171 (number)

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

← 170 171 172 →
Cardinalone hundred seventy-one
Ordinal171st
(one hundred seventy-first)
Factorization32 × 19
Divisors1, 3, 9, 19, 57, 171
Greek numeralΡΟΑ´
Roman numeralCLXXI
Binary101010112
Ternary201003
Octal2538
Duodecimal12312
HexadecimalAB16

In mathematicsEdit

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]

See alsoEdit

ReferencesEdit

  1. ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A001045 (Jacobsthal sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A006905 (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.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A007569 (Number of nodes in regular n-gon with all diagonals drawn)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.