Jekyll2018-08-15T21:54:50+00:00https://11011110.github.io/blog/11011110Geometry, graphs, algorithms, and moreDavid EppsteinLinkage2018-08-15T14:54:00+00:002018-08-15T14:54:00+00:00https://11011110.github.io/blog/2018/08/15/linkage<ul>
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<p><a href="http://www.neverendingbooks.org/rotations-of-kleins-quartic">Rotations of Klein’s quartic</a> (<a href="https://plus.google.com/100003628603413742554/posts/eUgYhvD6Jtw">G+</a>). Lieven Le Bruyn uses both geometric and group-theoretic arguments to understand the symmetries of this surface.</p>
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<p><a href="https://www.chronicle.com/article/These-Professors-Don-t-Work/244120">Predatory journals that list academics as being on their editorial boards, without asking, and then won’t remove them even when asked</a> (<a href="https://plus.google.com/100003628603413742554/posts/4wQP4qGVMV8">G+</a>). Just in case you were under the impression that taking money to publish bad papers and spamming calls for papers to researchers in unrelated areas were the only annoying things they did.</p>
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<p><a href="https://www.wired.com/story/guerrilla-wikipedia-editors-who-combat-conspiracy-theories/">The “guerrilla” Wikipedia editors who combat conspiracy theories</a> (<a href="https://plus.google.com/100003628603413742554/posts/2tHQznaeQkm">G+</a>).</p>
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<p><a href="https://johncarlosbaez.wordpress.com/2018/07/13/random-points-on-a-group/">Random points on a group</a> (<a href="https://plus.google.com/100003628603413742554/posts/P9QhLdSYy3n">G+</a>). John Baez uses character theory to explain why the even moments of distances between randomly-selected points on a circle or on a 3-sphere form combinatorially-significant integer sequences, but other dimensions give non-integers. It turns out to be closely related to the fact that the spheres of those dimensions are compact Lie groups.</p>
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<p><a href="https://www.cs.umd.edu/users/samir/stoc2018/">Videos from the workshop in honor of Vijay Vazirani are now up</a> (<a href="https://plus.google.com/100003628603413742554/posts/hXe9YjBLPzx">G+</a>, <a href="https://blog.computationalcomplexity.org/2018/08/the-future-of-tcs-workshop-celebrating.html">via</a>). Which gives me an opportunity to ask what’s known about a commutative but non-associative binary operation on pairs <script type="math/tex">(x,y)</script> that takes the <script type="math/tex">x</script> whose <script type="math/tex">y</script> is maximum and then adds the <script type="math/tex">y</script> values, used by Manuel Blum as part of a mathematical model for pain.</p>
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<p><a href="https://www.nytimes.com/2018/08/08/science/garnets-tunnels-microorganisms.html">Intricate tunnels in garnet crystals</a> (<a href="https://plus.google.com/100003628603413742554/posts/AjFQb9mvsBU">G+</a>, <a href="https://www.metafilter.com/175835/garnet-tunnels">via</a>), thought to be the tracks of microbial growth.</p>
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<p><a href="https://boingboing.net/2018/08/09/fixed-position-harmful.html">Kill sticky headers</a> (<a href="https://plus.google.com/100003628603413742554/posts/9TQ6cUEj5CQ">G+</a>). Annoyed by stuck-in-place web site banners that get in the way of reading the content you’re trying to read? This useful little bookmarklet can help.</p>
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<p><a href="http://www.cutoutfoldup.com/977-rhombic-spirallohedron.php">How to make a rhombic spirallohedron</a> (<a href="https://plus.google.com/100003628603413742554/posts/8au9CE3TqJA">G+</a>, <a href="https://blogs.ams.org/blogonmathblogs/2018/04/30/arts-and-crafts-night/">via</a>). There are lots of convex polyhedra having rhombuses as faces — the zonohedra formed from the Minkowski sum of unit line segments (no three parallel to a single plane, to avoid faces with more than four sides). But I don’t know much about these non-convex rhombohedra.</p>
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<p><a href="https://en.wikipedia.org/wiki/Merge-insertion_sort">Merge-insertion sort</a> (<a href="https://plus.google.com/100003628603413742554/posts/E3mipqAwTTE">G+</a>). New Wikipedia article on a comparison sorting algorithm that for two decades held the record for the fewest number of comparisons known.</p>
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<p><a href="http://www.nasonline.org/news-and-multimedia/news/May-1-2018-NAS-Election.html">New National Academy of Sciences members</a> (<a href="https://plus.google.com/100003628603413742554/posts/KrJiQGbNGyx">G+</a>). Congratulations to Sanjeev Arora, Umesh Vazirani, and Mihalis Yannakakis, who are adding to the representation of theoretical computer science within the National Academy!</p>
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<p><a href="https://www.ilyaraz.org/static/papers/spectral_gap.pdf">Data-dependent hashing via nonlinear spectral gaps</a> (Andoni et al, STOC 2018) and a <a href="https://www.quantamagazine.org/universal-method-to-sort-complex-information-found-20180813/">clickbaity <em>Quanta</em> article about it</a> (<a href="https://plus.google.com/100003628603413742554/posts/JiyYdT2HoMz">G+</a>, <a href="https://plus.google.com/+QuantamagazineOrgNews/posts/1VLxjQ9Cm6f">via</a>). “A universal method to sort information”? Really it’s about using embeddability of expander graphs to distinguish metric spaces that have nontrivial approximate nearest-neighbor data structures from those that don’t, and developing such data structures for all normed spaces.</p>
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<p><a href="http://www.post-gazette.com/business/tech-news/2018/08/14/lenore-manuel-blum-carnegie-mellon-university-school-computer-science-project-olympus/stories/201808140055">Lenore and Manuel Blum resign from CMU</a> (<a href="https://plus.google.com/100003628603413742554/posts/46JXpxQ754m">G+</a>, <a href="https://news.ycombinator.com/item?id=17761211">via</a>) over “professional harassment” and “sexist management”.</p>
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</ul>David EppsteinRotations of Klein’s quartic (G+). Lieven Le Bruyn uses both geometric and group-theoretic arguments to understand the symmetries of this surface.Finding obstacle-avoiding point sets can be hard2018-08-07T22:05:00+00:002018-08-07T22:05:00+00:00https://11011110.github.io/blog/2018/08/07/finding-obstacle-avoiding<p>My new preprint for today is my first follow-up paper to my book, <a href="https://www.cambridge.org/eppstein"><em>Discrete Configurations in Discrete Geometry</em></a>, and the first published solution to one of its open problems. It’s with <a href="https://cs.ucsb.edu/people/faculty/lokshtanov">Daniel Lokshtanov</a> (in the process of moving from the University of Bergen to the University of California, Santa Barbara) and I hope to have another paper eventually with him on some more research we did related to the book, but for now there’s only the one. It’s called “The parameterized complexity of finding point sets with hereditary properties” (<a href="https://arxiv.org/abs/1808.02162">arXiv:1808.02162</a>) and I’ll be presenting it later this month at <a href="http://algo2018.hiit.fi/ipec/">IPEC in Helsinki</a> while Daniel gets ready to move house.</p>
<p>The book is about finite sets of Euclidean points and their properties.
