75 (seventy-five) is the natural number following 74 and preceding 76.
In mathematics
75 is a self number because there is no integer that added up to its own digits adds up to 75.[1] It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number, as well as a nonagonal number.[2][3]
It is also the fourth ordered Bell number, and a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7, 5, 12, 17, 29, 46, 75...[4]
75 is the count of the number of weak orderings on a set of four items.[5]
Excluding the infinite sets, there are 75 uniform polyhedra in the third dimension, which incorporate star polyhedra as well. Inclusive of 7 families of prisms and antiprisms, there are also 75 uniform compound polyhedra.
In other fields
Seventy-five is:
- The atomic number of rhenium
- The age limit for Canadian senators[6]
- A common name for the Canon de 75 modèle 1897, a French World War I gun
- The department number of the city of Paris
- The number of balls in a standard game of Bingo in the United States
References
- ^ Sloane, N. J. A. (ed.). "Sequence A003052". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001106". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002411". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007629". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000670". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ “Who are our senators and what do they do?”, Parliament of Canada, retrieved 2014-02-02.