174 (number)
title: "174 (number)" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["integers"] topic_path: "general/integers" source: "https://en.wikipedia.org/wiki/174_(number)" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::data[format=table title="Infobox number"]
| Field | Value |
|---|---|
| number | 174 |
| divisor | 1, 2, 3, 6, 29, 58, 87, 174 |
| :: |
| number = 174 | divisor=1, 2, 3, 6, 29, 58, 87, 174 174 (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. There are 174 invertible 3\times 3 (0,1)-matrices.{{cite journal | last = Živković | first = Miodrag | arxiv = math/0511636 | doi = 10.1016/j.laa.2005.10.010 | issue = 1 | journal = Linear Algebra and Its Applications | mr = 2209249 | pages = 310–346 | title = Classification of small (0,1) matrices | volume = 414 | year = 2006}} 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.{{cite journal | last1 = Pellerin | first1 = Jeanne | last2 = Verhetsel | first2 = Kilian | last3 = Remacle | first3 = Jean-François | arxiv = 1801.01288 | date = December 2018 | doi = 10.1145/3272127.3275037 | issue = 6 | journal = ACM Transactions on Graphics | pages = 1–9 | title = There are 174 subdivisions of the hexahedron into tetrahedra | volume = 37| s2cid = 54136193
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.{{cite journal | last1 = Gebel | first1 = J. | last2 = Pethö | first2 = A. | last3 = Zimmer | first3 = H. G. | doi = 10.1023/A:1000281602647 | issue = 3 | journal = Compositio Mathematica | mr = 1602064 | pages = 335–367 | title = On Mordell's equation | volume = 110 | year = 1998| s2cid = 122592480 | doi-access = free
References
References
- {{cite OEIS. A000682. Semi-meanders: number of ways a semi-infinite directed curve can cross a straight line n times
- {{cite OEIS. A055165. Number of invertible n X n matrices with entries equal to 0 or 1
- {{cite OEIS. A031508
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