Many of the properties I’m interested in are defined by a constant number of <em>obstacles</em>, smaller point sets whose presence (in any combinatorially equivalent form) stops the property from being true. For instance a point set is in <em>general position</em> if it avoids having three points in a line, and it is in <em>convex position</em> if it also avoids having a triangle of three points surrounding a fourth point (this is <a href="https://en.wikipedia.org/wiki/Carath%C3%A9odory%27s_theorem_(convex_hull)">Carathéodory’s theorem</a>). If you have a point set that’s not in convex position, and you want to find a convex-position subset that’s as large as possible, there’s a known polynomial-time algorithm (Section 11.4 of my book). But what about other properties? How easily can you find the largest subset with a given property?</p>
<p>To study this from the point of view of parameterized complexity we should augment the problem with a numerical parameter that encapsulates all its difficulty. The problem is <em>fixed-parameter tractable</em> when its running time is a polynomial in the input size (independent of the parameter) multiplied by a function of the parameter. For finding large obstacle-avoiding subsets, one natural choice for the parameter is how many points you have to remove. Can you eliminate all the copies of the obstacles by removing only <script type="math/tex">r</script> points? This is always fixed-parameter tractable as a special case of more general hitting set problems. But the other choice is to make the parameter be the size of the subset you’re seeking. Does a given input have a subset of <script type="math/tex">k</script> points that avoids all the obstacles?</p>
<p>When I wrote the book, all the examples I knew for problems of finding <script type="math/tex">k</script>-point obstacle-avoiding subsets were either polynomial (like the <script type="math/tex">k</script>-point convex subset problem) or at least fixed-parameter tractable (as the problem of finding <script type="math/tex">k</script> points in general position turns out to be). So I posed as an open problem the question of whether these problems are always fixed-parameter tractable. The answer turns out to be no. The new paper provides an example of a set of obstacles for which this problem is hard under standard complexity-theoretic assumptions.</p>
<p>Here are the three hard-to-avoid obstacles:</p>
<p style="text-align:center"><img src="/blog/assets/2018/forbidden.svg" alt="Three obstacles for a hard property" /></p>
<p>And here’s a rough picture of what a hard instance looks like:</p>
<p style="text-align:center"><img src="/blog/assets/2018/yard.svg" alt="Hard instance for a hard property" /></p>
<p>(The actual instances will have more than three horizontal lines, and only some of its triples of blue and yellow points will be collinear.)</p>
<p>We set the parameter <script type="math/tex">k</script> to a value that forces every <script type="math/tex">k</script>-point obstacle-avoiding subset to include all red and blue points, plus one yellow point per horizontal line. It could not include more than three points per horizontal line, because the left obstacle prevents that, and it could not include all red points and two yellow points on the same line, because the middle obstacle prevents that.</p>
<p>The effect of the right obstacle is more subtle. In any subset that avoids it, the yellow points have to line up in the same way as the blue points. That is, whenever three lines have the property that their three blue points on each side line up (as they do in this example), the three yellow points in the middle must also line up. We use this property to show that instances of (partitioned) <a href="https://en.wikipedia.org/wiki/Subgraph_isomorphism_problem">subgraph isomorphism</a>, looking for one graph as part of another larger graph, can be translated into point sets like this. The three-point lines in the blue points will be arranged to represent triples of an edge and its two endpoints in the graph we are trying to find, and the three-point lines in the yellow points will correspond in the same way to triples of an edge and its two endpoints in the larger graph we are searching. The details of the reduction are a bit messy, though, because we have to use points with small integer coordinates, get them all to line up in the right ways, and prove that the obstacles don’t show up accidentally in some other way.</p>
<p>Those aren’t the only results of the paper; it also shows that some natural classes of obstacles lead to tractable problems. For instance, this is true whenever none of the obstacles is collinear, whenever one of the obstacles is in convex position, or whenever there is only one obstacle. But we failed to completely classify which sets of obstacles lead to tractable problems and which don’t (unlike the analogous questions for induced subgraphs of graphs, where a complete classification is known). So even though we knocked out one of the open problems from the book, there’s definitely more research left to do in the same direction.</p>
<p>(<a href="https://11011110.github.io/blog/2018/08/07/finding-obstacle-avoiding.html">G+</a>)</p>David EppsteinMy new preprint for today is my first follow-up paper to my book, Discrete Configurations in Discrete Geometry, and the first published solution to one of its open problems. It’s with Daniel Lokshtanov (in the process of moving from the University of Bergen to the University of California, Santa Barbara) and I hope to have another paper eventually with him on some more research we did related to the book, but for now there’s only the one. It’s called “The parameterized complexity of finding point sets with hereditary properties” (arXiv:1808.02162) and I’ll be presenting it later this month at IPEC in Helsinki while Daniel gets ready to move house.Congratulations, Dr. Gupta!2018-08-06T21:33:00+00:002018-08-06T21:33:00+00:00https://11011110.github.io/blog/2018/08/06/congratulations-dr-gupta<p><a href="https://www.ics.uci.edu/~guptasid/">Siddharth Gupta</a> passed his doctoral defense today! Sid has been a student here at UC Irvine, jointly supervised by Mike Goodrich and myself, after earning a master’s degree in mathematics four years ago from the <a href="https://en.wikipedia.org/wiki/Birla_Institute_of_Technology_and_Science,_Pilani_%E2%80%93_Goa_Campus">Birla Institute of Technology and Science, Pilani – Goa Campus</a>.</p>
