2 (two) is a
number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual number ...
,
numeral and
digit. It 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
1 and preceding
3. It is the smallest and only even
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), 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 it forms the basis of a
duality, it has
religious
Religion is usually defined as a social- cultural system of designated behaviors and practices, morals, beliefs, worldviews, texts, sanctified places, prophecies, ethics, or organizations, that generally relates humanity to supernatur ...
and
spiritual significance in many
cultures.
Evolution
Arabic digit
The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic
Brahmic script, where "2" was written as two horizontal lines. The modern
Chinese and
Japanese languages (and Korean
Hanja
Hanja (Hangul: ; Hanja: , ), alternatively known as Hancha, are Chinese characters () used in the writing of Korean. Hanja was used as early as the Gojoseon period, the first ever Korean kingdom.
(, ) refers to Sino-Korean vocabulary, ...
) still use this method. The
Gupta script
The Gupta script (sometimes referred to as Gupta Brahmi script or Late Brahmi script)Sharma, Ram. '' 'Brahmi Script' ''. Delhi: BR Publishing Corp, 2002 was used for writing Sanskrit and is associated with the Gupta Empire of the Indian subcon ...
rotated the two lines 45 degrees, making them diagonal. The top line was sometimes also shortened and had its bottom end curve towards the center of the bottom line. In the
Nagari script, the top line was written more like a curve connecting to the bottom line. In the Arabic
Ghubar writing, the bottom line was completely vertical, and the digit looked like a dotless closing question mark. Restoring the bottom line to its original horizontal position, but keeping the top line as a curve that connects to the bottom line leads to our modern digit.
In fonts with
text figures
Text figures (also known as non-lining, lowercase, old style, ranging, hanging, medieval, billing, or antique figures or numerals) are numerals designed with varying heights in a fashion that resembles a typical line of running text, hence the ...
, digit 2 usually is of
x-height
upright 2.0, alt=A diagram showing the line terms used in typography
In typography, the x-height, or corpus size, is the distance between the baseline and the mean line of lowercase letters in a typeface. Typically, this is the height of the le ...
, for example, .
Etymology of ''two''
The word ''two'' is derived from the
Old English
Old English (, ), or Anglo-Saxon, is the earliest recorded form of the English language, spoken in England and southern and eastern Scotland in the early Middle Ages. It was brought to Great Britain by Anglo-Saxon settlers in the mid-5th ...
words (
feminine
Femininity (also called womanliness) is a set of attributes, behaviors, and roles generally associated with women and girls. Femininity can be understood as socially constructed, and there is also some evidence that some behaviors considered fe ...
), (neuter), and (masculine, which survives today in the form
twain).
The pronunciation , like that of ''who'' is due to the
labialization
Labialization is a secondary articulatory feature of sounds in some languages. Labialized sounds involve the lips while the remainder of the oral cavity produces another sound. The term is normally restricted to consonants. When vowels involv ...
of the vowel by the ''w'' (combare from
womb
The uterus (from Latin ''uterus'', plural ''uteri'') or womb () is the organ in the reproductive system of most female mammals, including humans that accommodates the embryonic and fetal development of one or more embryos until birth. The ut ...
), which then disappeared before the related sound. The successive stages of pronunciation for the Old English would thus be , , , , and finally .
[
]
In mathematics
Two is the smallest prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), 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 ...
, and the only even prime number, and for this reason it is sometimes called "the oddest prime". As the smallest prime number, it is also the smallest non-zero pronic number, and the only pronic prime. The next prime is three, which makes two and three the only two consecutive prime numbers. Two is the first prime number that does not have a proper twin prime
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 p ...
with a difference two, while three is the first such prime number to have a twin prime. In consequence, the first pair of twin primes, three and five
5 is a number, numeral, and glyph.
5, five or number 5 may also refer to:
* AD 5, the fifth year of the AD era
* 5 BC, the fifth year before the AD era
Literature
* ''5'' (visual novel), a 2008 visual novel by Ram
* ''5'' (comics), an awa ...
, encase four
4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures.
