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The Fields Medals are commonly regarded as mathematics' closest analog to the Nobel Prize (which does not exist in mathematics), and are awarded every four years by the ...

A flexagon-like structure created by connecting the ends of a strip of four squares after folding along 45 degrees diagonals. Using a number of folding movements, it is ...

A graceful permutation sigma on n letters is a permutation such that {|sigma(i)-sigma(i+1)|:i=1,2,...,n-1}={1,2,...,n-1}. For example, there are four graceful permutations on ...

The polyhedron compound of the great icosahedron (U_(53)) and the small stellated dodecahedron (U_(34)), sometimes known as the great cid. Four faces meet at each edge of the ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the incircle (with center I) and the A-excircle (with center J_A). Of these, three correspond to the ...

A Jordan curve is a plane curve which is topologically equivalent to (a homeomorphic image of) the unit circle, i.e., it is simple and closed. It is not known if every Jordan ...

There are four fixed points (mod 1) of Minkowski's question mark function ?(x), namely x=0, 1/2, f and 1-f, where f<1/2 is a constant known as the Minkowski-Bower constant ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

The maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of ...

It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...