Visual Insight
http://blogs.ams.org/visualinsight
Mathematics Made VisibleTue, 01 Sep 2015 06:39:50 +0000en-UShourly1http://wordpress.org/?v=4.2.4Hypercube of Duads
http://blogs.ams.org/visualinsight/2015/09/01/hypercube-of-duads/
http://blogs.ams.org/visualinsight/2015/09/01/hypercube-of-duads/#commentsTue, 01 Sep 2015 01:00:41 +0000http://blogs.ams.org/visualinsight/?p=1879http://blogs.ams.org/visualinsight/2015/09/01/hypercube-of-duads/feed/0Tutte–Coxeter Graph
http://blogs.ams.org/visualinsight/2015/08/15/tutte-coxeter-graph/
http://blogs.ams.org/visualinsight/2015/08/15/tutte-coxeter-graph/#commentsSat, 15 Aug 2015 01:00:53 +0000http://blogs.ams.org/visualinsight/?p=1752Tutte--Coxeter graph. This graph was discovered by the famous graph theorist William Thomas Tutte in 1947, but its remarkable properties were studied further by him and the geometer H. S. M. Coxeter in a pair of papers published in 1958.]]>http://blogs.ams.org/visualinsight/2015/08/15/tutte-coxeter-graph/feed/0Heawood Graph
http://blogs.ams.org/visualinsight/2015/08/01/heawood-graph/
http://blogs.ams.org/visualinsight/2015/08/01/heawood-graph/#commentsSat, 01 Aug 2015 01:00:54 +0000http://blogs.ams.org/visualinsight/?p=1747Heawood graph. This graph can be drawn on a torus with no edges crossing in such a way that it divides the torus into 7 hexagons, each pair of which shares an edge. In 1890, Percy John Heawood proved that for any map drawn on a torus, it takes at most 7 colors to ensure that no two countries sharing a common boundary have the same color. The Heawood graph proves that the number 7 is optimal.]]>http://blogs.ams.org/visualinsight/2015/08/01/heawood-graph/feed/2Dyck Words
http://blogs.ams.org/visualinsight/2015/07/15/dyck-words/
http://blogs.ams.org/visualinsight/2015/07/15/dyck-words/#commentsWed, 15 Jul 2015 01:00:17 +0000http://blogs.ams.org/visualinsight/?p=1719Tilman Piesk shows the 14 Dyck words of length 8. A Dyck word is a balanced string of left and parentheses. In the picture, a left parenthesis is shown as upward-slanting line segment, and a right parenthesis as a downward-slanting one. ]]>http://blogs.ams.org/visualinsight/2015/07/15/dyck-words/feed/0Petersen Graph
http://blogs.ams.org/visualinsight/2015/07/01/petersen-graph/
http://blogs.ams.org/visualinsight/2015/07/01/petersen-graph/#commentsWed, 01 Jul 2015 01:00:44 +0000http://blogs.ams.org/visualinsight/?p=1702Petersen graph. ]]>http://blogs.ams.org/visualinsight/2015/07/01/petersen-graph/feed/0Lattice of Partitions
http://blogs.ams.org/visualinsight/2015/06/15/lattice-of-partitions/
http://blogs.ams.org/visualinsight/2015/06/15/lattice-of-partitions/#commentsMon, 15 Jun 2015 01:00:11 +0000http://blogs.ams.org/visualinsight/?p=1673Tilman Piesk shows the 15 partitions of a 4-element set, ordered by refinement. Finer partitions are connected to coarser ones by lines going down. In the finest partition, on top, each of the 4 elements is in its own subset. In the coarsest one, on bottom, all 4 elements are in the same subset.]]>http://blogs.ams.org/visualinsight/2015/06/15/lattice-of-partitions/feed/2Harmonic Orbit
http://blogs.ams.org/visualinsight/2015/06/01/harmonic-orbit/
http://blogs.ams.org/visualinsight/2015/06/01/harmonic-orbit/#commentsMon, 01 Jun 2015 01:00:49 +0000http://blogs.ams.org/visualinsight/?p=1637Kepler problem concerns a particle moving under the influence of gravity, like a planet moving around the Sun. Newton showed the orbit of such a particle is an ellipse, assuming it doesn't fly off to infinity. There are many ways to prove this, but the most illuminating is to reparametrize time and think of the orbit as a circle in 4 dimensions. When the circle is projected down to 3-dimensional space, it becomes an ellipse. The animation in this post, created by Greg Egan, shows how this works. ]]>http://blogs.ams.org/visualinsight/2015/06/01/harmonic-orbit/feed/2Dodecahedron With 5 Tetrahedra
http://blogs.ams.org/visualinsight/2015/05/15/dodecahedron-with-5-tetrahedra/
http://blogs.ams.org/visualinsight/2015/05/15/dodecahedron-with-5-tetrahedra/#commentsFri, 15 May 2015 01:00:12 +0000http://blogs.ams.org/visualinsight/?p=1611Greg Egan shows 5 ways to inscribe a regular tetrahedron in a regular dodecahedron. The union of all these is a nonconvex polyhedron called the compound of 5 tetrahedra, first described by Edmund Hess in 1876.]]>http://blogs.ams.org/visualinsight/2015/05/15/dodecahedron-with-5-tetrahedra/feed/0Twin Dodecahedra
http://blogs.ams.org/visualinsight/2015/05/01/twin-dodecahedra/
http://blogs.ams.org/visualinsight/2015/05/01/twin-dodecahedra/#commentsFri, 01 May 2015 01:00:14 +0000http://blogs.ams.org/visualinsight/?p=1483Greg Egan has drawn two regular dodecahedra, in red and blue. They share 8 corners—and these are the corners of a cube, shown in green. Adrian Ocneanu calls these twin dodecahedra, and has proved some fascinating results about them.]]>http://blogs.ams.org/visualinsight/2015/05/01/twin-dodecahedra/feed/8Sphere in Mirrored Spheroid
http://blogs.ams.org/visualinsight/2015/04/15/sphere-in-mirrored-spheroid/
http://blogs.ams.org/visualinsight/2015/04/15/sphere-in-mirrored-spheroid/#commentsWed, 15 Apr 2015 01:00:41 +0000http://blogs.ams.org/visualinsight/?p=1461spheroid is an ellipsoid with an axis of rotational symmetry. This image created by John Valentine shows a sphere inside a mirrored spheroid, reflected almost endlessly. ]]>http://blogs.ams.org/visualinsight/2015/04/15/sphere-in-mirrored-spheroid/feed/5