In mathematics
Four is the smallest ...
in-between, which is the square of two, or . Two is the first Sophie Germain prime, the first factorial prime, the first Lucas prime, and the first Ramanujan prime
In mathematics, a Ramanujan prime is a prime number that satisfies a result proven by Srinivasa Ramanujan relating to the prime-counting function.
Origins and definition
In 1919, Ramanujan published a new proof of Bertrand's postulate which, ...
. It is also a Motzkin number, a Bell number, an all-Harshad number
In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base.
Harshad numbers in base are also known as -harshad (or -Niven) numbers.
Harshad number ...
, a meandric number In mathematics, a meander or closed meander is a self-avoiding closed curve which intersects a line a number of times. Intuitively, a meander can be viewed as a road crossing a river through a number of bridges.
Meander
Given a fixed oriented li ...
, a semi-meandric number, an open meandric number, and the third (or fourth) Fibonacci number.
An integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
is called ''even
Even may refer to:
General
* Even (given name), a Norwegian male personal name
* Even (surname)
* Even (people), an ethnic group from Siberia and Russian Far East
**Even language, a language spoken by the Evens
* Odd and Even, a solitaire game wh ...
'' if it is divisible by 2. For integers written in a numeral system based on an even number such as decimal
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 numeral ...
, divisibility by 2 is easily tested by merely looking at the last digit. If it is even, then the whole number is even. In particular, when written in the decimal system, all multiples of 2 will end in 0, 2, 4, 6, or 8.
Two is the base of the binary system, the numeral system
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
The same sequence of symbo ...
with the fewest tokens that allows denoting a natural number substantially more concisely (with tokens) than a direct representation by the corresponding count of a single token (with tokens). This binary number system is used extensively in computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, ...
.
The square root of 2
The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as \sqrt or 2^, and is an algebraic number. Technically, it should be called the princi ...
was the first known irrational number. Taking the square root
In mathematics, a square root of a number is a number such that ; in other words, a number whose '' square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because .
...
of a number is such a common and essential mathematical operation, that the spot on the root sign where the index would normally be written for cubic and other roots, may simply be left blank for square roots, as it is tacitly understood.
Powers of two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent.
In a context where only integers are considered, is restricted to non-negati ...
are central to the concept of Mersenne prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17 ...
s, and important to computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
. Two is the first Mersenne prime exponent. They are also essential to Fermat primes and Pierpont prime
In number theory, a Pierpont prime is a prime number of the form
2^u\cdot 3^v + 1\,
for some nonnegative integers and . That is, they are the prime numbers for which is 3-smooth. They are named after the mathematician James Pierpont, who us ...
s, which have consequences in the constructability
Constructability (or buildability) is a concept that denotes ease of construction. It can be central to project management techniques to review construction processes from start to finish during pre-construction phase. Buildability assessment is ...
of regular polygons using basic tools.
In a set-theoretical construction of the natural numbers, two is identified with the set . This latter set is important in category theory
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, ca ...
: it is a subobject classifier In category theory, a subobject classifier is a special object Ω of a category such that, intuitively, the subobjects of any object ''X'' in the category correspond to the morphisms from ''X'' to Ω. In typical examples, that morphism assigns "true ...
in the category of sets. A set that is a field has a minimum of two elements.
A Cantor space is a topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called poin ...
homeomorphic
In the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomor ...
to the Cantor set
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.
T ...
. The countably infinite product topology
In topology and related areas of mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more natural-seem ...
of the simplest discrete two-point space, , is the traditional elementary example of a Cantor space.
An number is '' deficient'' when the sum of its divisors is less than twice the number, whereas an abundant number has a sum of its proper divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...
s that is larger than the number itself. Primitive abundant numbers are abundant numbers whose proper divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...
s are all deficient.
An number is '' perfect'' if it is equal to its aliquot sum, or the sum of all of its positive divisors excluding the number itself. This is equivalent to describing a perfect number as having a sum of divisors
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (includin ...
equal to .
