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Revision as of 20:32, 26 August 2022
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Many letters of the Latin alphabet, both capital and small, are used in mathematics, science, and engineering to denote by convention specific or abstracted constants, variables of a certain type, units, multipliers, or physical entities. Certain letters, when combined with special formatting, take on special meaning.
Below is an alphabetical list of the letters of the alphabet with some of their uses. The field in which the convention applies is mathematics unless otherwise noted.
Aa
- A represents:
- the first point of a triangle[1]
- the digit "10" in hexadecimal[2] and other positional numeral systems with a radix of 11 or greater[3]
- the unit ampere for electric current in physics[4]
- the area of a figure[5]
- the mass number or nucleon number of an element in chemistry[6]
- the Helmholtz free energy of a closed thermodynamic system of constant pressure and temperature[7]
- a vector potential, in electromagnetics it can refer to the magnetic vector potential[8]
- an Abelian group in abstract algebra
- the Glaisher–Kinkelin constant[9]
- atomic weight, denoted by Ar [10]
- work in classical mechanics[10]
- the pre-exponential factor[10] in the Arrhenius Equation[11]
- electron affinity[10]
- represents the algebraic numbers[12] or affine space in algebraic geometry.
- a represents:
- the first side of a triangle (opposite point A)[1]
- the scale factor of the expanding universe in cosmology[13]
- the acceleration in mechanics equations[5]
- the x-intercept of a line using the line equation[14]
- the unit are for area (100 m2)[15]
- the unit prefix atto (10−18)[16]
- the first term in a sequence or series[17]
Bb
- B represents:
- the digit "11" in hexadecimal[2] and other positional numeral systems with a radix of 12 or greater[3]
- the second point of a triangle[1]
- a ball (also denoted by ℬ () or )[18]
- a basis of a vector space or of a filter (both also denoted by ℬ ())
- in econometrics and time-series statistics it is often used for the backshift or lag operator, the formal parameter of the lag polynomial
- the magnetic field, denoted or
- B with various subscripts represents several variations of Brun's constant and Betti numbers; it can also be used to mean the Bernoulli numbers.
- b represents:
- the second side of a triangle (opposite point B)
- the impact parameter in nuclear scattering
- the y-intercept of a line using the line equation
- usually with an index, sometimes with an arrow over it, a basis vector
- a breadth[10]
- the molality of a solution[10]
Cc
- C represents:
- the third point of a triangle
- the digit "12" in hexadecimal and other positional numeral systems with a radix of 13 or greater
- the unit coulomb of electrical charge[10]
- capacitance in electrical theory
- with indices denoting the number of combinations, a binomial coefficient
- together with a degree symbol (°), the Celsius measurement of temperature = °C[10]
- the circumference of a circle or other closed curve
- the complement of a set (lowercase c and the symbol ∁ are also used)
- an arbitrary category
- the number concentration[10]
- represents the set of complex numbers.
- A vertically elongated C with an integer subscript n sometimes denotes the n-th coefficient of a formal power series.
- c represents:
- the unit prefix centi (10−2)[10]
- the amount concentration in chemistry[10]
- the speed of light in a vacuum[19]
- the third side of a triangle (opposite corner C)
- Lowercase Fraktur denotes the cardinality of the set of real numbers (the "continuum"), or, equivalently, of the power set of natural numbers.
