171 (number)
| ||||
|---|---|---|---|---|
| Cardinal | one hundred seventy-one | |||
| Ordinal | 171st (one hundred seventy-first) | |||
| Factorization | 32 × 19 | |||
| Divisors | 1, 3, 9, 19, 57, 171 | |||
| Greek numeral | ΡΟΑ´ | |||
| Roman numeral | CLXXI | |||
| Binary | 101010112 | |||
| Ternary | 201003 | |||
| Quaternary | 22234 | |||
| Quinary | 11415 | |||
| Senary | 4436 | |||
| Octal | 2538 | |||
| Duodecimal | 12312 | |||
| Hexadecimal | AB16 | |||
| Vigesimal | 8B20 | |||
| Base 36 | 4R36 | |||
171 (one hundred [and] seventy-one) is the natural number following 170 and preceding 172.
In mathematics
171 is a triangular number[1] and a Jacobsthal number.[2]
There are 171 transitive relations on three labeled elements,[3] and 171 combinatorially distinct ways of subdividing a cuboid by flat cuts into a mesh of tetrahedra, without adding extra vertices.[4]
The diagonals of a regular decagon meet at 171 points, including both crossings and the vertices of the decagon.[5]
There are 171 faces and edges in the 57-cell, an abstract 4-polytope with hemi-dodecahedral cells that is its own dual polytope.[6]
Within moonshine theory of sporadic groups, the friendly giant [math]\displaystyle{ \mathbb {M} }[/math] is defined as having cyclic groups ⟨ [math]\displaystyle{ m }[/math] ⟩ that are linked with the function,
- [math]\displaystyle{ f_{m}(\tau) = q^{-1} + a_{1}q + a_{2}q^{2} + ... , \text{ } a_{k} }[/math] ∈ [math]\displaystyle{ \mathbb{Z}, \text{ } q = e^{2\pi i \tau}, \text{ } \tau\gt 0; }[/math] where [math]\displaystyle{ q }[/math] is the character of [math]\displaystyle{ \mathbb {M} }[/math] at [math]\displaystyle{ m }[/math].
This generates 171 moonshine groups within [math]\displaystyle{ \mathbb {M} }[/math] associated with [math]\displaystyle{ f_{m} }[/math] that are principal moduli for different genus zero congruence groups commensurable with the projective linear group [math]\displaystyle{ \operatorname{PSL_2}(\mathbb{Z}) }[/math].[7]
See also
- The year AD 171 or 171 BC
- List of highways numbered 171
- All pages with titles containing 171
References
- ↑ Sloane, N. J. A., ed. "Sequence A000217 (Triangular numbers)". OEIS Foundation. https://oeis.org/A000217.
- ↑ Sloane, N. J. A., ed. "Sequence A001045 (Jacobsthal sequence)". OEIS Foundation. https://oeis.org/A001045.
- ↑ Sloane, N. J. A., ed. "Sequence A006905 (Number of transitive relations on n labeled nodes)". OEIS Foundation. https://oeis.org/A006905.
- ↑ 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 A007569 (Number of nodes in regular n-gon with all diagonals drawn)". OEIS Foundation. https://oeis.org/A007569.
- ↑ McMullen, Peter; Schulte, Egon (2002). Abstract Regular Polytopes. Encyclopedia of Mathematics and its Applications. 92. Cambridge: Cambridge University Press. pp. 185–186, 502. doi:10.1017/CBO9780511546686. ISBN 0-521-81496-0. https://books.google.com/books?id=JfmlMYe6MJgC&pg=PA185.
- ↑ Conway, John; Mckay, John; Sebbar, Abdellah (2004). "On the Discrete Groups of Moonshine". Proceedings of the American Mathematical Society 132 (8): 2233. doi:10.1090/S0002-9939-04-07421-0. https://www.ams.org/journals/proc/2004-132-08/S0002-9939-04-07421-0/S0002-9939-04-07421-0.pdf.
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