Visual Insight
https://blogs.ams.org/visualinsight
Mathematics Made VisibleThu, 08 Feb 2018 23:14:33 +0000en-UShourly1https://wordpress.org/?v=4.9.559802484Chmutov Octic
https://blogs.ams.org/visualinsight/2017/01/01/chmutov-octic/
https://blogs.ams.org/visualinsight/2017/01/01/chmutov-octic/#commentsSun, 01 Jan 2017 01:00:42 +0000http://blogs.ams.org/visualinsight/?p=3006octic surface is one defined by a polynomial equation of degree 8. This image by Abdelaziz Nait Merzouk shows an octic discovered by Chmutov with 154 real ordinary double points or nodes: that is, points where it looks like the origin of the cone in 3-dimensional space defined by $x^2 + y^2 = z^2$.]]>https://blogs.ams.org/visualinsight/2017/01/01/chmutov-octic/feed/23006Romik’s Ambidextrous Sofa
https://blogs.ams.org/visualinsight/2016/12/15/romiks-ambidextrous-sofa/
https://blogs.ams.org/visualinsight/2016/12/15/romiks-ambidextrous-sofa/#respondThu, 15 Dec 2016 01:00:32 +0000http://blogs.ams.org/visualinsight/?p=2978ambidextrous moving sofa problem is to find the planar shape of maximal area that can negotiate right-angled turns both to the right and to the left in a hallway of width 1. The current best known solution was found by Dan Romik, and is shown here. ]]>https://blogs.ams.org/visualinsight/2016/12/15/romiks-ambidextrous-sofa/feed/02978Truncated {6,3,3} Honeycomb
https://blogs.ams.org/visualinsight/2016/12/01/truncated-633-honeycomb/
https://blogs.ams.org/visualinsight/2016/12/01/truncated-633-honeycomb/#respondThu, 01 Dec 2016 01:00:05 +0000http://blogs.ams.org/visualinsight/?p=2939truncated {6,3,3} honeycomb in hyperbolic space.
]]>https://blogs.ams.org/visualinsight/2016/12/01/truncated-633-honeycomb/feed/02939Bunimovich Stadium
https://blogs.ams.org/visualinsight/2016/11/15/bunimovich-stadium/
https://blogs.ams.org/visualinsight/2016/11/15/bunimovich-stadium/#commentsTue, 15 Nov 2016 01:00:34 +0000http://blogs.ams.org/visualinsight/?p=2945https://blogs.ams.org/visualinsight/2016/11/15/bunimovich-stadium/feed/22945Escudero Nonic
https://blogs.ams.org/visualinsight/2016/11/01/escudero-nonic/
https://blogs.ams.org/visualinsight/2016/11/01/escudero-nonic/#respondTue, 01 Nov 2016 01:00:23 +0000http://blogs.ams.org/visualinsight/?p=2909nonic surface is one defined by a polynomial equation of degree 9. This image by Juan García Escudero shows a nonic surface called \(Q_9\), which has 220 real ordinary double points: that is, points where it looks like the origin of the cone in 3-dimensional space defined by \(x^2 + y^2 = z^2\).]]>https://blogs.ams.org/visualinsight/2016/11/01/escudero-nonic/feed/02909Laves Graph
https://blogs.ams.org/visualinsight/2016/10/15/laves-graph/
https://blogs.ams.org/visualinsight/2016/10/15/laves-graph/#respondSat, 15 Oct 2016 01:00:44 +0000http://blogs.ams.org/visualinsight/?p=2895Greg Egan shows the Laves graph, a structure discovered by the crystallographer Fritz Laves in 1932. It is also called the '\(\mathrm{K}_4\) crystal', since is an embedding of the maximal abelian cover of the complete graph on 4 vertices in 3-dimensional Euclidean space. It is also called the 'triamond', since it is a theoretically possible — but never yet seen — crystal structure for carbon. ]]>https://blogs.ams.org/visualinsight/2016/10/15/laves-graph/feed/02895Diamond Cubic
https://blogs.ams.org/visualinsight/2016/10/01/diamond-cubic/
https://blogs.ams.org/visualinsight/2016/10/01/diamond-cubic/#commentsSat, 01 Oct 2016 01:00:15 +0000http://blogs.ams.org/visualinsight/?p=2845Greg Egan shows the pattern of carbon atoms in a diamond, called the diamond cubic. Each atom is bonded to four neighbors. This pattern is found not just in carbon but also other elements in the same column of the periodic table: silicon, germanium, and tin. ]]>https://blogs.ams.org/visualinsight/2016/10/01/diamond-cubic/feed/12845Togliatti Quintic
https://blogs.ams.org/visualinsight/2016/09/15/togliatti-quintic-surface/
https://blogs.ams.org/visualinsight/2016/09/15/togliatti-quintic-surface/#respondThu, 15 Sep 2016 01:00:55 +0000http://blogs.ams.org/visualinsight/?p=2833quintic surface is one defined by a polynomial equation of degree 5. A nodal surface is one whose only singularities are ordinary double points: that is, points where it looks like the origin of the cone in 3-dimensional space defined by \(x^2 + y^2 = z^2\). A Togliatti surface is a quintic nodal surface with the largest possible number of ordinary double points, namely 31. Here Abdelaziz Nait Merzouk has drawn the real points of a Togliatti surface.]]>https://blogs.ams.org/visualinsight/2016/09/15/togliatti-quintic-surface/feed/02833Kummer Quartic
https://blogs.ams.org/visualinsight/2016/09/01/kummers-quartic-surface/
https://blogs.ams.org/visualinsight/2016/09/01/kummers-quartic-surface/#respondThu, 01 Sep 2016 01:00:46 +0000http://blogs.ams.org/visualinsight/?p=2813quartic surface is one defined by a polynomial equation of degree 4. An ordinary double point is a point where a surface looks like the origin of the cone in 3-dimensional space defined by $x^2 + y^2 = z^2$. The Kummer surfaces are the quartic surfaces with the largest possible number of ordinary double points, namely 16. This picture by Abdelaziz Nait Merzouk shows the real points of a Kummer surface.]]>https://blogs.ams.org/visualinsight/2016/09/01/kummers-quartic-surface/feed/02813Cayley’s Nodal Cubic Surface
https://blogs.ams.org/visualinsight/2016/08/15/cayleys-nodal-cubic-surface/
https://blogs.ams.org/visualinsight/2016/08/15/cayleys-nodal-cubic-surface/#commentsMon, 15 Aug 2016 01:00:49 +0000http://blogs.ams.org/visualinsight/?p=2791cubic surface is one defined by a polynomial equation of degree 3. Cayley's nodal cubic surface, drawn above by Abdelaziz Nait Merzouk, is the cubic surface with the largest possible number of ordinary double points and no other singularities: that is, points where it looks like the origin of the cone in 3-dimensional space defined by \(x^2 + y^2 = z^2\). It has 4 ordinary double points, shown here at the vertices of a regular tetrahedron.]]>https://blogs.ams.org/visualinsight/2016/08/15/cayleys-nodal-cubic-surface/feed/22791