Sculpted date "1481" in the Convent church of Maria Steinach inAlgund,South Tirol,Italy. The upward loop signifies the number 4.
Brahmic numerals represented 1, 2, and 3 with as many lines. 4 was simplified by joining its four lines into a cross that looks like the modern plus sign. TheShunga would add a horizontal line on top of the digit, and theKshatrapa andPallava evolved the digit to a point where the speed of writing was a secondary concern. TheArabs' 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 the finishing curve and gradually made the digit less cursive, ending up with a digit very close to the original Brahmin cross.[1]
While the shape of the character for the digit 4 has anascender in most moderntypefaces, in typefaces withtext figures the glyph usually has adescender, as, for example, in.
Lagrange's four-square theorem states that every positive integer can be written as the sum of at most foursquares.[4][5] Four is one of fourall-Harshad numbers. Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e..
A four-sided plane figure is aquadrilateral or quadrangle, sometimes also called atetragon. It can be further classified as arectangle oroblong,kite,rhombus, andsquare.
Four is the only square number where is a prime number.
Thefour-color theorem states that aplanar graph (or, equivalently, a flatmap of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors.[7] Three colors are not, in general, sufficient to guarantee this.[8] The largest planarcomplete graph has four vertices.[9]
A solid figure with four faces as well as four vertices is atetrahedron, which is the smallest possible number of faces and vertices apolyhedron can have.[10] The regular tetrahedron, also called a 3-simplex, is the simplestPlatonic solid.[11] It has fourregular triangles as faces that are themselves atdual positions with the vertices of another tetrahedron.[12]
The symbolic meanings of the number four are linked to those of the cross and the square. "Almost from prehistoric times, the number four was employed to signify what was solid, what could be touched and felt. Its relationship to the cross (four points) made it an outstanding symbol of wholeness and universality, a symbol which drew all to itself". Where lines of latitude and longitude intersect, they divide the earth into four proportions. Throughout the world kings and chieftains have been called "lord of the four suns" or "lord of the four quarters of the earth",[18] which is understood to refer to the extent of their powers both territorially and in terms of total control of their subjects' doings.
Four represents the fourmatriarchs (Sarah, Rebecca, Rachel, and Leah); the four sides of the world, the four extremes.
Christianity
Four represents the 3+1 of theHoly Trinity engendered as the one God and has a particular significance in Christian Theology because of that. In Augustinian numerology, four represents the earth and earthly affairs.
In technology
Ininternet slang, "4" can replace the word "for" (as "four" and "for" are pronounced similarly). For example, typing "4u" instead of "for you".
InLeetspeak, "4" may be used to replace the letter "A".
Other groups of four
Approximately four weeks (4 times 7 days) to a lunar month (synodic month = 29.54 days). Thus the number four is universally an integral part of primitive sacred calendars.
^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
^Spencer, Joel (1996), Chudnovsky, David V.; Chudnovsky, Gregory V.; Nathanson, Melvyn B. (eds.), "Four Squares with Few Squares",Number Theory: New York Seminar 1991–1995, New York, NY: Springer US, pp. 295–297,doi:10.1007/978-1-4612-2418-1_22,ISBN978-1-4612-2418-1
^Hilbert, David; Cohn-Vossen, Stephan (1999).Geometry and the Imagination. American Mathematical Soc. p. 143.ISBN978-0-8218-1998-2....the tetrahedron plays an anomalous role in that it is self-dual, whereas the four remaining polyhedra are mutually dual in pairs...
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