229 (two hundred ndtwenty-nine) 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 n ...

following

228 Year 228 ( CCXXVIII) was a leap 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 Modestus and Maecius (or, less frequently, year 981 '' Ab urbe con ...

and preceding

230 Year 230 (Roman numerals, CCXXX) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Agricola and Clementinus (or, less frequently, year ...

In mathematics

It is a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

, and a

regular prime In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli num ...

. It is also a

full reptend prime In number theory, a full reptend prime, full repetend prime, proper primeDickson, Leonard E., 1952, ''History of the Theory of Numbers, Volume 1'', Chelsea Public. Co. or long prime in base ''b'' is an odd prime number ''p'' such that the Fermat q ...

, meaning that the decimal expansion of the

unit fraction A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/''n''. Examples are 1/1, 1/2, 1/3, 1/4, 1/5, et ...

1/229 repeats periodically with as long a period as possible. With

227 Year 227 ( CCXXVII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Senecio and Fulvius (or, less frequently, year 980 ''Ab urbe condi ...

it is the larger of a pair of

twin primes A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...

, and it is also the start of a sequence of three consecutive

squarefree number In mathematics, a square-free integer (or squarefree integer) is an integer which is divisible by no square number other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, is square-fr ...

s. It is the smallest prime that, when added to the reverse of its decimal representation, yields another prime: 229 + 922 = 1151. There are 229

cyclic permutation In mathematics, and in particular in group theory, a cyclic permutation (or cycle) is a permutation of the elements of some set ''X'' which maps the elements of some subset ''S'' of ''X'' to each other in a cyclic fashion, while fixing (that is, ma ...

s of the numbers from 1 to 7 in which none of the numbers is mapped to its successor (mod 7), 229

rooted tree In graph theory, a tree is an undirected graph in which any two vertices are connected by ''exactly one'' path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by ''a ...

structures formed from nine

carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent In chemistry, the valence (US spelling) or valency (British spelling) of an element is the measure of its combining capacity with o ...

atoms, and 229 triangulations of a polygon formed by adding three vertices to each side of a triangle. There are also 229 different

projective configuration In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the ...

s of type (12₃12₃), in which twelve points and twelve lines meet with three lines through each of the points and three points on each of the lines, all of which may be realized by straight lines in the

Euclidean plane In mathematics, the Euclidean plane is a Euclidean space of dimension two. That is, a geometric setting in which two real quantities are required to determine the position of each point ( element of the plane), which includes affine notions of ...

. The

complete graph In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is c ...

''K''₁₃ has 229

crossings Crossings may refer to: * ''Crossings'' (Buffy novel), a 2002 original novel based on the U.S. television series ''Buffy the Vampire Slayer'' * Crossings (game), a two-player abstract strategy board game invented by Robert Abbott * ''Crossings'' ...

in its straight-line drawing with the fewest possible crossings..

In mathematics

References

See also