'2' ('two') is a
number,
numeral, and
glyph. It is the
natural number following
1 and preceding
3.
In mathematics
Two has many properties in
mathematics.
[1] An
integer is called ''
even'' if it is divisible by 2. For integers written in a numeral system based on an even number, such as decimal and hexadecimal, divisibility by 2 is easily tested by merely looking at the one's place digit. If it's 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 smallest and the first
prime number, and the only even one (for this reason it is sometimes humorously called "the oddest prime"). The next prime is
three. 2 is the first
Sophie Germain prime, the first
factorial prime, the first
Lucas prime, and the first
Smarandache-Wellin prime. It is an
Eisenstein prime with no imaginary part and real part of the form
. It is also a
Stern prime, a
Pell number, and a
Markov number, appearing in infinitely many solutions to the Markov Diophantine equation involving odd-indexed Pell numbers.
It is the third
Fibonacci number, and the third and fifth
Perrin numbers.
Despite being a prime, two is also a
highly composite number, because it has more divisors than the number one. The next highly composite number is
four.
Vulgar fractions with 2 or 5 in the
denominator do not yield infinite
decimal expansions, as is the case with most primes, because they are prime factors of
ten, the base.
Two is the
base of the simplest
numeral system in which natural numbers can be written concisely, being the length of the number a logarithm of the value of the number (whereas in base 1 the length of the number is the value of the number itself); the
binary system is used in
computers.
For any number ''x'':
:''x''+''x'' = 2·''x''
addition to
multiplication
:''x''·''x'' = ''x''
2 multiplication to
exponentiation
:''x''
''x'' = ''x''↑↑2
exponentiation to
tetration
Two also has the unique property that 2+2 = 2·2 = 2²=''2''↑↑2=''2''↑↑↑2, and so on, no matter how high the operation is.
Two is the only number x such that the sum of the reciprocals of the powers of x equals itself. In symbols:
This comes from the fact that:
Powers of two are central to the concept of
Mersenne primes, and important to
computer science. Two is the first Mersenne prime exponent.
Taking the square root of a number is such a common mathematical operation, that the spot on the root sign where the exponent would normally be written for cubic roots and other such roots, is left blank for square roots, as it is considered tacit.
The
square root of two was the first known
irrational number.
The smallest
field has two elements.
In the
set-theoretical construction of the natural numbers, 2 is identified with the set {{Ø},Ø}. This latter set is important in
category theory: it is a
subobject classifier in the category of sets.
Two is a
primorial, as well as its own
factorial. Two often occurs in numerical sequences, such as the
Fibonacci number sequence, but not quite as often as one does. Two is also a
Motzkin number, a
Bell number, an
all-Harshad number, a
meandric number, a
semi-meandric number, and an
open meandric number.
Two is the number of
n-Queens Problem solutions for n = 4. With one exception, all known solutions to
Znám's problem start with 2.
Two also has the unique property such that:
:
and also
:
for ''a'' not equal to zero
Two has a connection to triangular numbers:
Where
gives the nth d-dimensional simplex number. When d=2,
The number of domino tilings of a 2×2
checkerboard is 2.
For any polyhedron homeomorphic to a sphere, the
Euler characteristic is
List of basic calculations
{|class="wikitable" style="text-align: center; background: white"
|-
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Division
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!width="5px"|
!11
!12
!13
!14
!15
|-
|
|'2'
|1
|
|
0 (number).
5
|0.4
|
|
|0.
25
|
|0.2
!
|
|
|
|
|
|-
|
|0.5
|1
|1.5
|'2'
|2.5
|3
|3.5
|4
|4.5
|5
!
|5.5
|6
|6.5
|
7
|7.5
|}
{|class="wikitable" style="text-align: center; background: white"
|-
!width="105px"|
Exponentiation
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!width="5px"|
!11
!12
!13
|-
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|'2'
|4
|8
|16
|32
|
64
|
128
|
256
|
512
|
1024
!
|2048
|4096
|8192
|-
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|1
|4
|
9
|16
|25
|36
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49
|64
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81
|
100
!
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121
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144
|
169
|}
Evolution of the glyph
Evolution2glyph.png
The
glyph we use today in the Western world to represent the number 2 traces its roots back to the Brahmin Indians, who wrote 2 as two horizontal lines (it is still written that way in modern
Chinese and
Japanese, and is analogous to the Roman numeral II). The
Gupta rotated the two lines 45 degrees, making them diagonal, and sometimes also made the top line shorter and made its bottom end curve towards the center of the bottom line. Apparently for speed, the
Nagari started making the top line more like a curve and connecting to the bottom line. The Ghubar Arabs made the bottom line completely vertical, and now the glyph 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 glyph.
