Jump to content

4: Difference between revisions

From Wikipedia, the free encyclopedia
Content deleted Content added
No edit summary
Line 95: Line 95:


Four is an [[Harshad number|all-Harshad number]] and a [[semi-meandric number]].
Four is an [[Harshad number|all-Harshad number]] and a [[semi-meandric number]].

4 15 50 4\/\/350|\/|3!


===List of basic calculations===
===List of basic calculations===

Revision as of 14:49, 22 October 2007

Template:Numbers (digits)
Cardinal 4
four
Ordinal 4th
fourth
Numeral system quaternary
Factorization
Divisors 1, 2, 4
Roman numeral IV or IIII
Roman numeral (Unicode) Ⅳ, ⅳ
Arabic ٤
Arabic (Urdu) ۴
Bengali
Chinese numeral
Devanāgarī
Hebrew ד (Daled)
Khmer
prefixes tetra- (from Greek)

quadri-/quadr- (from Latin)

Binary 100
Octal 4
Duodecimal 4
Hexadecimal 4
Vigesimal 4
This article discusses the number Four. For the year 4 AD, see 4. For other uses of 4, see 4 (disambiguation)

4 (four) is a number, numeral, and glyph. It is the natural number following 3 and preceding 5. Four is the only number in the English language for which the number of letters in its name is equal to the number itself. This is also true in several other languages.

In mathematics

Four is the smallest composite number, its proper divisors being 1 and 2. Four is also a highly composite number. The next highly composite number is 6.

Four is the second square number, the second centered triangular number.

4 is the smallest squared prime (). It has an aliquot sum of 3 which is itself prime. The aliquot sequence of 4 has 4 members (4,3 (number),1,0).

Four is the smallest composite number that is equal to the sum of its prime factors. (As a consequence of this, it is the smallest Smith number). However, it is the largest (and only) composite number for which is false.

It is also a Motzkin number.

In addition, . Continuing the pattern in Knuth's up-arrow notation, , and so on, for any number of up arrows.

A four-sided plane figure is a quadrilateral (quadrangle) or square, sometimes also called a tetragon. A circle divided by 4 makes right angles. Because of it, four (4) is the base number of plane (mathematics). Four cardinal directions, four seasons, duodecimal system, and vigesimal system are based on four.

A solid figure with four faces is a tetrahedron. The regular tetrahedron is the simplest Platonic solid. A tetrahedron, which can also be called a 3-simplex, has four triangular faces and four vertices. It is the only self-dual regular polyhedron.

The smallest non-cyclic group has four elements; it is the Klein four-group. Four is also the order of the smallest non-trivial groups that are not simple.

Four is the maximum number of dimensions of a real division algebra (the quaternions), by a theorem of Ferdinand Georg Frobenius.

The four-color theorem states that a planar graph (or, equivalently, a flat map of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors. Three colors are not, in general, sufficient to guarantee this. The largest planar complete graph has four vertices.

Lagrange's four-square theorem states that every positive integer can be written as the sum of at most four square numbers. Three are not always sufficient; 7 for instance cannot be written as the sum of three squares.

Four is the first positive non-Fibonacci number.

Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e.

Four is an all-Harshad number and a semi-meandric number.

4 15 50 4\/\/350|\/|3!

List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 200 400 4000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
4 2 1 0.8 0.5 0.4
0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864
1 16 81 256 625 1296 2401 4096 6561 10000 14641 20736 28561

Evolution of the glyph

Representing 1, 2 and 3 in as many lines as the number represents worked well enough, but writing four lines proved tiresome. The Brahmin Indians simplified 4 by joining its four lines into a cross that looks like our modern plus sign. The Sunga and other Indians would add a horizontal line on top of the numeral, and the Kshatrapa and Pallava evolved the numeral to a point where speed of writing was at best a secondary concern. The Arabs didn't have time for cursive fancy: their 4 still had the early concept of the cross, but for the sake of efficiency, was made in one stroke by connecting the "western" end to the "northern" end; the "eastern" end was finished off with a curve. The Europeans dropped off the finishing curve and gradually made the numeral less cursive, ending up with a glyph very close to the original Brahmin cross.[1]

While the shape of the 4 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in File:TextFigs148.png.

Also, 4 can be seen with an open top, just like in calculators.

In religion

In science

In astronomy

In biology

In chemistry

  • Valency of carbon (that is basis of life on the Earth) is four. Thanks to its tetrahedral crystal bond structure diamond (one of the natural allotropes of carbon) is the hardest known naturally occurring material. It is also the valence of silicon, whose compounds form the majority of the mass of the Earth's crust.
  • The atomic number of beryllium
  • There are four basic states of matter: solid, liquid, gas, and plasma.

In physics

In logic and philosophy

In technology

  • Most furniture has four legs - tables, chairs, etc.
  • Four horses (quadriga) is the maximal number of horses in one row for carriage.
  • Wide use of rectangles (with four angles and four sides) because they have effective form and capability for close adjacency to each other (houses, rooms, tables, bricks, sheets of paper, screens, film frames).
  • On most phones, the 4 key is associated with the letters G, H, and I, but on the BlackBerry it is the key for D and F.
  • In internet slang, "4" can replace the word "for" (as "four" and "for" are pronounced similarly). For example, typing "4u" instead of "for you".
  • In Leetspeak, "4" may be used to replace the letter "A".

In sports

In the sport of cricket, a four is a specific type of scoring event, scoring four runs.

In rugby union, the number of the lock forward, who usually jumps at number 2 in the line-out.

In rugby league, the number of one of the two centres. It is also the number of points awarded for a try.

In baseball, 4 represents the second baseman's position. It was also the jersey number of Lou Gehrig, Mel Ott, Joe Cronin, and Paul Molitor. It was the jersey number of Earl Weaver, long-time manager of the Baltimore Orioles.

In basketball, 4 represents the power forward position. Also, The term Final Four refers to the last four teams remaining in the NCAA playoff tournament. If a player completes a three-pointer while being fouled, the player is awarded one free-throw for a possible 4-point-play. The number for the Toronto Raptors foward Chris Bosh.

In ice hockey, 4 was the jersey number worn by Hall of Famers Jean Beliveau and Bobby Orr.

In American football, 4 is today most commonly identified with the jersey number of Green Bay Packers quarterback Brett Favre.

In rowing, a four refers to a boat for four rowers, with or without coxswain. In rowing nomenclature 4- reprsents a coxless four and 4+ represents a coxed four.

In football, number 4 is assigned in most cases to the centre back.

In other fields

International maritime signal flag for 4

See also 4 (disambiguation)

Groups of four

"And a river went out of Eden to water the garden; and from thence it was parted, and became into four heads. The name of the first is Pison: that is it which compasseth the whole land of Havilah, where there is gold; And the gold of that land is good: there is bdellium and the onyx stone. And the name of the second river is Gihon: the same is it that compasseth the whole land of Ethiopia. And the name of the third river is Hiddekel: that is it which goeth toward the east of Assyria. And the fourth river is Euphrates. ” - Genesis 2:10-14

References

  1. ^ 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): 394, Fig. 24.64
  • Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 55 - 58

Historical years

A.D. 4, 4 B.C., 1904, 2004, etc.