| ||||
---|---|---|---|---|
Cardinal | four | |||
Ordinal | 4th (fourth) | |||
Numeral system | quaternary | |||
Factorization | 22 | |||
Divisors | 1, 2, 4 | |||
Greek numeral | Δ´ | |||
Roman numeral |
| |||
Greek prefix | tetra- | |||
Latin prefix | quadri-/quadr- | |||
Binary | 1002 | |||
Ternary | 113 | |||
Senary | 46 | |||
Octal | 48 | |||
Duodecimal | 412 | |||
Hexadecimal | 416 | |||
Armenian | Դ | |||
Arabic, Kurdish | ٤ | |||
Persian, Sindhi | ۴ | |||
Shahmukhi, Urdu | ۴ | |||
Ge'ez | ፬ | |||
Bengali, Assamese | ৪ | |||
Chinese numeral | 四,亖,肆 | |||
Devanagari | ४ | |||
Telugu | ౪ | |||
Malayalam | ൪ | |||
Tamil | ௪ | |||
Hebrew | ד | |||
Khmer | ៤ | |||
Thai | ๔ | |||
Kannada | ೪ | |||
Burmese | ၄ | |||
Babylonian numeral | 𒐘 | |||
Egyptian hieroglyph, Chinese counting rod | |||| | |||
Maya numerals | •••• | |||
Morse code | .... _ |
4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures.
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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. The Shunga would add a horizontal line on top of the digit, and the Kshatrapa and Pallava evolved the digit to a point where the speed of writing was a secondary concern. The Arabs' 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 an ascender in most modern typefaces, in typefaces with text figures the glyph usually has a descender, as, for example, in .
On the seven-segment displays of pocket calculators and digital watches, as well as certain optical character recognition fonts, 4 is seen with an open top: . [2]
Television stations that operate on channel 4 have occasionally made use of another variation of the "open 4", with the open portion being on the side, rather than the top. This version resembles the Canadian Aboriginal syllabics letter ᔦ. The magnetic ink character recognition "CMC-7" font also uses this variety of "4". [3]
There are four elementary arithmetic operations in mathematics: addition (+), subtraction (−), multiplication (×), and division (÷).[ citation needed ]
Lagrange's four-square theorem states that every positive integer can be written as the sum of at most four squares. [4] [5] Four is one of four all-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 a quadrilateral or quadrangle, sometimes also called a tetragon. It can be further classified as a rectangle or oblong, kite, rhombus, and square.
Four is the highest degree general polynomial equation for which there is a solution in radicals. [6]
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. [7] Three colors are not, in general, sufficient to guarantee this. [8] The largest planar complete graph has four vertices. [9]
A solid figure with four faces as well as four vertices is a tetrahedron, which is the smallest possible number of faces and vertices a polyhedron can have. [10] The regular tetrahedron, also called a 3-simplex, is the simplest Platonic solid. [11] It has four regular triangles as faces that are themselves at dual positions with the vertices of another tetrahedron. [12] The tetrahedron is one of three regular polyhedra that tessellate space.[ citation needed ]
The smallest non-cyclic group has four elements; it is the Klein four-group. [13] An alternating groups are not simple for values ≤ .
There are four Hopf fibrations of hyperspheres:
They are defined as locally trivial fibrations that map for values of (aside from the trivial fibration mapping between two points and a circle). [14]
In Knuth's up-arrow notation, , and so forth, for any number of up arrows. [15]
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 × x | 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 | 16 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
4 ÷ x | 4 | 2 | 1.3 | 1 | 0.8 | 0.6 | 0.571428 | 0.5 | 0.4 | 0.4 | 0.36 | 0.3 | 0.307692 | 0.285714 | 0.26 | 0.25 |
x ÷ 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 | 4 |
Exponentiation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
4x | 4 | 16 | 64 | 256 | 1024 | 4096 | 16384 | 65536 | 262144 | 1048576 | 4194304 | 16777216 | 67108864 | 268435456 | 1073741824 | 4294967296 |
x4 | 1 | 16 | 81 | 256 | 625 | 1296 | 2401 | 4096 | 6561 | 10000 | 14641 | 20736 | 28561 | 38416 | 50625 | 65536 |
A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e., an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is radially equilateral. Its dual polyhedron is the rhombic dodecahedron.
In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. Such dual figures remain combinatorial or abstract polyhedra, but not all can also be constructed as geometric polyhedra. Starting with any given polyhedron, the dual of its dual is the original polyhedron.
