174 (number)

← 173 174 175 →
← 170 171 172 173 174 175 176 177 178 179 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
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, 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.

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 ${\displaystyle 3\times 3}$ (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]}

See also

• All pages with titles containing 174

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.