171 (number)

Last updated
170 171 172
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, clxxi
Binary 101010112
Ternary 201003
Senary 4436
Octal 2538
Duodecimal 12312
Hexadecimal AB16

171 (one hundred [and] seventy-one) is the natural number following 170 and preceding 172.

Contents

In mathematics

171 is the 18th 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 is defined as having cyclic groups ⟩ that are linked with the function,

where is the character of at .

This generates 171 moonshine groups within associated with that are principal moduli for different genus zero congruence groups commensurable with the projective linear group . [7]

See also

References

  1. Sloane, N. J. A. (ed.). "SequenceA000217(Triangular numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. Sloane, N. J. A. (ed.). "SequenceA001045(Jacobsthal sequence)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. Sloane, N. J. A. (ed.). "SequenceA006905(Number of transitive relations on n labeled nodes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  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.). "SequenceA007569(Number of nodes in regular n-gon with all diagonals drawn)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. McMullen, Peter; Schulte, Egon (2002). Abstract Regular Polytopes. Encyclopedia of Mathematics and its Applications. Vol. 92. Cambridge: Cambridge University Press. pp. 185–186, 502. doi:10.1017/CBO9780511546686. ISBN   0-521-81496-0. MR   1965665. S2CID   115688843.
  7. Conway, John; Mckay, John; Sebbar, Abdellah (2004). "On the Discrete Groups of Moonshine" (PDF). Proceedings of the American Mathematical Society. 132 (8): 2233. doi: 10.1090/S0002-9939-04-07421-0 . eISSN   1088-6826. JSTOR   4097448. S2CID   54828343.