In geometry, an octahedron is a polyhedron with eight faces. An octahedron can be considered as a square bipyramid. When the edges of a square bipyramid are all equal in length, it produces a regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. It is also an example of a deltahedron. An octahedron is the three-dimensional case of the more general concept of a cross polytope.
In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions n as an n-dimensional polytope or n-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope. In this context, "flat sides" means that the sides of a (k + 1)-polytope consist of k-polytopes that may have (k – 1)-polytopes in common.
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent regular polygons, and the same number of faces meet at each vertex. There are only five such polyhedra:
In geometry, a tetrahedron, also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra.
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles. The tesseract is one of the six convex regular 4-polytopes.
In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact. It is named after the Russian mathematician Pavel Alexandroff. More precisely, let X be a topological space. Then the Alexandroff extension of X is a certain compact space X* together with an open embedding c : X → X* such that the complement of X in X* consists of a single point, typically denoted ∞. The map c is a Hausdorff compactification if and only if X is a locally compact, noncompact Hausdorff space. For such spaces the Alexandroff extension is called the one-point compactification or Alexandroff compactification. The advantages of the Alexandroff compactification lie in its simple, often geometrically meaningful structure and the fact that it is in a precise sense minimal among all compactifications; the disadvantage lies in the fact that it only gives a Hausdorff compactification on the class of locally compact, noncompact Hausdorff spaces, unlike the Stone–Čech compactification which exists for any topological space.
8 (eight) is the natural number following 7 and preceding 9.
Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe. Thus Graham's number cannot be expressed even by physical universe-scale power towers of the form , even though Graham's number is indeed a power of 3.
In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 equilateral triangle faces, 12 vertices and 18 edges. It can be constructed by truncating all 4 vertices of a regular tetrahedron.
The notion of a fibration generalizes the notion of a fiber bundle and plays an important role in algebraic topology, a branch of mathematics.
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the numbers of points forming regular patterns within different shapes.
In differential topology, the Hopf fibration describes a 3-sphere in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle. Technically, Hopf found a many-to-one continuous function from the 3-sphere onto the 2-sphere such that each distinct point of the 2-sphere is mapped from a distinct great circle of the 3-sphere. Thus the 3-sphere is composed of fibers, where each fiber is a circle — one for each point of the 2-sphere.
In mathematics, the barycentric subdivision is a standard way to subdivide a given simplex into smaller ones. Its extension on simplicial complexes is a canonical method to refine them. Therefore, the barycentric subdivision is an important tool in algebraic topology.
In nuclear physics and particle physics, isospin (I) is a quantum number related to the up- and down quark content of the particle. Isospin is also known as isobaric spin or isotopic spin. Isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons.
In algebraic geometry, the normal cone of a subscheme of a scheme is a scheme analogous to the normal bundle or tubular neighborhood in differential geometry.
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number.
In the field of mathematics known as algebraic topology, the Gysin sequence is a long exact sequence which relates the cohomology classes of the base space, the fiber and the total space of a sphere bundle. The Gysin sequence is a useful tool for calculating the cohomology rings given the Euler class of the sphere bundle and vice versa. It was introduced by Gysin, and is generalized by the Serre spectral sequence.
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron composed of regular pentagonal faces, three meeting at each vertex. It is an example of Platonic solids, described as cosmic stellation by Plato in his dialogues, and it was used as part of Solar System proposed by Johannes Kepler. However, the regular dodecahedron, including the other Platonic solids, has already been described by other philosophers since antiquity.
7 is an example of an integer that can't be written as the sum of three squares.
There is no algebraic formula for the roots of the general polynomial of degrees 5 or higher.
(i.e. That there are maps for which three colors are not sufficient)
... The complete graph on the largest number of vertices that is planar is K4 and that a(K4) equals 4.
...the smallest possible number of faces that a polyhedron may have is four
...face of the platonic solid. The simplest of these shapes is the tetrahedron...
...the tetrahedron plays an anomalous role in that it is self-dual, whereas the four remaining polyhedra are mutually dual in pairs...
The Klein four-group is the smallest noncyclic group,...
2 ↑↑ ... ↑↑ 2 is always 4
The four main pilgrimages sites are: Lumbini, Bodh Gaya, Sarnath and Kusinara....four Noble Truths of Buddhism
He first observed the suffering of the world in the Four Passing Sites
The four great elements, earth, water, fire and wind...
The Buddhists adopted him as one of the four Devarajas or Heavenly Kings
The four right exertions are...
these four bases of psychic power
This book is about the four jhanas
...the states of the four arupajhanas.
There are four of them: loving-kindness, metta, compassion, karuna, sympathetic joy, mudita and equanimity, upekkha.