<p>I’ve already posted here about my joint research with Sid on <a href="/blog/2017/09/19/graphs-with-sparse.html">modeling real-world road networks</a> and <a href="/blog/2018/03/16/drawing-clustered-graphs.html">drawing clustered graphs</a>. He also has a publication with Goodrich and Manny Torres on <a href="http://arxiv.org/abs/1609.07239">reconstructing the evolution of road networks</a>, a paper from his master’s program on connected component labeling, and not-yet-published research on clustered planarity and on distance oracles for graphs. As I understand it his next step is to move to Israel, where he has accepted an offer to be a Zuckerman Postdoctoral Scholar at Ben-Gurion University, continuing his research on fixed-parameter tractability of graph algorithms.</p>
<p>Congratulations, Sid!</p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/hSWWxL429eB">G+</a>)</p>David EppsteinSiddharth Gupta passed his doctoral defense today! Sid has been a student here at UC Irvine, jointly supervised by Mike Goodrich and myself, after earning a master’s degree in mathematics four years ago from the Birla Institute of Technology and Science, Pilani – Goa Campus.Fingerprints and tangent bundles2018-08-03T23:16:00+00:002018-08-03T23:16:00+00:00https://11011110.github.io/blog/2018/08/03/fingerprints-tangent-bundles<p>The arXiv version of “Geometric fingerprint recognition via oriented point-set pattern matching”, my CCCG paper with Mike Goodrich, Jordan Jorgensen, and Manny Torres, has now appeared: it’s <a href="https://arxiv.org/abs/1808.00561">arXiv:1808.00561</a></p>
<p>The motivating problem for this work is to approximately match human fingerprints. The image below is a vintage example, from <a href="https://archive.org/stream/b20443493/b20443493#page/n92/mode/2up"><em>Guide to Finger-print Identification</em> (Faulds, 1905)</a>:</p>
<p style="text-align:center"><img src="/blog/assets/2018/fingerprint.jpg" alt="Thumb-print of Alfred Stratton, from Faulds (1905), p. 63" /></p>
<p>Fingerprints can be described combinatorially by their <a href="https://www.bayometric.com/minutiae-based-extraction-fingerprint-recognition/">minutiae</a>, points where the fingerprint pattern changes. These are points like the marked ones in the image. For instance they include the points at the ends of ridges or at the merger of two ridges. Once the fingerprints are described as sets of minutiae, the problem becomes one of matching one point set to another. But this is complicated by the fact that (beyond being labeled by the type of change they describe) the minutiae are not just pure Euclidean points. Each one is associated with a direction, as well as a position: the direction in which the associated ridges extend from the point. So the space in which the minutiae live is <script type="math/tex">\mathbb{R}^2\times S^1</script>, the product of a Euclidean plane with a circle of directions. Or, if you like, it’s the <a href="https://en.wikipedia.org/wiki/Unit_tangent_bundle">unit tangent bundle</a> <script type="math/tex">\operatorname{UT}(\mathbb{R}^2)</script>.</p>
<p>Transformations of the Euclidean plane such as translations, rotations, and scaling extend in a natural way to this space. The goal in our paper is to find a transformation by which a given small pattern point set (the minutiae that we find for a particular fingerprint scan) can be made to look like a subset of a larger host point set (all the minutiae). Here “look like” involves a definition of similarity of two point sets that combines both Euclidean distance and the differences between the orientations of points. The approach we take to finding the right transformation is more or less standard in this area: start by choosing a family of transformations that match certain representative points exactly, prove that one such transformation is within a constant factor of optimal, and then search within a larger family of perturbations of these exactly-matching ones, in order to reduce the constant factor to <script type="math/tex">1+\varepsilon</script>.</p>
<p>This does have some weaknesses, though. One is that the host point set has to include an approximate transformed copy of every pattern point, but real fingerprint databases are likely to be missing some minutiae. Another is that by measuring the quality of a match by the pair of points that are least well matched to each other, we are very vulnerable to outliers in the data (points that are perturbed, or completely missing). It would be better to use a more robust measure of the distance between two point sets. So I think there’s still plenty more research to do in this direction.</p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/FeikuVKjH7V">G+</a>)</p>David EppsteinThe arXiv version of “Geometric fingerprint recognition via oriented point-set pattern matching”, my CCCG paper with Mike Goodrich, Jordan Jorgensen, and Manny Torres, has now appeared: it’s arXiv:1808.00561Linkage2018-07-31T22:05:00+00:002018-07-31T22:05:00+00:00https://11011110.github.io/blog/2018/07/31/linkage<ul>
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<p><a href="https://boingboing.net/2018/06/26/software-formalities.html">ICE hacked its algorithmic risk-assessment tool so it recommended detention for everyone</a> (<a href="https://plus.google.com/100003628603413742554/posts/V7T8sbGPetu">G+</a>). Research on algorithmic fairness is only applicable to the extent that the authorities use decision-making algorithms in good faith.</p>
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<p><a href="https://mathlesstraveled.com/2018/07/12/drawing-orthogons-with-an-smt-solver/">Drawing orthogons with an SMT solver</a> (<a href="https://plus.google.com/100003628603413742554/posts/2CXsCH4y9yc">G+</a>). Brent Yorgey has been writing a sequence of blog posts on orthogonal simple polygons, considered to be equivalent when they have the same cyclic sequence of angles. They’re easy to realize from their angle sequence, but the problem becomes harder when you also want to minimize the perimeter.</p>
