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m-bracelets code
[15 January 2013: updated code to work with the latest versions of fgl and graphviz. Thanks to Conal Elliott for the updates!] By popular demand, here is the Haskell code I used to generate the images...
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17×17 4-coloring with no monochromatic rectangles
Quick, what’s special about the following picture? As just announced by Bill Gasarch, this is a grid which has been four-colored (that is, each point in the grid has been assigned one of four colors)...
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Random cyclic curves
Princeton Press just sent me a review copy of a new book by Frank Farris called Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. It looks amazing and I’m super excited to read it....
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Mystery curve, animated
As a follow-on to my previous post, here’s an animation (17MB) showing how the “mystery curve” arises as a sum of circular motions: Recall that the equation for the curve is . The big blue circle...
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Network reliability
Over on my other blog I’ve started writing about an interesting but apparently nontrivial problem, which some readers of this blog may find interesting as well. Suppose you have a network of computers...
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Now on mathstodon.xyz
Christian Lawson-Perfect and Colin Wright have set up an instance of Mastodon—a decentralized, open-source Twitter clone—as a place for mathy folks to be social. It’s appropriately named...
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The chromatic number of the plane, part 1
About a week ago, Aubrey de Grey published a paper titled “The chromatic number of the plane is at least 5”, which is a really cool result. It’s been widely reported already, so I’m actually a bit late...
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The chromatic number of the plane, part 2: lower bounds
In a previous post I explained the Hadwiger-Nelson problem—to determine the chromatic number of the plane—and I claimed that we now know the answer is either 5, 6, or 7. In the following few posts I...
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The chromatic number of the plane, part 3: a new lower bound
In my previous post I explained how we know that the chromatic number of the plane is at least 4. If we can construct a unit distance graph (a graph whose edges all have length ) which needs at least...
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The chromatic number of the plane, part 4: an upper bound
In my previous posts I explained lower bounds for the Hadwiger-Nelson problem: we know that the chromatic number of the plane is at least 5 because there exist unit distance graphs which we know need...
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