...four types of shravaka (stream enterer, oncereturner, nonreturner, and arhat)
We have already mentioned the four living creatures—the man, the lion, the ox and the eagle
The four horsemen of the Apocalypse are one of the most familiar images of Revelation
In a generally ignored but all-important paragraph of Genesis 2, we are told how the world was organized when it was created [...]. In short, the world was organized in terms of a primordial duality between the central sanctuary of Eden, and the outlying world watered by four rivers extending to the four corners of the world.
...as well as to the palm ( lulav ), myrtle ( hadas ), willow ( aravah ) and citron ( etrog ), the four species of plants
...be like Sarah, Rachel, Rebecca, and Leah, the foremothers of Judaism
The Passover Seder is particularly structured around fours: the Four Questions, the Four Sons, and four cups of wine.
The four holy cities of Judaism are Jerusalem, Hebron, Safed, and Tiberius.
There are four Vedas
that these four proper aims and objects
The Four Stages of Life
The four primary castes or strata of society:...
Brahma has four faces,...
...Eid al-Adha (Feast of Sacrifice) lasts four days ...
... four Rightly Guided Caliphs, Abu-Bakr, Umar ibn al-Khattab, Uthman ibn Affan and Ali ibn Abi Talib,...
According to Islam, the Four Arch Angels are: Jibraeel (Gabriel), Mikaeel (Michael), Izraeel (Azrael), and Israfil (Raphael).
The sacred months are four, Rajab, Dhu al-Qi'dah, Dhu al-Hijjah, and al-Muharram. During those four sacred months there were no war...
There are four books in Islam: Torah, Zaboor, Injeel and Holy Qur'an...
For those who take an oath for abstention from their wives, awaiting for four months is ordained;
...for four months and ten days.
Then take four birds, ...
The respite of four months...
And those who launch a charge against chaste women and do not produce four witnesses...
Taoism later incorporated the four symbols into its immortality system...
the four corners or extremities of the earth (Isa. xi, 12; Ezek. vii, 2.; Rev. vii, 1; xx, 8), corresponding, doubtless, with the four points of the compass
Four was a sacred number of Zia
In Chinese, Japanese, and Korean, the word for four is, unfortunately, an exact homonym for death
Svetovid is portrayed as having four heads ...
[...] The characteristic eight bit field is sometimes referred to as a byte, a four bit field can be referred to as a nibble. [...]
Oligomers containing two, three, four, five, six or even more subunits are known as dimers, trimers, tetramers, pentamers, hexamers, and so on.
The four inner planets (known as terrestrial, or rocky planets
...the gas giants (Jupiter and Saturn), and the icy giants (Uranus and Neptune)
including the four large Galilean moons that are easily visible from a hobby telescope
M4 is a globular star cluster near Antares in Scorpius.
IV, subgiants
The mammalian heart consists of four chambers,...
Except for the flies, mosquitoes, and some others, insects with wings have four wings.
metamorphosis is marked by four distinct stages
In the 'ABO' system, all blood belongs one of four major groups — A, B, AB or O
Four canines for tearing + Eight premolars for crushing +Twelve molars (including four wisdom teeth)
The cow's stomach is divided into four compartments.
Of course, carbon is not the only chemical element with a valence of +4 or -4
Beryllium has an atomic number of four
Plasma is one of the four fundamental states of matter, the others being solid, liquid, and gas.
should be regarded as a four-dimensional world
We have referred to the four fundamental forces in nature,...
The Four Functions Theorem of Ahlswede Daykin
This book examines Aristotle's four causes (material, formal, efficient, and final)
The OODA loop consists of four steps.
Plastic Recycling Symbol #4: LDPE
CMYK is the standard four-color model used for all full-color print jobs that will be output on an offset printing press
...the 4 key (labeled with the letters g, h and i)...
A byte also contains two 4-bit nibbles...
... called common time and denoted by C, which has four beats per measure
The number, character and sequence of movements in the symphony, moreover, did not stabilize until the 1770s when the familiar format of four movements...
...the four houses of Hogwarts School of Witchcraft and Wizardry: Gryffindor, Ravenclaw, Hufflepuff, and Slytherin
Every year that is divisible by four, except the Centennial years, and every Centennial year divisible by 400, is a leap year...
Each of the familiar cardinal directions is equivalent to a particular true bearing: north (0°), east (90°), south (180°), and west (270°)
...four substances or humors: blood, yellow bile, black bile and phlegm
The four playing card suits, as you probably already know, are spades, hearts, diamonds, and clubs