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<p><a href="https://thehighergeometer.wordpress.com/2018/07/19/special-issue-of-geombinatorics-on-recent-progress-on-the-chromatic-number-of-the-plane/">Special issue of <em>Geombinatorics</em> on recent progress on the chromatic number of the plane</a> (<a href="https://plus.google.com/100003628603413742554/posts/4858FfHrURd">G+</a>). The new lower bounds on the chromatic number of the plane have now been published. This post collects links to free copies of the papers.</p>
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<p><a href="https://www.chronicle.com/article/Some-Colleges-Cautiously/243968">Some colleges cautiously embrace Wikipedia</a> (<a href="https://plus.google.com/100003628603413742554/posts/XZVBcR13yKr">G+</a>). This <em>Chronicle of Higher Education</em> story reports on changing attitudes of academia towards Wikipedia: where previously it had often been something to warn students away from using, now academics and Wikipedians are working more closely together.</p>
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<p><a href="http://www.pepijnvanerp.nl/2017/03/far-fetched-mathematics-on-mars/">Far-fetched mathematics on Mars</a> (<a href="https://plus.google.com/100003628603413742554/posts/YmArE7w2J5M">G+</a>). Pepijn van Erp deconstructs the discrete-geometry equivalent of numerology.</p>
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<p><a href="https://www.youtube.com/watch?v=mBOdZ6nhDJg">Walking table</a> (<a href="https://plus.google.com/100003628603413742554/posts/SeVp8u1df3K">G+</a>). A table that walks (purely mechanically) when you push it. See also <a href="http://www.scheublinlindeman.nl/walking-table.html">designer Wouter Scheublin’s web site</a>.</p>
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<p><a href="https://www.youtube.com/watch?v=bvLD54GnOTk">Review of <em>A Million Random Digits</em></a> (<a href="https://plus.google.com/100003628603413742554/posts/PHcju9Ls27Q">G+</a>). Purporting to be a review of a calculating device, this video morphs into a rant about how random numbers are the antithesis of mathematics, since they are deliberately constructed to have no patterns in them. That’s clearly debatable, but (like all of Chris Staecker’s videos) it’s entertaining and thought-provoking.</p>
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<p><a href="https://www.theguardian.com/careers/2018/jul/24/meet-the-female-codebreakers-of-bletchley-park">Meet the female codebreakers of Bletchley Park</a> (<a href="https://plus.google.com/100003628603413742554/posts/fr3i16m7nGd">G+</a>, <a href="https://plus.google.com/114992454076690518209/posts/bXs28XBASjE">via</a>). <em>The Guardian</em> profiles Joan Joslin, Betty Webb, and Joyce Aylard.</p>
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<p><a href="https://www.youtube.com/watch?v=2vnqSwWAn34">Earthquakes, circles, and spheres</a> (<a href="https://plus.google.com/100003628603413742554/posts/JfZXYiDpCyH">G+</a>). Tadashi Tokieda discusses how the radical axes of each pair of any three circles (the lines through their crossing points, when the circles cross) always meet at a single point, the radical center; how the proof of this is more easily understood by lifting to 3d than in the plane, and how this is all useful for triangulating the epicenters of earthquakes. In a followup video <a href="https://www.youtube.com/watch?v=lubGnk0UZt0">Balls and cones</a> he discusses a similar 3d lifting based proof of a theorem about bitangents of circles.</p>
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<p><a href="https://www.theguardian.com/education/2018/jul/24/academic-writes-270-wikipedia-pages-year-female-scientists-noticed">Academic writes 270 Wikipedia pages in a year to get female scientists noticed</a> (<a href="https://plus.google.com/100003628603413742554/posts/WHbNUCQTKno">G+</a>). <em>The Guardian</em> on Wikipedian <a href="https://en.wikipedia.org/wiki/Jess_Wade">Jess Wade</a>. See also <a href="https://elpais.com/elpais/2018/07/10/inenglish/1531237118_130796.html"><em>El Pais</em></a>.</p>
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<p><a href="http://noquay.co.uk/inglenooks.php">Inglenook Sidings</a> (<a href="https://plus.google.com/100003628603413742554/posts/5C6edV4DqeQ">G+</a>, <a href="https://www.wired.com/2007/04/my-son-age-3-is/">via</a>). A puzzle in which one must assemble a randomly-determined sequence of five train cars from a group of eight, by pushing and pulling the cars on a short branched section of track. Somewhat reminiscent of <a href="https://faculty.math.illinois.edu/~west/regs/stacksort.html">sorting using stacks</a>.</p>
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<p><a href="https://blogs.ams.org/beyondreviews/2015/04/28/using-mathscinet-at-home-or-on-the-road/">Remote access to MathSciNet</a> (<a href="https://plus.google.com/100003628603413742554/posts/AKdSf7cEXJJ">G+</a>). While connected to a subscribing network, you can store an access code on your laptop that will remain valid for three months.</p>
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<p><a href="https://scientistseessquirrel.wordpress.com/2015/06/10/can-a-scientific-paper-be-too-short-part-ii/">Can a scientific paper be too short?</a> (<a href="https://plus.google.com/100003628603413742554/posts/caiAzBtd9mm">G+</a>). Conway and Soifer tried to make their paper on covering triangles by triangles even shorter, but their editor got fussy.</p>
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<p><a href="https://cameroncounts.wordpress.com/2018/07/29/open-access-and-the-arxiv/">Open access and the arXiv</a> (<a href="https://plus.google.com/100003628603413742554/posts/W7fkGGezYbF">G+</a>). Peter Cameron reports that Research England are disallowing arXiv preprints from meeting their requirement that all publications used for assessment purposes be open access. The stated reason is that “there is no mechanism for linking a paper on the arXiv with the published version of the paper” but this is untrue.</p>
