Gonzalo Ciruelos set out to discover which country was the roundest in shape.

We can define roundness in many ways. For example, as you may know, the circle is the shape that given a fixed perimeter maximizes the area. This definition has many problems. One of the problems is that countries generally have chaotic perimeters (also known as borders), so they tend to be much longer than they seem to be.

For that reason, we have to define roundness some other way. We represent countries as a plane region, i.e., a compact set C⊂R2C⊂R2. I will define its roundness as

That's about where I tune out! Turns out the answer is Sierra Leone. Click through to see lots of mathy thingies on the screen, the runners-up, the *least* round countries, and the source code. Read the rest

“Enjoy the parabolic envelopes that form while those bright, sparkling, parabolic curves are etched into the sky tonight.”

Thinkgeek's Pi Fleece keeps you warm and irrational with the first 413 digits of Pi in machine-washable fleece, measuring 45"x64".
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Samuel Hansen's fantastic math podcast is everything a technical program should be deep but accessible, thoughtful but funny, and free for all; the new season is on Kickstarter for a few more hours! I put in $35.
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Why does a flat pizza slice flop over unless you bend it into a curve? Thank Gaussian curvature, the 19th century mathematical principle that underpins everything from corrugated cardboard to eggshells to Pringles chips.
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Brilliant, high-speed math vlogger Vi Hart has revisited the topic of the sizes of infinities.
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India's Zetatrek citizen science initiative is online workshop starting on 19th July, where science and math hobbyists from all over the world are invited to study the original manuscripts of Sir Isaac Newton.
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Just in time for you to get the most out of "The Fault in Our Stars," the incomparable, fast-talking mathblogger Vi Hart's latest video is a sparkling-clear explanation of one of my favorite math-ideas: the relative size of different infinities. If that's not enough for you, have a listen to this episode of the Math for Primates podcast.

Proof some infinities are bigger than other infinities
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Chris Mooney of the Inquiring Minds podcast interviewed Jordan Ellenberg about his book How Not to Be Wrong: The Power of Mathematical Thinking, and in a fascinating accompanying post, Mooney investigates whether mathematics are "liberal." His argument is that liberal thought is characterized by "wishy washy" uncertainty and that math professors tend to vote left:
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Brooke Powers assigned her middle-school math class a probability exercise with no single correct answer and was monumentally frustrated by her kids' inability to accept the idea of a problem without a canonical solution. After a long and productive wrangle with her kids about how critical thinking works and why divergent problem-solving is much more important than mechanically calculating an answer that you could just get out of a computer, she salvaged the exercise and made something genuinely wonderful out of it.
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I've been writing about Thomas Piketty's magisterial economics bestseller Capital in the Twenty First Century for some time now (previously), and have been taking a close interest in criticisms of his work, especially the Financial Times's critique of his methods and his long, detailed response. I freely admit that I lack the stats and economics background to make sense of this highly technical part of the debate, but I think that Wonkblog's analysis looks sound, as does the More or Less play-by-play (MP3).
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Here's Randall Munroe's TED talk about his What If? series, in which he answers big, weird questions about baseballs travelling at the speed of light and such, which is also the subject of a hotly anticipated forthcoming book. The talk is a mix of war-stories and insight into what makes Munroe (who is a fascinating dude) tick.
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Anton Purisma has launched a civil rights suit against an airport Au Bon Pain restaurant;

he's asking for $2,000,000,000,
000,000,000,000,000,000,000,000,000. That would be two undecillion dollars.

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In a stirring editorial in the New Scientist, University of Edinburgh mathematician Tom Leinster calls on the world's mathematicians to boycott working for the NSA, which describes itself as the "largest employer of mathematicians in the US" and which may the world's number one employer of mathematicians. Leinster suggests that mathematicians could refuse to work for the NSA, that university heads could refuse to grant professors leave to work at NSA or GCHQ, that national mathematical societies could refuse NSA job-posting ads, and even "expel members who work for agencies of mass surveillance."
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Writing in the Financial Times, Tim Harford (The Undercover Economist Strikes Back, Adapt, etc) offers a nuanced, but ultimately damning critique of Big Data and its promises. Harford's point is that Big Data's premise is that sampling bias can be overcome by simply sampling *everything*, but the actual data-sets that make up Big Data are anything but comprehensive, and are even more prone to the statistical errors that haunt regular analytic science.

What's more, much of Big Data is "theory free" -- the correlation is observable and repeatable, so it is assumed to be real, even if you don't know why it exists -- but theory-free conclusions are brittle: "If you have no idea what is behind a correlation, you have no idea what might cause that correlation to break down." Harford builds on recent critiques of Google Flu (the poster child for Big Data) and goes further. This is your must-read for today.
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Chapter nine of Homeland opens with about 400 digits of Pi. When Wil Wheaton read the chapter, he soldiered through it, reading out Pi for a whopping four minutes! Here's the raw studio audio (MP3) of Wil and director Gabrielle De Cuir playing numbers station.

There's less than a week left during which you can get the independently produced Homeland audiobook through the Humble Ebook Bundle! Read the rest