Английская Википедия:171 (number)
Шаблон:Infobox number 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>\mathbb {M}</math> is defined as having cyclic groups ⟨ <math>m</math> ⟩ that are linked with the function,
- <math>f_{m}(\tau) = q^{-1} + a_{1}q + a_{2}q^{2} + ... , \text{ } a_{k}</math> ∈ <math>\mathbb{Z}, \text{ } q = e^{2\pi i \tau}, \text{ } \tau>0;</math> where <math>q</math> is the character of <math>\mathbb {M}</math> at <math>m</math>.
This generates 171 moonshine groups within <math>\mathbb {M}</math> associated with <math>f_{m}</math> that are principal moduli for different genus zero congruence groups commensurable with the projective linear group <math>\operatorname{PSL_2}(\mathbb{Z})</math>.[7]
See also
- The year AD 171 or 171 BC
- List of highways numbered 171
- Шаблон:In title
References
Шаблон:Reflist Шаблон:Integers