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# Posts

### November 29, 2015

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No summary available for this post.
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Tattoo by Harry Ricardo   http://im-possible.info/english/art/misc/tattoo/index.html   Author - https://www.instagram.com/harryricardo/

### November 28, 2015

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Andrew Casson’s invariant for homology 3-spheres An exposition by John D McCarthy and Selman Akbulut
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Again, let be a group and a subgroup of . Then we can define a binary relation on elements of , called , as follows: if and only if there is some such that . That is, for any two … Continue reading →

### November 27, 2015

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Impossible Cube Pendant   by Joshua Stockwell   http://im-possible.info/english/art/applied_art/joshua-stockwell.html   Author - https://www.etsy.com/ru/shop/AuInspiredDesign
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Let be a group and a subgroup of . Then for each element we can define a left coset of by . That is, is the set we get by combining (on the left) with every element of . For … Continue reading →
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via xkcd.com at http://s.calchumor.com/1MV9PoP [...]

### November 26, 2015

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TrekNotes is a travel journal with a different image printed as the background of each page. The cover of each book is chosen by the customer, with a map of anywhere in the world. The photographs are mine, and then I built up a small node.js app to run as the e-commerce site.
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Monument Valley   by Eric Benacek   http://im-possible.info/english/art/misc/fan-art/eric-benacek.html   Author - http://www.erathic.com/
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Ok Shanghai, you’re great. We’re in awe. Your methods are indeed successful and I wish to God that all our maths teachers had subject knowledge like you guys do. But I seem to be having a memory lapse. I can’t for the life of me think about how maths teaching got to where it is … Continue reading →
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So in the remainder of the month, we’ll prove that in any group , the order of each element must evenly divide the order (size) of the group. I said in an earlier post that this is called Lagrange’s Theorem; … Continue reading →
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(Click on the comic if you can't see the full image.) (C)Copyright 2015, C. Burke.It's actually 3 1/8 pecans because cutting 1/7 of a pecan is as impossible as cutting .141592... pecans. Actually, it's more likely that a pecan was split in half and then cut four more times to make 8 pieces, but they wouldn't exactly be actually pieces of eight. Happy Thanksgiving to you and yours! Come back often for more funny math and geeky comics.

### November 25, 2015

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via MathMajorProblems
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A few days ago we made use of Bézout’s Identity, which states that if and have a greatest common divisor , then there exist integers and such that . For completeness, let’s prove it. Consider the set of all linear … Continue reading →
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NeuralTalk2 uses neural networks to caption images quickly. To demonstrate, the video below shows a webcam feed that continuously updates with new image captions based on what the computer sees.…Tags: classification, images, neural networks
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Millions of Americans will fly home this Thanksgiving weekend. (Based on my morning commute, the holiday already started a couple of days early.) Josh Katz and Quoctrung Bui for the…Tags: flights, New York Times, Thanksgiving
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ibmblr:While the blueprints of nature have existed since… well… the beginning of time, the fractal math revealing these hidden patterns was only discovered in the 1970s. But that didn’t stop software designer and fractal enthusiast Ken Shirriff from bending time to generate a classic Mandelbrot fractal on a 50-year-old IBM 1401 mainframe. Running antique punch cards, Ken had to wait 12 long minutes for the heavy-duty scientific calculation job to complete, thanks to a 15-second CPU […]

### November 24, 2015

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//helloWorld(function(path) { return '/1608/' + path})//via xkcd.com at http://s.calchumor.com/1Nr2C5F [...]
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So, where are we? We assumed that is divisible by , but is not prime. We picked a divisor of and used it to define a group , and yesterday we showed that has order in . Today we’ll use … Continue reading →
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Metadata can tell you a lot, and most of us agree that it's not “just metadata” at this point. The Share Lab shows what one can find, just using everyday…Tags: metadata, privacy

### November 23, 2015

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Yesterday, from the assumption that is divisible by , we deduced the equations and which hold in the group . So what do these tell us about the order of ? Well, first of all, the second equation tells us … Continue reading →
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Sketches by anitpop0   http://im-possible.info/english/art/pencil/antipop0.html
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Above is a map from Five-Thirty-Eight's survey of Thanksgiving eating traditions nationwide. It shows the most disproportionately common Thanksgiving side dish by region. I grew up in Florida, but we never got on the mac and cheese Thanksgiving bandwagon. Likewise, living now in Maryland, squash doesn't make it on our plates. Our family seems to match the midwest more, with green bean casserole and rolls (not biscuits). And for dessert we are looking forward to pumpkin, pecan, and apple pie. […]
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It's true. Sometimes it's okay for the y-axis to start at a non-zero value, which is why Johnny Harris and Matthew Yglesias for Vox tell people to shut up about…Tags: baseline, Vox
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(Click on the comic if you can't see the full image.) (C)Copyright 2015, C. Burke.Any time there is a group of Adventurers, they'll be sure to find The Negative One in their midst. Good chance that I used a similar joke to this before. But I like the Picaroons. The more of them, the better! Come back often for more funny math and geeky comics.

### November 22, 2015

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Impossible T   by traceeaaa   http://im-possible.info/english/art/various/traceeaaa.html   Author - https://www.instagram.com/traceeaaa/
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Now we’re going to figure out the order of in the group . Remember that we started by assuming that passed the Lucas-Lehmer test, that is, that is divisible by . Remember that we also showed for all . In … Continue reading →
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24 circle theorem questions. Some are pretty tough. Answers also included. circle theorems
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via xkcd.com at http://s.calchumor.com/1T9dV0W [...]
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Aaron Burr: Alexander joins forces with James Madison and John Jay to write a series of essays defending the new United States Constitution, entitled The Federalist Papers. The plan was to write a total of twenty-five essays, the work divided evenly among the three men. me: But… twenty-five doesn’t divide evenly by three…