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<p><a href="https://boingboing.net/2018/07/30/what-happens-when-you-let-comp.html">What happens when you let computers optimize floorplans</a> (<a href="https://plus.google.com/100003628603413742554/posts/DbUpoUbfAhM">G+</a>). Needs a little more architectural expertise, but interesting results despite that.</p>
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<p><a href="https://www.quantamagazine.org/teenager-finds-classical-alternative-to-quantum-recommendation-algorithm-20180731/">Classical alternative to quantum recommendation</a> (<a href="https://plus.google.com/100003628603413742554/posts/CJSvWsn4Mfp">G+</a>, <a href="https://news.ycombinator.com/item?id=17654220">via</a>). <em>Quanta</em> on undergrad Ewin Tang’s work with Scott Aaronson to find a fast classical algorithm for a problem on recommendation systems previously thought to only be solvable quickly by quantum computers.</p>
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</ul>David EppsteinICE hacked its algorithmic risk-assessment tool so it recommended detention for everyone (G+). Research on algorithmic fairness is only applicable to the extent that the authorities use decision-making algorithms in good faith.Linkage2018-07-15T16:16:00+00:002018-07-15T16:16:00+00:00https://11011110.github.io/blog/2018/07/15/linkage<ul>
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<p><a href="http://arjay.typepad.com/vallejo_nocturno/2016/02/theft-of-concepts.html">Marcel Duchamp, early hero of the taking-credit-for-others’-work movement</a> (<a href="https://plus.google.com/100003628603413742554/posts/ZXTTXodcEcQ">G+</a>, <a href="https://boingboing.net/2018/07/02/duchamps-famous-urinal-sculp.html">via</a>).</p>
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<p><a href="https://boingboing.net/2018/07/04/one-day-left.html">Several European-language Wikipedias go dark in protest of EU copyright proposal</a> (<a href="https://plus.google.com/100003628603413742554/posts/3spx73fNCUQ">G+</a>). Fortunately it was eventually rejected.</p>
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<p><a href="http://beachpackagingdesign.com/boxvox/packaging-structure-or-a-blueprint-of-space">Space-filling shape with curved hypar faces</a> (<a href="https://plus.google.com/100003628603413742554/posts/4ktV5fuMvHi">G+</a>, <a href="https://plus.google.com/+TimHutton/posts/YUo5kiAqhgr">via</a>).</p>
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<p><a href="https://en.wikipedia.org/wiki/Wikipedia:Wikipedia_Signpost/2018-06-29/Blog">An open letter from the Wikimedia Foundation to the government of Turkey</a> (<a href="https://plus.google.com/100003628603413742554/posts/K1X9R28exr4">G+</a>), in protest of Turkey’s year-long block of Wikipedia access for their citizens and residents.</p>
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<p><a href="http://www.ams.org/government/outreach/CongressBriefingAMSMSRImay2018">Computational origami on stage at Capitol Hill briefing</a> (<a href="https://plus.google.com/100003628603413742554/posts/UeJo47H2YEH">G+</a>). Erik Demaine tells congress why fundamental research on topics such as folding is important.</p>
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<p><a href="https://adamsheffer.wordpress.com/2018/07/07/discrete-geometry-classic-two-distance-sets/">Two-distance sets</a> (<a href="https://plus.google.com/100003628603413742554/posts/bZ39pAfoaYz">G+</a>). See also the closely related new Wikipedia article on <a href="https://en.wikipedia.org/wiki/Isosceles_set">isosceles sets</a>, sets of points where every triple has at most two distinct distances.</p>
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<p><a href="http://blogs.oregonstate.edu/glencora/2018/07/02/discrimination-and-the-conference-publication-system/">Discrimination and the conference publication system</a> (<a href="https://plus.google.com/100003628603413742554/posts/EgDCFhpPpTq">G+</a>). Cora Borradaile argues that the pressure on computer scientists to travel to conferences discriminates against those for whom travel is difficult as well as those who face greater likelihood of harassment in face-to-face situations.</p>
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<p><a href="https://aperiodical.com/2018/07/alexander-bogomolny-creator-of-cut-the-knot-has-died/">Alexander Bogomolny, creator of Cut the Knot, has died</a> (<a href="https://plus.google.com/100003628603413742554/posts/84XmYhhtBrM">G+</a>, <a href="https://plus.google.com/+Aperiodical/posts/ggJNSQiteWE">via</a>). Very sad news. I hope he made some arrangements to keep <a href="https://www.cut-the-knot.org/">his website</a> going after him, because there’s a lot of great content there.</p>
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<p><a href="https://blogs.scientificamerican.com/roots-of-unity/a-few-of-my-favorite-spaces-antoines-necklace/">Antoine’s necklace</a> (<a href="https://plus.google.com/100003628603413742554/posts/RyrQ4zFBgGu">G+</a>). Despite the Cantor set being totally disconnected, it can be embedded into 3d in a way that gives its complement a complicated topology. <a href="https://en.wikipedia.org/wiki/Antoine%27s_necklace">The corresponding Wikipedia article</a> uses the same image, by an editor named Blacklemon67 who also has an interesting post on <a href="http://www.blackle-mori.com/projects/the-paper-trick/">how to use folded A4 paper to compute rational approximations to <script type="math/tex">\sqrt{2}</script></a>.</p>
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<p><a href="https://www.michaelfogleman.com/rush/">Michael Fogleman constructs “a database of all interesting Rush Hour configurations”</a> (<a href="https://plus.google.com/100003628603413742554/posts/M6bbMGGfEuy">G+</a>, <a href="https://news.ycombinator.com/item?id=17509601">via</a>), and speculates on how visualization of the state space of each connected component of states might be used to more accurately estimate the difficulty of a puzzle.</p>
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<p><a href="http://www.julietemckenna.com/?p=2945">What can SFF fandom do about the inherent bias of Wikipedia?</a> (<a href="https://plus.google.com/100003628603413742554/posts/4M8wxYFuYFg">G+</a>). Fantasy author Juliet McKenna writes about the experience of having a Wikipedia biography put up for deletion, and about the broader context of systematic bias on Wikipedia and the forces arrayed on both sides of the issue. Much of what she writes applies well beyond SFF fandom.</p>
