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.

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A003052". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A001106". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A002411". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A007629". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A000670". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.


Allikas: https://en.wikipedia.org/wiki/75_(number)
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