75 (seventy-five) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
74 and preceding
76.
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In mathematics
75 is a
self number because there is no integer that added up to its own digits adds up to 75. It is the sum of the first five
pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular number, triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotational ...
s, and therefore a
pentagonal pyramidal number, as well as a
nonagonal number.
It is also the fourth
ordered Bell number, and a
Keith number
In recreational mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number n in a given number base b with k digits such that when a sequence is created such that the first k terms are the k d ...
, because it recurs in a
Fibonacci
Leonardo Bonacci ( – ), commonly known as Fibonacci, was an Italians, Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".
The name he is commonly called, ''Fibonacci ...
-like sequence started from its
base 10
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of t ...
digits:
7,
5,
12,
17,
29,
46, 75...
75 is the count of the number of
weak ordering
In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set (mathematics), set, some of whose members may be Tie (draw), tied with each other. Weak orders are a general ...
s on a set of four items.
Excluding the
infinite set
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.
Properties
The set of natural numbers (whose existence is postulated by the axiom of infinity) is infinite. It is the only set ...
s, there are 75
uniform polyhedra
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows that all vertices are congruent. Uniform polyhedra may be regular (if also fac ...
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
Integers
{{Num-stub