174 (number)

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.^[1] There are 174 invertible ${\displaystyle 3\times 3}$ (0,1)-matrices.^[2][3] 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.^[4]

The Mordell curve ${\displaystyle y^{2}=x^{3}-174}$ has rank three, and 174 is the smallest positive integer for which ${\displaystyle y^{2}=x^{3}-k}$ has this rank. The corresponding number for curves ${\displaystyle y^{2}=x^{3}+k}$ is 113.^[5][6]

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