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<p><a href="http://www.news-gazette.com/news/local/2018-07-12/robotics-expert-be-first-woman-lead-ui-computer-science-department.html">Nancy Amato hired as new CS department chair at UIUC</a> (<a href="https://plus.google.com/100003628603413742554/posts/NrBbiaU2S9V">G+</a>, <a href="https://plus.google.com/+JeffErickson/posts/VSDvEkWCUbr">via</a>, <a href="https://plus.google.com/101113174615409489753">via2</a>). I just saw Nancy last month at SWAT, where she gave a great talk on motion planning problems as one of the invited speakers. I’m sure she’ll be an excellent new chair. Congratulations, Nancy! And congratulations, too, to UIUC, for getting her.</p>
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<p><em><a href="https://www.maa.org/press/maa-reviews/forbidden-configurations-in-discrete-geometry">Forbidden Configurations in Discrete Geometry</a></em> (<a href="https://plus.google.com/100003628603413742554/posts/7efEyuuUu6Q">G+</a>). Darren Glass and <em>MAA Reviews</em> publish the first review (at least the first I’ve seen) of my new book.</p>
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<p><a href="https://ggstem.wordpress.com/">Grandma Got STEM</a> (<a href="https://plus.google.com/100003628603413742554/posts/WdNyLwpmYB1">G+</a>), Harvey Mudd mathematician Rachel Levy’s blog filled with stories of earlier generations of women in science, technology, engineering, and mathematics. See also new Wikipedia articles on <a href="https://en.wikipedia.org/wiki/Grandma_Got_STEM">the blog</a>, <a href="https://en.wikipedia.org/wiki/Rachel_Levy_%28mathematician%29">Levy</a>, and <a href="https://en.wikipedia.org/wiki/Flukeprint">flukeprints</a> (the tracks left by whales on the surface of the ocean, one of the topics in Levy’s fluid dynamics research).</p>
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</ul>David EppsteinMarcel Duchamp, early hero of the taking-credit-for-others’-work movement (G+, via).Malmö and the minimal surface2018-07-01T17:32:00+00:002018-07-01T17:32:00+00:00https://11011110.github.io/blog/2018/07/01/malmo-minimal-surface<p>Ok, the last batch of photos from my recent trip, the ones from Malmö, is now up. Or actually the last two batches are now up, because I took so many <a href="http://www.ics.uci.edu/~eppstein/pix/rubato/">photos of Eva Hild’s <em>Rubato</em> (2015)</a> that I put them into a separate batch from the <a href="http://www.ics.uci.edu/~eppstein/pix/malmo">other Malmö photos</a>.</p>
<p style="text-align:center"><img src="http://www.ics.uci.edu/~eppstein/pix/rubato/1-m.jpg" alt="Rubato (Eva Hild, 2015)" style="border-style:solid;border-color:black;" /></p>
<p>I think it’s a minimal surface, but it’s hard to tell for sure; I don’t know of a good visual way to check whether the mean curvature is zero. It was originally painted flat white, but by now the surface has developed interesting contour lines from rain and dust, visible in some of the closer-up shots.</p>
<p style="text-align:center"><img src="http://www.ics.uci.edu/~eppstein/pix/rubato/4-m.jpg" alt="Rubato (Eva Hild, 2015)" style="border-style:solid;border-color:black;" /></p>
<p>The part of Malmö that I spent most of my time in is a recently-rebuilt former docklands, modern in architecture, with plenty more abstract art. Here’s one piece (<em>Passage</em>, Maha Mustafa, 2016) framing the Niagara Building of the University of Malmö, where the <a href="http://csconferences.mah.se/swat2018/">SWAT conference</a> was held.</p>
<p style="text-align:center"><img src="http://www.ics.uci.edu/~eppstein/pix/malmo/PassageToNiagara-m.jpg" alt="Niagara Building of the University of Malmö as seen through _Passage_ (Maha Mustafa, 2016)" style="border-style:solid;border-color:black;" /></p>
<p>Sadly, I never did find any of the <a href="https://www.atlasobscura.com/places/anonymouse-shops-for-mice">tiny mouse shops</a>.</p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/YdNTRyEJz3c">G+</a>)</p>David EppsteinOk, the last batch of photos from my recent trip, the ones from Malmö, is now up. Or actually the last two batches are now up, because I took so many photos of Eva Hild’s Rubato (2015) that I put them into a separate batch from the other Malmö photos.Linkage2018-06-30T15:46:00+00:002018-06-30T15:46:00+00:00https://11011110.github.io/blog/2018/06/30/linkage<ul>
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<p><a href="http://www.thisiscolossal.com/2018/06/bubbles-melody-yang/">Melody Yang explains her bubble-blowing craft</a> (<a href="https://plus.google.com/100003628603413742554/posts/74aSZrx9Adr">G+</a>, <a href="https://plus.google.com/+Colossal/posts/Sju1eKYgMR4">via</a>).</p>
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<p><a href="https://www.nature.com/articles/d41586-018-03837-7">EU copyright reforms draw fire from scientists</a> (<a href="https://plus.google.com/100003628603413742554/posts/833qpam2NHQ">G+</a>, <a href="https://news.ycombinator.com/item?id=17315480">via</a>). “Concerns focus on a provision that would let publishers claim royalties for the use of snippets of information, such as tables” … “the proposed rule might even force scientists to pay fees to publishers for references they include”. The publishers’ response, which basically amounts to “don’t be silly, why would you think we would do that” rather than any explanation why they would be prevented from doing that, is not reassuring.</p>
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<p><a href="http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html">The Meaning of Life is 42 – But the Cost of Living is Capped at <s>329</s> 50</a> (<a href="https://plus.google.com/100003628603413742554/posts/jLdZzoqKQRM">G+</a>). Anything that can be constructed from gliders in Conway’s Game of Life can be constructed using only 50 gliders. <a href="http://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html">See second post for more details</a>.</p>
