174 (number)

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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
Senary 4506
Octal 2568
Duodecimal 12612
Hexadecimal AE16

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

Contents

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 (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 has rank three, and 174 is the smallest positive integer for which has this rank. The corresponding number for curves 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

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References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA000682(Semi-meanders: number of ways a semi-infinite directed curve can cross a straight line n times)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA055165(Number of invertible n X n matrices with entries equal to 0 or 1)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. ↑ Živković, Miodrag (2006). "Classification of small (0,1) matrices". Linear Algebra and Its Applications. 414 (1): 310–346. arXiv: math/0511636 . doi:10.1016/j.laa.2005.10.010. MR   2209249.
  4. ↑ 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. arXiv: 1801.01288 . doi:10.1145/3272127.3275037. S2CID   54136193.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA031508(Smallest k>0 such that the elliptic curve y^2 = x^3 - k has rank n, if k exists)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. ↑ Gebel, J.; Pethö, A.; Zimmer, H. G. (1998). "On Mordell's equation". Compositio Mathematica. 110 (3): 335–367. doi: 10.1023/A:1000281602647 . MR   1602064. S2CID   122592480. See table, p. 352.
  7. ↑ Schaeffer, Jonathan (March 2005). "Solving checkers: first result". ICGA Journal. 28 (1): 32–36. doi:10.3233/icg-2005-28107.
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