75 (seventy-five) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
following
74 and preceding
76.
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In mathematics
75 is a
self number
In number theory, a self number or Devlali number in a given number base b is a natural number that cannot be written as the sum of any other natural number n and the individual digits of n. 20 is a self number (in base 10), because no such combina ...
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 and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The ...
s, and therefore a
pentagonal pyramidal number A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an -sided polygon of points. ...
, as well as a
nonagonal number A nonagonal number (or an enneagonal number) is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the constr ...
.
It is also the fourth
ordered Bell number
In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the number of weak orderings on a set of ''n'' elements (orderings of the elements into a sequence allowing ties, such as might arise as the outcome ...
, and a
Keith number
In number theory, 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 digits of n and ...
, because it recurs in a
Fibonacci
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Wester ...
-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 of the Hindu–Arabic numer ...
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, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered ...
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 s ...
s, there are 75
uniform polyhedra
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent.
Uniform polyhedra may be regular (if also ...
in the third dimension, which incorporate
star polyhedra as well. Inclusive of 7 families of
prisms and
antiprisms
In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation .
Antiprisms are a subclass o ...
, there are also 75
uniform compound polyhedra.
In other fields
Seventy-five is:
*The atomic number of
rhenium
Rhenium is a chemical element with the symbol Re and atomic number 75. It is a silvery-gray, heavy, third-row transition metal in group 7 of the periodic table. With an estimated average concentration of 1 part per billion (ppb), rhenium is one ...
*The age limit for
Canadian senator
The Senate of Canada (french: region=CA, Sénat du Canada) is the upper house of the Parliament of Canada. Together with the Crown and the House of Commons, they comprise the bicameral legislature of Canada.
The Senate is modelled after the Bri ...
s
“Who are our senators and what do they do?”
Parliament of Canada, retrieved 2014-02-02.
*A common name for the Canon de 75 modèle 1897
The French 75 mm field gun was a quick-firing field artillery piece adopted in March 1898. Its official French designation was: Matériel de 75mm Mle 1897. It was commonly known as the French 75, simply the 75 and Soixante-Quinze (Frenc ...
, a French World War I gun
*The department number of the city of Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...
*The number of balls in a standard game of Bingo
Bingo or B-I-N-G-O may refer to:
Arts and entertainment Gaming
* Bingo, a game using a printed card of numbers
** Bingo (British version), a game using a printed card of 15 numbers on three lines; most commonly played in the UK and Ireland
** Bi ...
in the United States
References
{{Integers, zero
Integers