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Smale's problems are a list of 18 challenging problems for the twenty-first century proposed by Field medalist Steven Smale. These problems were inspired in part by Hilbert's ...

Taking a connected graph or network with a high graph diameter and adding a very small number of edges randomly, the diameter tends to drop drastically. This is known as the ...

The snub cubical graph is the Archimedean graph on 24 nodes and 60 edges obtained by taking the skeleton of the snub cube. It is a quintic graph, is planar, Hamiltonian, and ...

The snub dodecahedral graph is a quintic graph on 60 nodes and 150 edges that corresponds to the skeleton of the snub dodecahedron, great inverted snub icosidodecahedron, ...

While early soccer balls were constructed in a number of ways, a fairly stadard 32-panel ball was designed by Danish national team goalkeeer Eigil Nielsen in 1962. This was ...

The Soifer graph, illustrated above in a number of embeddings, is a planar graph on 9 nodes that tangles the Kempe chains in Kempe's algorithm and thus provides an example of ...

The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. ...

"The" square graphs is the cycle graph C_4. It is isomorphic to the complete bipartite graph K_(2,2). Like all cycle graphs, the line graph of C_4 is isomorphic to itself. A ...

There are a number of interesting results related to the tiling of squares. For example, M. Laczkovich has shown that there are exactly three shapes of non-right triangles ...

A "square" word consists of two identical adjacent subwords (for example, acbacb). A squarefree word contains no square words as subwords (for example, abcacbabcb). The only ...