174_(number) Knowpia

← 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 $3\times 3$ (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 $y^{2}=x^{3}-174$ 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.^[5]^[6]

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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A055165 (Number of invertible n X n matrices with entries equal to 0 or 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ 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.
^ 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.
^ 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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ 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.

[1] Sloane, N. J. A. (ed.). "Sequence A000682 (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.). "Sequence A055165 (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.). "Sequence A031508 (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.

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Summary

In mathematics

See also

References