2

2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and the only even prime number.

Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.

Mathematics

The number 2 is the second natural number, after 1. Each natural number, including 2, is constructed by succession, that is, by adding 1 to the previous natural number.^[1] 2 is the smallest and the only even prime number, and the first Ramanujan prime.^[2] It is also the first superior highly composite number,^[3] and the first colossally abundant number.^[4]

An integer is determined to be even if it is divisible by two. When written in base 10, all multiples of 2 will end in 0, 2, 4, 6, or 8;^[5] more generally, in any even base, even numbers will end with an even digit.

Binary is a number system with a base of two, where each "bit" (binary digit) is either 0 (off) or 1 (on). It is used extensively in computing, since simple on-off logic is relatively simple to keep track of with electronics.^[6]

A digon is a polygon with two sides (or edges) and two vertices.^[7]: 52 In Euclidean space, digons are degenerate, collapsing to a line segment between the two vertices.^[8] In spherical geometry, however, non-degenerate digons can exist.^[9]

Two distinct points in a plane are always sufficient to define a unique line in a nontrivial Euclidean space.^[10]

The integers modulo 2 form the finite field \mathbb F_2, the smallest finite field. It has two elements, usually denoted 0 and 1, and addition in \mathbb F_2 corresponds to parity. Thus reduction modulo 2 records the parity of an integer: even integers are congruent to 0 modulo 2, and odd integers are congruent to 1 modulo 2. In algebra, structures of characteristic 2 have special behavior because 1+1=0; in particular, every element satisfies x=-x. For this reason, many algebraic constructions have separate forms in characteristic 2.^[11]

A symmetry of order two is called an involution.

List of basic calculations

As a word

Two is most commonly a determiner used with plural countable nouns, as in two days or I'll take these two.^[12] Two is a noun when it refers to the number two as in two plus two is four.

The word two is derived from the Old English words twā (feminine), tū (neuter), and twēġen (masculine, which survives today in the form twain).^[13]

Evolution of the 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) still use this method. The Gupta script 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.^[14]

In science

• The first magic number - number of electrons in the innermost electron shell of an atom.^[15]
• The chemical element with atomic number 2 is helium.

See also

• Binary number
• Square root of 2
• −2

References

1. ^ Colman, Samuel (1912). 'Nature's Harmonic Unity: A Treatise on Its Relation to Proportional Form'. Coan, C. Arthur (ed.). New York and London: G.P. Putnam's Sons. p. 10.
2. ^ "Sloane's A104272 : Ramanujan primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2011-04-28. Retrieved 2016-06-01.
3. ^ "A002201 - OEIS". oeis.org. Archived 2010-12-29 at the Wayback Machine. Retrieved 2024-11-28.
4. ^ "A004490 - OEIS". oeis.org. Archived 2012-05-25 at the Wayback Machine. Retrieved 2024-11-28.
5. ^ Retrieved 2022-12-15.
6. ^ "How computers see the world - Binary - KS3 Computer Science Revision". BBC Bitesize. Retrieved 2024-06-05.
7. ^ Wilson, Robin (2014). Four Colors Suffice. Revised color ed. Princeton University Press. ISBN 978-0-691-15822-8.
8. ^ Weisstein, Eric W. "Digon." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Digon.html
9. ^ "Polygons on the Sphere". sites.math.washington.edu. Notes from Math 445 for February 9, 2004. February 9, 2004. Retrieved 2026-02-15.
10. ^ Carrell, Jim. "Chapter 1 | Euclidean Spaces and Their Geometry". MATH 307 Applied Linear Algebra. Archived 2024-06-05 at the Wayback Machine. Retrieved 2024-06-05.
11. ^ Knus, Max-Albert; Merkurjev, Alexander; Rost, Markus; Tignol, Jean-Pierre (1998). The Book of Involutions. Vol. 44. American Mathematical Society Colloquium Publications. Providence, Rhode Island: American Mathematical Society. ISBN 978-0-8218-0904-4.
12. ^ Huddleston, Rodney D.; Pullum, Geoffrey K.; Reynolds, Brett (2022). A student's introduction to English grammar. 2nd ed. Cambridge, United Kingdom: Cambridge University Press. p. 117. ISBN 978-1-316-51464-1. OCLC 1255524478
13. ^
14. ^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 393, Fig. 24.62
15. ^ Watkins, Thayer. "The Complete Explanation of the Nuclear Magic Numbers Which Indicate the Filling of Nucleonic Shells and the Revelation of Special Numbers Indicating the Filling of Subshells Within Those Shells". San José State University. Archived from the original on 2019-12-02. Retrieved 2019-12-22.

External links

• Prime curiosities: 2