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<p>With their move to steal babies from immigrants, <a href="https://www.dailykos.com/stories/1772671">the Trump regime upgrades itself from horrible, incompetent, and corrupt to criminals against humanity</a> (<a href="https://plus.google.com/100003628603413742554/posts/Z2F5mgmZsoa">G+</a>). So by now we already have mass ethnic concentration camps, with announced sizes bigger than the ones for the Japanese in WWII. How long until they become literal death camps and we reach an outright existential threat to the free people of the rest of the world?</p>
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<p><a href="https://mathoverflow.net/q/302034/440">How much smoothness does the tennis ball theorem need?</a> (<a href="https://plus.google.com/100003628603413742554/posts/fW3ydd8CmFT">G+</a>). A follow-up post on MathOverflow to the new Wikipedia article that I linked to a couple weeks ago.</p>
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<p><a href="http://www.neverendingbooks.org/penrose-tiles-in-helsinki">Penrose tiles in Helsinki</a> (<a href="https://plus.google.com/100003628603413742554/posts/LLTz5yRgcnA">G+</a>, <a href="https://plus.google.com/+JukkaSuomela/posts/bCYb9rJXupS">via</a>). Something for the mathematical tourist to see when visiting Helsinki for <a href="http://algo2018.hiit.fi/">ALGO 2018</a> this August. From the via link, <a href="http://simokivela.blogspot.com/2014/08/keskuskadun-penrose.html">here’s a post in Finnish with more detail</a>.</p>
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<p><a href="https://plus.google.com/113086553300459368002/posts/VHy3Tu1GvM6">The Golden Samosa</a> (<a href="https://plus.google.com/100003628603413742554/posts/7sGwE7f8i2D">G+</a>). Greg Egan folds a triangle to maximize the doubly-covered area.</p>
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<p><a href="https://drive.google.com/open?id=1oVk94BCbEXB4Kur8dwNuGcKP7Q8sVYzG">The July–August 2018 issue</a> of the <a href="https://sites.google.com/site/awmmath/awm/newsletter">AWM Newsletter</a> includes the news that Kathryn Mann has been awarded the Birman Research Prize in Topology and Geometry for her work on moduli spaces of group actions on manifolds, and that Pamela Gorkin will be this year’s Falconer lecturer (<a href="https://plus.google.com/100003628603413742554/posts/cQ5kin1FsUD">G+</a>). Also, I have a piece in there about women in mathematics on Wikipedia.</p>
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<p><a href="https://blogs.scientificamerican.com/roots-of-unity/stepping-into-a-three-torus/">Stepping into a Three-Torus</a> (<a href="https://plus.google.com/100003628603413742554/posts/3vLofCaXPwW">G+</a>). I suppose strictly speaking the orbifold you get from mirroring all six sides of a cube isn’t a 3-torus, but a quotient of it. In any case Evelyn Lamb reports on an artistic installation that does this, and the effect on the viewer of being placed within this kind of space.</p>
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<p><a href="https://mickburton.co.uk/2018/05/09/continuous-line-artist-view-of-hakens-gordian-knot/">Continuous Line Artist view of Haken’s Gordian Knot</a> (<a href="https://plus.google.com/100003628603413742554/posts/7hwuECcv43C">G+</a>). Mick Burton, an artist known for drawings that use a single continuous line to create the impression of complex and naturalistic shapes, looks at knot theory, self-overlapping curves, and the visualization of Seifert surfaces.</p>
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<p><a href="http://blog.computationalcomplexity.org/2018/06/hoteling.html">Hoteling</a> (<a href="https://plus.google.com/100003628603413742554/posts/KuzPuKTX3M2">G+</a>, <a href="https://plus.google.com/+LanceFortnow/posts/7RMJMxc66EG">via</a>). Lance Fortnow blogs about “hoteling”, the practice of not giving employees offices or even cubicles or their own desks but instead making them sit at unreserved tables in an open floor plan. He asks: “Would hoteling work in the academic world?”, and immediately answers “Never”. But, when I recently visited the University of Malmö for SWAT, I learned that they do exactly that.</p>
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<p><a href="https://www.theguardian.com/science/political-science/2018/jun/29/elsevier-are-corrupting-open-science-in-europe">EU sets Elsevier as the fox to guard the henhouse of open access</a> (<a href="https://plus.google.com/100003628603413742554/posts/SUgmEBfivpb">G+</a>, <a href="https://news.ycombinator.com/item?id=17429705">via</a>).</p>
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</ul>David EppsteinMelody Yang explains her bubble-blowing craft (G+, via).Copenhagen and the non-Penrose pentagonal paving2018-06-26T13:56:00+00:002018-06-26T13:56:00+00:00https://11011110.github.io/blog/2018/06/26/copenhagen-non-penrose<p>Copenhagen is a city of oddly-shaped spires, but if you look down you might also see something interesting.</p>
<p style="text-align:center"><img src="http://www.ics.uci.edu/~eppstein/pix/copenhagen/Amagertorv-m.jpg" alt="Amagertorv, Copenhagen" style="border-style:solid;border-color:black;" /></p>
<p>This is <a href="https://en.wikipedia.org/wiki/Amagertorv">Amagertorv</a>, one of Copenhagen’s central squares, famous for its <a href="https://en.wikipedia.org/wiki/Stork_Fountain">Stork Fountain</a>. Bjørn Nørgaard’s pavement design, a bit covered in grime after 25 years, is also interesting, with paving stones arranged in neat regular pentagons. When I saw this, I had recently read of <a href="https://plus.google.com/100003628603413742554/posts/LLTz5yRgcnA">Helsinki’s Penrose-tiled pavement</a> and was excited to think that maybe there was a rival Penrose-tiled nordic capital. Could the Amagertorv tiles also be a Penrose tiling? Sadly, no.</p>
<p>The pattern of the tiles becomes clearer if one looks at them from above, say in Google maps’ satellite view.</p>
<p style="text-align:center"><img src="/blog/assets/2018/Amagertorv-from-Google-maps.jpg" alt="Amagertorv, satellite view from Google maps" /></p>
<p>We can already see that the tiling is not aperiodic, but is it necessarily so?