In fonts with
text figures, 2 usually has the same height as a lowercase X, for example,
Text figures 256.svg
.
In science
★ The number of
polynucleotide strands in a
DNA double helix.
★ The first
Magic Number.
★ The
atomic number of
helium.
★ Group '2' in the
Periodic table of the elements consists of the
alkaline earth metals whose usual
valence is +2.
★ Period '2' in the Periodic table consists of the eight elements
lithium through
neon.
Astronomy
★
★
Messier object M2, a magnitude 6.5
globular cluster in the constellation
Aquarius.
★ The
New General Catalogue object NGC 2, a
magnitude 14.2
spiral galaxy in the
constellation Pegasus
★ The
Saros number of the
solar eclipse series which began on
May 4 2861 BC and ended on
June 21 1563 BC . The duration of Saros series 2 was 1298.1 years, and it contained 73 solar eclipses.
★ The Saros
number of the
lunar eclipse series which began on
February 21 2541 BC and ended on
April 22 1225 BC. The duration of Saros series 2 was 1316.2 years, and it contained 74 lunar eclipses.
★ The Roman numeral II stands for
bright giant in the
Yerkes spectral classification scheme.
★ 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)
★ A
binary star is a
stellar system consisting of two
stars
orbiting around their
center of mass.
In religion
★ In Taoism, The Tao is manifested in the pairs of opposites, the Yin and the Yang. The world results from the interaction of the pairs of opposites.
★ The duality of all things is an important notion in most cultures and religions:
#In
Judaism, everything
God created is a duality—e.g. heaven and earth, sea and land, male and female. The first word of the
Torah, בראשית ("In the beginning"), begins with a ''
bet'', the
gematria of 2, to signify the dual nature of all created things
#In
Pythagorean philosophy, the
dyad is the second thing created
★ The
Ten Commandments were given in the form of two tablets (''Shnei Luchot HaBrit'')
★ Two candles are traditionally kindled to usher in the
Shabbat, recalling the two different ways Shabbat is referred to in the two times the
Ten Commandments are recorded in the
Torah. These two expressions are known in
Hebrew as שמור וזכור ("guard" and "remember"), as in "Guard the Shabbat day to sanctify it" (Deut. 5:12) and "Remember the Shabbat day to sanctify it" (Ex. 20:8)
★ Two
challahs (''lechem mishnah'') are placed on the table for each
Shabbat meal and a blessing made over them, to commemorate the double portion of
manna which fell in the
desert every Friday to cover that day's meals and the Shabbat meals
★ In
Jewish law, the testimony of two witnesses are required to verify and validate events, such as
marriage, divorce, and a crime that warrants
capital punishment
★
Rosh Hashana, the first day of the Jewish year, is a 2-day holiday
★ "Second-Day Yom Tov" (''Yom Tov Sheini Shebegaliyot'') is a rabbinical enactment that mandates a two-day celebration for each of the one-day
Jewish festivals (i.e., the first and seventh day of
Passover, the day of
Shavuot, the first day of
Sukkot, and the day of
Shemini Atzeret) outside the land of
Israel
★ Two goats of identical age and appearance were brought as
sacrifices during the
Yom Kippur service in the
Temple in Jerusalem. One was sacrificed on the altar; the
other was sent out to the desert as an offering to
Azazel
★ In
Wicca, the
deity is represented in two forms, the
Goddess and the
God, although they may have many different aspects, depending upon ones preference or
Tradition.
★ Animals boarded
Noah's Ark two by two.
In culture
The most common philosophical
dichotomy is perhaps the one of
good and
evil, but there are many others. See
dualism for an overview. In
Hegelian
dialectic, the process of
synthesis creates two perspectives from one.
Two (二, ''èr'') is a good
number in Chinese culture. There is a Chinese saying "good things come in pairs". It is common to use double symbols in product brandnames, e.g. double happiness, double coin, double elephants etc.
Cantonese people like the number two because it sounds the same as the word "easy" (易) in
Cantonese.
In
Finland, two
candles are lit on
Independence Day. Putting them on the windowsill invokes the symbolical meaning of division, and thus independence.
