Changes

==Etymology==

==Etymology==

[https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] twa, two, from [https://nordan.daynal.org/wiki/index.php?title=English#ca._600-1100.09THE_OLD_ENGLISH.2C_OR_ANGLO-SAXON_PERIOD Old English] twā  ([[feminine]] & neuter); akin to Old English twēgen two ([[masculine]]), tū (neuter), Old High German zwēne, [[Latin]] duo, Greek dyo

[https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] twa, two, from [https://nordan.daynal.org/wiki/index.php?title=English#ca._600-1100.09THE_OLD_ENGLISH.2C_OR_ANGLO-SAXON_PERIOD Old English] twā  ([[feminine]] & neuter); akin to Old English twēgen two ([[masculine]]), tū (neuter), Old High German zwēne, [[Latin]] duo, Greek dyo

*Date: before [http://www.wikipedia.org/wiki/12th_Century 12th century]

*Date: before [https://www.wikipedia.org/wiki/12th_Century 12th century]

==Definitions==

==Definitions==

*1 : [[being]] one more than [[one]] in [[number]]

*1 : [[being]] one more than [[one]] in [[number]]

2 (two) is a [[number]], numeral, and glyph. It is the natural number following [[One|1]]  and preceding [[Three|3]].

2 (two) is a [[number]], numeral, and glyph. It is the natural number following [[One|1]]  and preceding [[Three|3]].

==In mathematics==

==In mathematics==

Two has many properties in [[mathematics]]. An [http://en.wikipedia.org/wiki/Integer 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 [http://en.wikipedia.org/wiki/Hexadecimal hexadecimal], 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 has many properties in [[mathematics]]. An [https://en.wikipedia.org/wiki/Integer 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 [https://en.wikipedia.org/wiki/Hexadecimal hexadecimal], 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 smallest and the first [http://en.wikipedia.org/wiki/Prime_number prime number], and the only even one[2] (for this [[reason]] it is sometimes called "the oddest prime". The next prime is [[three]]. Two and three are the only two consecutive [http://en.wikipedia.org/wiki/Prime_number prime numbers]. 2 is the first [http://en.wikipedia.org/wiki/Sophie_Germain_prime Sophie Germain prime], the first [http://en.wikipedia.org/wiki/Factorial_prime factorial prime], the first [http://en.wikipedia.org/wiki/Lucas_prime Lucas prime], and the first [http://en.wikipedia.org/wiki/Smarandache-Wellin_prime Smarandache-Wellin prime]. It is an [http://en.wikipedia.org/wiki/Eisenstein_prime Eisenstein prime] with no imaginary part and real part of the form 3n − 1. It is also a [http://en.wikipedia.org/wiki/Stern_prime Stern prime], a [http://en.wikipedia.org/wiki/Pell_number Pell number], the first [http://en.wikipedia.org/wiki/Fibonacci_prime Fibonacci prime], and a [http://en.wikipedia.org/wiki/Markov_number Markov number], appearing in infinitely many solutions to the Markov Diophantine equation involving odd-indexed Pell numbers.

Two is the smallest and the first [https://en.wikipedia.org/wiki/Prime_number prime number], and the only even one[2] (for this [[reason]] it is sometimes called "the oddest prime". The next prime is [[three]]. Two and three are the only two consecutive [https://en.wikipedia.org/wiki/Prime_number prime numbers]. 2 is the first [https://en.wikipedia.org/wiki/Sophie_Germain_prime Sophie Germain prime], the first [https://en.wikipedia.org/wiki/Factorial_prime factorial prime], the first [https://en.wikipedia.org/wiki/Lucas_prime Lucas prime], and the first [https://en.wikipedia.org/wiki/Smarandache-Wellin_prime Smarandache-Wellin prime]. It is an [https://en.wikipedia.org/wiki/Eisenstein_prime Eisenstein prime] with no imaginary part and real part of the form 3n − 1. It is also a [https://en.wikipedia.org/wiki/Stern_prime Stern prime], a [https://en.wikipedia.org/wiki/Pell_number Pell number], the first [https://en.wikipedia.org/wiki/Fibonacci_prime Fibonacci prime], and a [https://en.wikipedia.org/wiki/Markov_number 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.

It is the third Fibonacci number, and the third and fifth Perrin numbers.

Despite being a prime, two is also a [http://en.wikipedia.org/wiki/Highly_composite_number highly composite number], because it has more divisors than the number one. The next highly composite number is four.

Despite being a prime, two is also a [https://en.wikipedia.org/wiki/Highly_composite_number highly composite number], because it has more divisors than the number one. The next highly composite number is four.

[http://en.wikipedia.org/wiki/Vulgar_fraction Vulgar fractions] with 2 or 5 in the [http://en.wikipedia.org/wiki/Denominator denominator] do not yield infinite [http://en.wikipedia.org/wiki/Decimal_representation decimal expansions], as is the case with most primes, because 2 and 5 are factors of ten, the decimal base.

[https://en.wikipedia.org/wiki/Vulgar_fraction Vulgar fractions] with 2 or 5 in the [https://en.wikipedia.org/wiki/Denominator denominator] do not yield infinite [https://en.wikipedia.org/wiki/Decimal_representation decimal expansions], as is the case with most primes, because 2 and 5 are factors of ten, the decimal base.

Two is the [http://en.wikipedia.org/wiki/Radix base] of the simplest [http://en.wikipedia.org/wiki/Numeral_system 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.

Two is the [https://en.wikipedia.org/wiki/Radix base] of the simplest [https://en.wikipedia.org/wiki/Numeral_system 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.

==Evolution of the glyph==

==Evolution of the glyph==

The [http://en.wikipedia.org/wiki/Glyph 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 [http://en.wikipedia.org/wiki/Chinese_written_language Chinese] and [http://en.wikipedia.org/wiki/Japanese_writing_system Japanese]). The [http://en.wikipedia.org/wiki/Gupta_script 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.

The [https://en.wikipedia.org/wiki/Glyph 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 [https://en.wikipedia.org/wiki/Chinese_written_language Chinese] and [https://en.wikipedia.org/wiki/Japanese_writing_system Japanese]). The [https://en.wikipedia.org/wiki/Gupta_script 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.

==See also==

==See also==

*'''''[[Dual]]'''''

*'''''[[Dual]]'''''

[[Category: Mathematics]]

[[Category: Mathematics]]