232 (two hundred ndthirty-two) 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 231 and preceding

233 __NOTOC__ Year 233 ( CCXXXIII) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Claudius and Paternus (or, less frequently, year 986 ...

In mathematics

232 is both a central polygonal number and a

cake number In mathematics, the cake number, denoted by ''Cn'', is the maximum of the number of regions into which a 3-dimensional cube can be partitioned by exactly ''n'' planes. The cake number is so-called because one may imagine each partition of the cu ...

. It is both a

decagonal number A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of decagonal number ...

and a centered 11-gonal number. It is also a

refactorable number A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n. The first few refactorable numbers are listed in as : 1, 2, 8, 9, 12, 18, ...

, a Motzkin sum, an

idoneal number In mathematics, Euler's idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers ''D'' such that any integer expressible in only one way as ''x''2 ± ''Dy''2 (where ''x''2 is relatively prime to ''Dy ...

, a Riordan number and a

noncototient In mathematics, a noncototient is a positive integer ''n'' that cannot be expressed as the difference between a positive integer ''m'' and the number of coprime integers below it. That is, ''m'' − φ(''m'') = ''n'', where � ...

. 232 is a

telephone number A telephone number is a sequence of digits assigned to a landline telephone subscriber station connected to a telephone line or to a wireless electronic telephony device, such as a radio telephone or a mobile telephone, or to other devices f ...

: in a system of seven telephone users, there are 232 different ways of pairing up some of the users. There are also exactly 232 different eight-vertex connected

indifference graph In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting two vertices by an edge when their numbers are within one unit of each other.. Indifference ...

s, and 232

bracelets A bracelet is an article of jewellery that is worn around the wrist. Bracelets may serve different uses, such as being worn as an ornament. When worn as ornaments, bracelets may have a supportive function to hold other items of decoration, suc ...

with eight beads of one color and seven of another. Because this number has the form , it follows that there are exactly 232 different functions from a set of four elements to a proper subset of the same set.

References

Integers {{Num-stub