Or maybe the same stones could have been rearranged somehow to form a Penrose tiling? Still, the answer is no.</p>
<p>The paving stones consist of dark triangles and light spacers that, together, form regular pentagons, red stones that form <script type="math/tex">36^\circ</script>–<script type="math/tex">144^\circ</script> rhombi (usually called “diamonds” in the context of Penrose tiling), and several other smaller stones that connect them together into a seamless pavement.</p>
<p style="text-align:center"><img src="/blog/assets/2018/Amagertorv.svg" alt="Pentagon-diamond tiling with 5-way dihedral symmetry" /></p>
<p>The smaller connecting stones force the dark-light pentagons and red diamonds to meet at only two types of vertex: a degree-four vertex with three pentagons and the sharp corner of a diamond, and a degree-three vertex with two pentagons and the acute corner of a diamond.</p>
<p>The Penrose tilings include two tilings with five-fold dihedral symmetry. If we try to replicate the same symmetry with these regular pentagons and diamonds, we must put a pentagon in the center, adjacent to five other pentagons. But once these choices have been made, the whole tiling is fixed: the remaining tiles must spread out in five periodically-tiled wedges from the center, as I have shown above. By leaving a hole at the center of symmetry (covered with the Stork Fountain), Nørgaard found a different symmetric solution, with ten narrower periodically-tiled wedges, but I think this only has cyclic symmetry and not dihedral symmetry. (That is, it is slightly different from its mirror reflection, and so has only the same total number of symmetries as the five-fold tiling.) Because the pentagon and diamond tiles (with their two types of constrained vertices) have no symmetric but aperiodic tiling, they cannot be made to form arbitrary Penrose tilings.</p>
<p style="text-align:center"><img src="/blog/assets/2018/StorkFountain.svg" alt="Pentagon-diamond tiling with 10-way cyclic symmetry and a central hole" /></p>
<p>For more from Copenhagen, see <a href="https://www.ics.uci.edu/~eppstein/pix/copenhagen/">my online gallery</a>, including the glowing nostrils of <a href="Gefion Fountain">Gefjon’s oxen</a>, a <a href="https://en.wikipedia.org/wiki/Nine_Men%27s_Morris">Nine Men’s Morris</a> board built into the corner of the city hall, and an engraving of a Danish king of whom all but the head has been transformed into calligraphy.</p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/dp2RyWmRJ62">G+</a>)</p>David EppsteinCopenhagen is a city of oddly-shaped spires, but if you look down you might also see something interesting.La Maddalena and the non-Reuleaux table2018-06-24T12:07:00+00:002018-06-24T12:07:00+00:00https://11011110.github.io/blog/2018/06/24/la-maddalena-non-reuleaux<p>I recently returned from a trip to Europe, with a one-day stopover in Rome, a visit to La Maddalena (a small resort island between Sardinia and Corsica) for <a href="https://sites.google.com/view/fun2018/">FUN 2018</a>, another stopover in Copenhagen, and a visit to Malmö, Sweden, for <a href="http://csconferences.mah.se/swat2018/index.html">SWAT 2018</a>. I’m still processing photos, but <a href="https://www.ics.uci.edu/~eppstein/pix/lamaddalena/">the first batch, from La Maddalena</a>, is now up.</p>
<p>Despite being annoying to get to (an hour’s drive and another half-hour ferry ride from the nearest minor airport), La Maddalena is a very pleasant place to hold a conference, with a beautiful coastline and great food. The hotel was a little quirky (for instance, no potable water in the taps) and just enough inland to not have an ocean view, but it was still comfortable enough. Here’s what I could see from my hotel room:</p>
<p style="text-align:center"><img src="http://www.ics.uci.edu/~eppstein/pix/lamaddalena/LaNereidi1-m.jpg" alt="The view from La Neireidi, La Maddalena" style="border-style:solid;border-color:black;" /></p>
<p>You might notice the little triangular patio table on the balcony. Like <a href="/blog/2018/04/17/mythical-reuleaux-manhole.html">several other kinds of rounded triangle</a>, this is not a Reuleaux triangle, even if one ignores the rounded-off corners. On a Reuleaux triangle, the tangents to the two circular arcs that meet at a vertex would form <script type="math/tex">120^\circ</script> angles; here, the angle seems somewhat acute. And the distance from corner to corner is noticably larger than the distance from a corner to the middle of the opposite side. It’s clearer in a top view:</p>
<p style="text-align:center"><img src="/blog/assets/2018/non-reuleaux-table.jpg" alt="Top view of the non-Reuleaux table, compared to a right circular triangle" /></p>
<p>Notice how much more room there is on the top and bottom margins of the square frame than on the left and right. I’ve superimposed a circular triangle with right-angled corners (also not Reuleaux) to show that the sides of the table are even a little bit straighter than the superimposed triangle. I’m not sure whether they’re circular arcs or some other curve, but if they are circular I’d guess they span only about a <script type="math/tex">20^\circ</script> arc, compared to <script type="math/tex">30^\circ</script> for the superimposed triangle.</p>
<p><a href="https://www.ics.uci.edu/~eppstein/pix/lamaddalena/">The rest of the gallery</a> is less about furniture geometry and more about pretty views, so check it out. The one below is from the end of the conference excursion, a boat trip to some nearby islands.</p>
<p style="text-align:center"><img src="http://www.ics.uci.edu/~eppstein/pix/lamaddalena/SunsetJetty-m.jpg" alt="La Maddalena at sunset" style="border-style:solid;border-color:black;" /></p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/Afocmn7aUBc">G+</a>)</p>David EppsteinI recently returned from a trip to Europe, with a one-day stopover in Rome, a visit to La Maddalena (a small resort island between Sardinia and Corsica) for FUN 2018, another stopover in Copenhagen, and a visit to Malmö, Sweden, for SWAT 2018. I’m still processing photos, but the first batch, from La Maddalena, is now up.