Two has the unique property that up through any level of hyperoperation, here denoted in Knuth's up-arrow notation, all equivalent to
Two consecutive twos (as in "22" for "two twos"), or equivalently "2-2", is the only fixed point of John Conway's look-and-say function.
Two is the only number such that the sum of the reciprocals of the natural powers of equals itself. In symbols,
:
Euler's number can be simplified to equal,
The circumference
In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out ...
of a circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is cons ...
of radius is .
The sum of the reciprocals of all non-zero triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...
s converges to .
2 is the harmonic mean
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired.
The harmonic mean can be expressed as the recipro ...
of the divisors of 6, the smallest Ore number greater than one.
There are no magic square
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...
s, and as such they are the only null by magic square set.
In a Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidea ...
of any dimension greater than zero, two distinct points
Point or points may refer to:
Places
* Point, Lewis, a peninsula in the Outer Hebrides, Scotland
* Point, Texas, a city in Rains County, Texas, United States
* Point, the NE tip and a ferry terminal of Lismore, Inner Hebrides, Scotland
* Points ...
determine a line
Line most often refers to:
* Line (geometry), object with zero thickness and curvature that stretches to infinity
* Telephone line, a single-user circuit on a telephone communication system
Line, lines, The Line, or LINE may also refer to:
Art ...
.
In two dimensions, a digon is a polygon with two sides (or edges) and two vertices. On a circle, it is a tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ...
with two antipodal points
In mathematics, antipodal points of a sphere are those diametrically opposite to each other (the specific qualities of such a definition are that a line drawn from the one to the other passes through the center of the sphere so forms a true ...
and 180° arc edges.
The simplest tessellation in two-dimensional space
In mathematics, a plane is a Euclidean ( flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as ...
, though an improper tessellation, is that of two -sided apeirogon
In geometry, an apeirogon () or infinite polygon is a generalized polygon with a countably infinite number of sides. Apeirogons are the two-dimensional case of infinite polytopes.
In some literature, the term "apeirogon" may refer only to t ...
s joined along all their edges, coincident about a line
Line most often refers to:
* Line (geometry), object with zero thickness and curvature that stretches to infinity
* Telephone line, a single-user circuit on a telephone communication system
Line, lines, The Line, or LINE may also refer to:
Art ...
that divides the plane in two. This order-2 apeirogonal tiling is the arithmetic limit of the family of dihedra .
For any polyhedron homeomorphic to a sphere, the Euler characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological spac ...
is , where is the number of vertices, is the number of edge
Edge or EDGE may refer to:
Technology Computing
* Edge computing, a network load-balancing system
* Edge device, an entry point to a computer network
* Adobe Edge, a graphical development application
* Microsoft Edge, a web browser developed ...
s, and is the number of face
The face is the front of an animal's head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may aff ...
s. A double torus has a Euler characteristic of , on the other hand, and a non-orientable surface of like genus
Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial nom ...
has a characteristic .
The long diagonal of a regular hexagon
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
Regular hexagon
A '' regular hexagon'' has ...
is of length two when its sides are of unit length. Whereas a square of unit side length has a diagonal equal to the square root of two, and a cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross.
The cube is the only ...
of unit side length has a space diagonal equal to the square root of three
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is denoted mathematically as \sqrt or 3^. It is more precisely called the principal square root of 3 to distinguish it from the negative nu ...
, a space diagonal inside a tesseract
In geometry, a tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of e ...
measures two when its side lengths are of length one.
There are two known sublime number In number theory, a sublime number is a positive integer which has a perfect number of positive factors (including itself), and whose positive factors add up to another perfect number.
The number 12, for example, is a sublime number. It has a p ...
s, which are numbers with a perfect number of factors, whose sum itself yields a perfect number
In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number.
...
. 12 is one of the two sublime numbers, with the other being 76 digits long.
List of basic calculations
In science
*The number of polynucleotide strands in a DNA double helix
A double is a look-alike or doppelgänger; one person or being that resembles another.
Double, The Double or Dubble may also refer to:
Film and television
* Double (filmmaking), someone who substitutes for the credited actor of a character
* ...
.
*The first magic number.
*The atomic number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of ever ...
of helium
Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic ta ...