The numeral 2 is sometimes used as a shorthand for "to", such as
b2b (business-to-business). This form of abbreviation is especially common in the world of
popular music,
hip-hop, rap, and
R&B, where the "too" or "to" in group names, album titles, and song names is replaced with "2". The
Eurodance group
2 Unlimited is one example. In some cases, the
Roman numeral II is substituted, as seen in the name of R&B group
Boyz II Men. The names of
computer software that translate data from one format into another also commonly employ the numeral 2, such as
dvi2ps and
texi2roff.
In pre-1972
Indonesian and
Malay orthography, ''2'' was shorthand for the
reduplication that forms plurals: ''orang'' "person", ''orang-orang'' or ''orang2'' "people".
Words that can be used as synonyms for two include
brace,
couple,
deuce,
duet, ,
pair,
twain,
twins, and both.
In
rhetorics,
hendiadys is a
figure of speech where two words with similar or identical meanings are used where one would be sufficient.
Among children, or when otherwise calling for subtlety, the phrase "number 2" can refer to the act of
defecating (with
urination being "number 1").
In sports
In
American football, 2 is a jersey number that can be worn by quarterbacks, kickers, and punters.
In
American football, a team can achieve 2 points via a
two-point conversion after scoring a touchdown or via a
safety.
In
baseball, two represents the
catcher's position.
2 is the retired number for former baseball great
Charlie Gehringer.
2 was the number used by
Leo Durocher as baseball player, coach, and manager from the early 1930s until his retirement.
In
football, number 2 is assigned in most cases to the right defender or
fullback
In
basketball terminology, two represents the
shooting guard or "off guard".
In
cricket, 2 is the number of members of the batting side of the field of play at any one time.
From
1991 until his retirement in
2005, 2 was the number borne on the car of
NASCAR
Nextel Cup driver
Rusty Wallace. It was also the number of the car which
Dale Earnhardt drove to the first of his seven season championships in
1980.
Kurt Busch, as of
2006 drives the 2 car.
In
rugby league, 2 is the jersey number of the starting
right wing. It is also the number of points received for a successful conversion after a try is scored or a successful penalty kick.
In
rugby union, 2 is the jersey number of the starting
hooker. It is also the number of points received for a successful conversion after a try is scored.
In
rowing, 2- refers to a coxless pair; 2+ refers to a coxed pair; 2x refers to a coxless double.
In technology
Two is the
DVD region in
Europe,
South Africa, the
Middle East and
Japan.
Two is the first digit of international
telephone dialing codes primarily for countries in
Africa. On most phones, the 2 key is associated with the letters
A,
B, and
C.
On American
computer keyboards, the "2" key is associated with the "
@" symbol. On British
computer keyboards, the "2" key is associated with the
" symbol.
The "
two meter band" in
amateur radio includes the frequencies from 144 to 146 MHz. In the Americas, the two meter band extends to 148 MHz.
Binary is the basis of nearly all computers, and it a system based on two digits.
Music
The Roman numeral ii is the supertonic scale degree, chord, or diatonic function, when distinguished II = major and ii = minor.
★
Franz Schubert and
Felix Mendelssohn each wrote two trios for piano, violin, and violoncello.
★
Béla Bartók,
Sergei Prokofiev,
Dmitri Shostakovich, and
Felix Mendelssohn each wrote two concertos for violin and orchestra.
★
Dmitri Shostakovich wrote two concertos for violoncello and orchestra.
★
Edward Elgar completed two symphonies.
In other fields
Groups of two:
★
Lists of pairs
★
★
list of twins
Two is:
★ The denomination of
U.S. paper currency with
Thomas Jefferson's portrait on it; (last issued 2003;
as of 2006 rarely seen in general circulation).
★ The denomination of the
Canadian monetary coin featuring a
polar bear, commonly known as the "
toonie" after the $1 coin, the
loonie.
★ The denomination of the
$2 New Zealand coin, featuring the white heron.
★ The name of several fictional characters: '''
Number Two'''.
★ The designation of the
Trans-Canada Highway in most of the province of
New Brunswick.
★
U.S. Route 2, two separated highways in the northern tier of the United States, the western segment connecting
Everett, Washington to
St. Ignace, Michigan and the eastern route connecting
Rouses Point, New York to
Houlton, Maine.
★ The lowest channel of television in the United States, Canada, and Mexico on which television signals are broadcast.
★ One of the radio
callsign prefixes allocated to the
United Kingdom.
★ In
Astrology,
Taurus is the 2nd
sign of the
Zodiac.
References
1. Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 41–44
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