried Fruit Slices because she found it strange that when sliced fruit dried, it not only shrunk but changed shape completely, in a predictable manner. For example, as it dries, an apple slice curls up into a hyperbolic plane! Hart did some experiments and found that it made no difference whether she cut the apple vertically or horizontally, or whether the peel was removed. The same effect can be seen in potato chips, which are fried instead of dried. See Hart's other posts on slicing apples into mathematical shapes.

Cutting the Cheese

High school senior Luyi does many things with geometric shapes. Recently she cut the cheese into a multitude of shapes. A solid cube of cheese became a hexagonal prism, then with some intricate-but-understandable steps, Luyi was left with "one funky-shaped polyhedron and six small congruent tetrahedra." Then the fun starts, as you can find the volume of your irregular polygon by calculating the volume of the shapes you cut off! Or, you could just get the crackers out and finish off this experiment.

Also check out Luyi's Dark and white chocolate Sierpinski triangle brownies. Now every time I come across a Sierpinski triangle, I will start to feel hungry.

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iStock // Ekaterina Minaeva
Man Buys Two Metric Tons of LEGO Bricks; Sorts Them Via Machine Learning
May 21, 2017
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iStock // Ekaterina Minaeva

Jacques Mattheij made a small, but awesome, mistake. He went on eBay one evening and bid on a bunch of bulk LEGO brick auctions, then went to sleep. Upon waking, he discovered that he was the high bidder on many, and was now the proud owner of two tons of LEGO bricks. (This is about 4400 pounds.) He wrote, "[L]esson 1: if you win almost all bids you are bidding too high."

Mattheij had noticed that bulk, unsorted bricks sell for something like €10/kilogram, whereas sets are roughly €40/kg and rare parts go for up to €100/kg. Much of the value of the bricks is in their sorting. If he could reduce the entropy of these bins of unsorted bricks, he could make a tidy profit. While many people do this work by hand, the problem is enormous—just the kind of challenge for a computer. Mattheij writes:

There are 38000+ shapes and there are 100+ possible shades of color (you can roughly tell how old someone is by asking them what lego colors they remember from their youth).

In the following months, Mattheij built a proof-of-concept sorting system using, of course, LEGO. He broke the problem down into a series of sub-problems (including "feeding LEGO reliably from a hopper is surprisingly hard," one of those facts of nature that will stymie even the best system design). After tinkering with the prototype at length, he expanded the system to a surprisingly complex system of conveyer belts (powered by a home treadmill), various pieces of cabinetry, and "copious quantities of crazy glue."

Here's a video showing the current system running at low speed:

The key part of the system was running the bricks past a camera paired with a computer running a neural net-based image classifier. That allows the computer (when sufficiently trained on brick images) to recognize bricks and thus categorize them by color, shape, or other parameters. Remember that as bricks pass by, they can be in any orientation, can be dirty, can even be stuck to other pieces. So having a flexible software system is key to recognizing—in a fraction of a second—what a given brick is, in order to sort it out. When a match is found, a jet of compressed air pops the piece off the conveyer belt and into a waiting bin.

After much experimentation, Mattheij rewrote the software (several times in fact) to accomplish a variety of basic tasks. At its core, the system takes images from a webcam and feeds them to a neural network to do the classification. Of course, the neural net needs to be "trained" by showing it lots of images, and telling it what those images represent. Mattheij's breakthrough was allowing the machine to effectively train itself, with guidance: Running pieces through allows the system to take its own photos, make a guess, and build on that guess. As long as Mattheij corrects the incorrect guesses, he ends up with a decent (and self-reinforcing) corpus of training data. As the machine continues running, it can rack up more training, allowing it to recognize a broad variety of pieces on the fly.

Here's another video, focusing on how the pieces move on conveyer belts (running at slow speed so puny humans can follow). You can also see the air jets in action:

In an email interview, Mattheij told Mental Floss that the system currently sorts LEGO bricks into more than 50 categories. It can also be run in a color-sorting mode to bin the parts across 12 color groups. (Thus at present you'd likely do a two-pass sort on the bricks: once for shape, then a separate pass for color.) He continues to refine the system, with a focus on making its recognition abilities faster. At some point down the line, he plans to make the software portion open source. You're on your own as far as building conveyer belts, bins, and so forth.

Check out Mattheij's writeup in two parts for more information. It starts with an overview of the story, followed up with a deep dive on the software. He's also tweeting about the project (among other things). And if you look around a bit, you'll find bulk LEGO brick auctions online—it's definitely a thing!

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Nick Briggs/Comic Relief
What Happened to Jamie and Aurelia From Love Actually?
May 26, 2017
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Nick Briggs/Comic Relief

Fans of the romantic-comedy Love Actually recently got a bonus reunion in the form of Red Nose Day Actually, a short charity special that gave audiences a peek at where their favorite characters ended up almost 15 years later.

One of the most improbable pairings from the original film was between Jamie (Colin Firth) and Aurelia (Lúcia Moniz), who fell in love despite almost no shared vocabulary. Jamie is English, and Aurelia is Portuguese, and they know just enough of each other’s native tongues for Jamie to propose and Aurelia to accept.

A decade and a half on, they have both improved their knowledge of each other’s languages—if not perfectly, in Jamie’s case. But apparently, their love is much stronger than his grasp on Portuguese grammar, because they’ve got three bilingual kids and another on the way. (And still enjoy having important romantic moments in the car.)

In 2015, Love Actually script editor Emma Freud revealed via Twitter what happened between Karen and Harry (Emma Thompson and Alan Rickman, who passed away last year). Most of the other couples get happy endings in the short—even if Hugh Grant's character hasn't gotten any better at dancing.

[h/t TV Guide]