75 (seventy-five) is the natural number following 74 and preceding 76.
75 is the fourth ordered Bell number, and counts the number of weak orderings on a set of four items.
As the sum of the first five pentagonal numbers, 75 is a pentagonal pyramidal number. It is also an enneagonal number.
It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7, 5, 12, 17, 29, 46, 75... But there is no integer that added up to its own digits adds up to 75, hence 75 is a self number.
Excluding the infinite sets, there are 75 uniform polyhedra (or 76 if edges are allowed to coincide).
In other fields
Seventy-five is also:
- ^ “Who are our senators and what do they do?”, Parliament of Canada, retrieved 2014-02-02.