174 (number)
| ||||
|---|---|---|---|---|
| Cardinal | one hundred seventy-four | |||
| Ordinal | 174th (one hundred seventy-fourth) | |||
| Factorization | 2 × 3 × 29 | |||
| Divisors | 1, 2, 3, 6, 29, 58, 87, 174 | |||
| Greek numeral | ΡΟΔ´ | |||
| Roman numeral | CLXXIV | |||
| Binary | 101011102 | |||
| Ternary | 201103 | |||
| Quaternary | 22324 | |||
| Quinary | 11445 | |||
| Senary | 4506 | |||
| Octal | 2568 | |||
| Duodecimal | 12612 | |||
| Hexadecimal | AE16 | |||
| Vigesimal | 8E20 | |||
| Base 36 | 4U36 | |||
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.[1] There are 174 invertible [math]\displaystyle{ 3\times 3 }[/math] (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 [math]\displaystyle{ y^2=x^3-174 }[/math] has rank three, and 174 is the smallest positive integer for which [math]\displaystyle{ y^2=x^3-k }[/math] has this rank. The corresponding number for curves [math]\displaystyle{ y^2=x^3+k }[/math] is 113.[5][6]
In other fields
In English draughts or checkers, a common variation is the "three-move restriction", in which the first three moves by both players are chosen at random. There are 174 different choices for these moves, although some systems for choosing these moves further restrict them to a subset that is believed to lead to an even position.[7]
See also
- The year AD 174 or 174 BC
- List of highways numbered 174
- All pages with titles containing 174
References
- ↑ Sloane, N. J. A., ed. "Sequence A000682 (Semi-meanders: number of ways a semi-infinite directed curve can cross a straight line n times)". OEIS Foundation. https://oeis.org/A000682.
- ↑ Sloane, N. J. A., ed. "Sequence A055165 (Number of invertible n X n matrices with entries equal to 0 or 1)". OEIS Foundation. https://oeis.org/A055165.
- ↑ Živković, Miodrag (2006). "Classification of small (0,1) matrices". Linear Algebra and Its Applications 414 (1): 310–346. doi:10.1016/j.laa.2005.10.010.
- ↑ Pellerin, Jeanne; Verhetsel, Kilian; Remacle, Jean-François (December 2018). "There are 174 subdivisions of the hexahedron into tetrahedra". ACM Transactions on Graphics 37 (6): 1–9. doi:10.1145/3272127.3275037.
- ↑ Sloane, N. J. A., ed. "Sequence A031508 (Smallest k>0 such that the elliptic curve y^2 = x^3 - k has rank n, if k exists)". OEIS Foundation. https://oeis.org/A031508.
- ↑ Gebel, J.; Pethö, A.; Zimmer, H. G. (1998). "On Mordell's equation". Compositio Mathematica 110 (3): 335–367. doi:10.1023/A:1000281602647. See table, p. 352.
- ↑ Schaeffer, Jonathan (March 2005). "Solving checkers: first result". ICGA Journal 28 (1): 32–36. doi:10.3233/icg-2005-28107.
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