.
*The ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because ...
code of " Start of Text".
*2 Pallas
Pallas ( minor-planet designation: 2 Pallas) is the second asteroid to have been discovered, after Ceres. It is believed to have a mineral composition similar to carbonaceous chondrite meteorites, like Ceres, though significantly less hy ...
, a large asteroid in the main belt and the second asteroid ever to be discovered.
*The Roman numeral II (usually) stands for the second-discovered satellite of a planet or minor planet (e.g. Pluto II or (87) Sylvia II Remus
Remus is the inner and smaller moon of the main-belt asteroid 87 Sylvia. It follows an almost-circular and close-to-equatorial orbit around the parent asteroid. In this respect it is similar to the other Sylvian moon Romulus.
Remus was discover ...
).
*A binary star
A binary star is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in ...
is a stellar system consisting of two star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
ing around their center of mass
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...
.
*The number of brain
A brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as Visual perception, vision. I ...
and cerebellar hemispheres.
In sports
*The number of points scored on a safety
Safety is the state of being "safe", the condition of being protected from harm or other danger. Safety can also refer to the control of recognized hazards in order to achieve an acceptable level of risk.
Meanings
There are two slightly di ...
in American football
American football (referred to simply as football in the United States and Canada), also known as gridiron, is a team sport played by two teams of eleven players on a rectangular field with goalposts at each end. The offense, the team wi ...
*A field goal
A field goal (FG) is a means of scoring in gridiron football. To score a field goal, the team in possession of the ball must place kick, or drop kick, the ball through the goal, i.e., between the uprights and over the crossbar. The entire ba ...
inside the three-point line is worth two points in basketball
Basketball is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular Basketball court, court, compete with the primary objective of #Shooting, shooting a basketball (ball), basketball (appr ...
.
*The two in basketball is called the Shooting Guard
The shooting guard (SG), also known as the two, two guard or off guard,Shooting guards are 6'3"–6'7"BBC Sports academy URL last accessed 2006-09-09. is one of the five traditional positions in a regulation basketball game. A shooting guard's m ...
*2 represents the catcher
Catcher is a position in baseball and softball. When a batter takes their turn to hit, the catcher crouches behind home plate, in front of the ( home) umpire, and receives the ball from the pitcher. In addition to this primary duty, the cat ...
position in baseball
Baseball is a bat-and-ball sport played between two teams of nine players each, taking turns batting and fielding. The game occurs over the course of several plays, with each play generally beginning when a player on the fielding t ...
.
Other
In pre-1972 Indonesian and Malay orthography, ''2'' was shorthand for the reduplication
In linguistics, reduplication is a morphological process in which the root or stem of a word (or part of it) or even the whole word is repeated exactly or with a slight change.
The classic observation on the semantics of reduplication is Edwa ...
that forms plurals: ''orang'' (person), ''orang-orang'' or ''orang2'' (people). In Astrology
Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Di ...
, Taurus is the second sign
A sign is an object, quality, event, or entity whose presence or occurrence indicates the probable presence or occurrence of something else. A natural sign bears a causal relation to its object—for instance, thunder is a sign of storm, or ...
of the Zodiac
The zodiac is a belt-shaped region of the sky that extends approximately 8° north or south (as measured in celestial latitude) of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The pa ...
. For Pythagorean numerology
Numerology (also known as arithmancy) is the belief in an occult, divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in ...
(a pseudoscience
Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method. Pseudoscience is often characterized by contradictory, exaggerated or unfalsifiable claim ...
) the number 2 represents duality, the positive and negative poles that come into balance and seek harmony.
See also
*List of highways numbered 2
The following highways are numbered 2. For roads numbered A2, see list of A2 roads. For roads numbered B2, see list of B2 roads. For roads numbered M2, see list of M2 roads. For roads numbered N2, see list of N2 roads.
International
* Asi ...
*Binary number
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" ( zero) and "1" (one).
The base-2 numeral system is a positional notati ...
References
External links
Prime curiosities: 2
{{DEFAULTSORT:2 (Number)
2 (number)
Integers