174 (number)

Template:Infobox number 174 (one hundred [and] seventy-four) is the natural number following 173 and preceding 175.

In mathematics

There are 174 7-crossing semi-meanders, ways of arranging a semi-infinite curve in the plane so that it crosses a straight line seven times. There are 174 invertible $3\times 3$ (0,1)-matrices. There are also 174 combinatorially distinct ways of subdividing a topological cuboid into a mesh of tetrahedra, without adding extra vertices, although not all can be represented geometrically by flat-sided polyhedra.

The Mordell curve $y^2=x^3-174$ has rank three, and 174 is the smallest positive integer for which $y^2=x^3-k$ has this rank. The corresponding number for curves $y^2=x^3+k$ is 113.

See also

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