Vi Hart, the Internet's favorite manic vlogging mathematician, has released a new video in which she teams up with math artists Andrea Hawksley and Gwen Fisher, and Gwen's sister Ruth of Sweets by Ruth. The four of them bake satisfyingly precise and geometric gingerbread polygons, then build up a variety of astounding three dimensional forms by piecing them together with icing. The video is both hunger-inspiring and brain-inspiring, and is likely to be the best thing you watch this week.
Tim sends us, "A way of encoding binary numbers into playing cards that I thought up. It usually allows many more bits than there are cards. The method can also store binary encoded letters of the English alphabet at less than 2 cards per letter on average, and has a theoretical ability to do less than 1 card per letter."
Tim isn't sure if his method of data-compression is novel or not, and neither am I. If you know of related work, please add it in the comments.
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The "squared" in Pi(R)^2 means that the area of a pizza grows
exponentially polynomially in relation to its diameter. As an interactive graph on Planet Money demonstrates, pizza places generally underprice their bigger pies relative to the amount of food contained in each. This is probably because energy and labor inputs account for the largest slice of the pizza-baking ahem pie, and ingredients are way down on the balance-sheet. Whatever the reason, if you're interested in getting more food for less money, larger pies are almost always a substantially better deal.
74,476 Reasons You Should Always Get The Bigger Pizza [Quoctrung Bui/Planet Money]
Elysium Woodworks's Etsy store is full of gorgeous, laser-etched, math- and science-themed cutting boards. They're about $35, made from bamboo, and take 5-6 weeks to fabricate.
(via Wil Wheaton)
The latest installment in Randall Munroe's XKCD "What If?" series is called Paint the Earth and it is amazing. One of Munroe's readers wanted to know "Has humanity produced enough paint to cover the entire land area of the Earth?" and Munroe uses this as a springboard for explaining Fermi estimation, a powerful, counter-intuitive tool that has applications in many fields.
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In the Boing Boing Flickr Pool the fractal-obsessed Fdecomite posts the latest iteration in a series of experiments with tessellated, Escher cookie-cutters. Bake-time expansion creates irregularities that lead to a chewy (literally) series of interlock-imperfections, which give old MC's classic a bio-organic air that rather invigorates it.
You can 3D print interlocking lizard cutters with a free model from Thingiverse. Fdecomite, if you're reading this, please post in the comments with a link to the cookie cutters you used here!
Update: From the comments, Fdecomite writes, "Hi, those are cookie cutters I made from aluminium foil.I also made some 3D printed Escher cookie cutters you can find in my Shapeways shop.
Escher Cookie Cutters - The Sequel
In Frequency, the latest XKCD cartoon, Randall Munroe has assembled a grid of animated GIFs representing various events in the universe, each keyed to blink in the frequency in which they occur in reality. As with the best of Munroe's work, it's a mix of the trenchant and the silly, and the juxtapositions are smart and provocative. There's real genius in putting "50,000 plastic bottles are produced" and "50,000 plastic bottles are recycled" next to each other, the former blinking much more often than the latter -- but the best part is "A Sagittarius named Amelia drinks a soda," just above them, mixing up the alarming and the humorous.
The other juxtapositions are just as delicious -- one birth/one death; China builds a car/Japan builds a car/Germany builds a car/US builds a car/someone else builds a car; someone buys "To Kill a Mockingbird"/someone's cat kills a mockingbird -- and so on. This being XKCD, you can be sure that Munroe has an absurdly well-thought-through process for establishing and documenting his numbers, too.
The tool-tip notes that he wanted to include pitch-drops in the chart, but "it turns out the gif format has some issues with decade-long loops."
Here's a brain-meltingly cool proof of the bizarre mathematical truth that the sum of all positive integers (1 + 2 + 3 + 4 + 5....) is -1/12. This is not only provably true, it's also foundational to certain testable elements of physics. In other words: not just a logical curiosity, but also the bedrock of real-world, useful stuff.
ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12
In the end of year episode (MP3) of the BBC's More or Less stats podcast, Tim Harford talks to a variety of interesting people about their "number of the year," with fascinating results.
But the crowning glory of the episode is Helen Arney's magnificent musical tribute to Mersenne 48, the largest Mersenne Prime ever calculated, which came to light in 2013. (Arney herself is going out on tour of the UK, for the delightfully named Full Frontal Nerdity tour)
I still don't
understand it, obviously, but "the sierpinski triangle page to end most sierpinski triangle pages
" has some sweet
fractals on it! The one above clearly depicts the optimal pattern of berms and defenses to be constructed
around the Waste Isolation Pilot Project in New Mexico
, lest future generations wander too close to its irradiant embrace. [Oftenpaper]
Jeff Moser's "A Stick Figure Guide to the Advanced Encryption Standard (AES)" beautifully presents the history, context, and workings of one of the most important pieces of math in the modern world. AES is at the core of virtually every privacy technology you use, and it holds the promise of building an NSA-proof, unsnoopable Internet.
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The Boy Who Loved Math: The Improbable Life of Paul Erdős is a beautifully written, beautifully illustrated kids' biography of Paul Erdős, the fantastically prolific itinerant mathematician who published more papers than any other mathematician in history.
Boy is written by Deborah Heiligman, with illustrations by LeUyen Pham, and the pair really worked to weave numbers and mathematics through the text, with lively, fun illustrations of a young Erdős learning about negative numbers, becoming obsessed with prime numbers and leading his high-school chums on a mathematical tour of Budapest. They also go to great lengths to capture the upside and downside of Erdős's legendary eccentricity -- his inability to fend for himself and his helplessness when it came to everyday tasks like cooking and doing laundry; his amazing generosity and brilliance and empathy in his working and personal life.
Ultimately, this is a book that celebrates the idea of following your weird, wooing the muse of the odd, and playing to your strengths rather than agonizing over your weaknesses. It's an inspiring and sweet tale of one of humanity's greatest mathematicians, and a parable about the magic of passion and obsession.
My daughter, who is five, demanded that I read it to her three times in a row, over three bedtimes, which is always a vote of confidence.
The Boy Who Loved Math: The Improbable Life of Paul Erdos
The illustrations and layouts in Boy are fabulous, and Roaring Brook was kind enough to supply us with three spreads (click each to embiggen):
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Business Insider's Walter Hickey did the math on Monopoly, calculating the most frequently landed-up squares (taking into account dice probability, Go To Jail events, and Community Chest/Chance cards) and conceived of a supposedly optimal strategy for buying and building upon property. I still hate Monopoly, but I suspect that this would make it less boring (for a while, at least).
How To Use Math To Crush Your Friends At Monopoly Like You've Never Done Before
Samuel sez, "ACMEScience.com is the home of many math and science podcasts, including the mathematical story series Relatively Prime. It has been run for the past four years in the spare time between jobs, and with cheap or second-hand equipment. Now ACMEScience wants to change its lot and turn itself into a full-time operation for the next year, and it plans to do this through its new Kickstarter project. If the project is funded it would mean new episodes of Relatively Prime, as well as at least one episode a week of the interview shows ACMEScience News Now and Strongly Connected Components."
I'm a great fan of Relatively Prime -- they're the ones who did the great piece on Chinook, the champion checkers-playing computer.