Dd
- D represents
- the digit "13" in hexadecimal and other positional numeral systems with a radix of 14 or greater
- diffusion coefficient or diffusivity in dimensions of [distance2/time]
- the differential operator in Euler's calculus notation
- dissociation energy[10]
- d represents
Ee
- E represents:
- the digit "14" in hexadecimal and other positional numeral systems with a radix of 15 or greater
- an exponent in decimal numbers. For example, 1.2E3 is 1.2×103 or 1200
- the set of edges in a graph or matroid
- the unit prefix exa (1018)[10]
- energy in physics[10]
- electric field denoted or
- electromotive force (denoted and measured in volts), refers to voltage
- an event (as in P(E), which reads "the probability P of event E occurring")
- in statistics, the expected value of a random variable, sometimes as
- Ek represents kinetic energy[10]
- (Arrhenius) activation energy, denoted Ea or EA[10]
- ionization energy, denoted Ei[10]
- electron affinity, denoted Eea[20]
- dissociation energy, denoted Ed[10]
- e represents:
- Euler's number, a transcendental number equal to 2.71828182845... which is used as the base for natural logarithms
- a vector of unit length, especially in the direction of one of the coordinates axes
- the elementary charge in physics
- an electron, usually denoted e− to distinguish against a positron e+
- the eccentricity of a conic section
- the identity element in a group
Ff
- F represents
- the digit "15" in hexadecimal and other positional numeral systems with a radix of 16 or greater
- the unit farad of electrical capacity[10]
- the Helmholtz free energy of a closed thermodynamic system of constant pressure and temperature
- together with a degree symbol (°) represents the Fahrenheit measurement of temperature = °F
- F represents
- force in mechanics equations[10]
- pFq is a hypergeometric series
- the probability distribution function in statistics
- a Fibonacci number
- an arbitrary functor
- a field
- an event space sigma algebra as part of a probability space, often as
- f represents:
- f represents:
- the generic designation of a function
Gg
- G represents
- an arbitrary graph, as in: G(V,E)
- an arbitrary group
- the unit prefix giga (109)[10]
- Newton's gravitational constant[10]
- the Einstein tensor
- the Gibbs energy
- the centroid of a triangle
- Catalan's constant
- weight measured in newtons[10]
- g represents:
- the generic designation of a second function
- the acceleration due to gravity on Earth
- a unit of mass, the gramme
Hh
- H represents:
- a Hilbert space
- the unit henry of magnetic inductance[10]
- the homology and cohomology functor
- the enthalpy
- the (Shannon) entropy of information
- the orthocenter of a triangle
- a partial sum of the harmonic series
- magnetic field, denoted
- the Hamilton function[10]
- H0 represents Hubble's parameter as measured today (100 h km·s−1·Mpc−1), with h being the associated error.
- represents the quaternions (after William Rowan Hamilton).
- ΔH‡ represents the standard enthalpy of activation[10] in the Eyring equation.[21]
- ℋ () represents the Hamiltonian in Hamiltonian mechanics.
- h represents:
- the class number in algebraic number theory
- a small increment in the argument of a function
- the unit hour for time (3600 s)
- the Planck constant (6.626 069(57)× 10−34 J·s)
- the unit prefix hecto (102)[10]
- the generic designation of a third function
- the altitude of a triangle
- a height[10]
Ii
- I represents:
- the closed unit interval, which contains all real numbers from 0 to 1, inclusive
- the identity matrix
- the Irradiance
- the moment of inertia[10]
- intensity in physics
- the incenter of a triangle
- the electric current[10]
- ionization energy, denoted I[10]
- I represents:
- the index of an indexed family
- i represents:
- the imaginary unit, a complex number that is the square root of −1
- a subscript to denote the ith term (that is, a general term or index) in a sequence or list
- the index to the elements of a vector, written as a subscript after the vector name
- the index to the rows of a matrix, written as the first subscript after the matrix name
- an index of summation using the sigma notation
- the unit vector in Cartesian coordinates going in the X-direction, usual bold i
Jj
- J represents:
- the unit joule of energy[10]
- the current density in electromagnetism denoted [10]
- the radiosity in thermal mechanics
- the moment of inertia[10]
- J represents:
- the scheme of a diagram in category theory
- j represents:
- the index to the columns of a matrix, written as the second subscript after the matrix name
- in electrical engineering, the square root of −1, instead of i
- in electrical engineering, the principal cube root of 1:
Kk
- K represents:
- k represents
- the unit prefix kilo- (103)[10]
- the Boltzmann constant, this is often represented as kB to avoid confusion with
- the wavenumber of the wave equation
- an integer, e.g. a dummy variable in summations, or an index of a matrix
- an unspecified (real) constant
- the spring constant of Hooke's law
- the spacetime curvature from the Friedmann equations in cosmology
- the rate constant (coefficient)[10]
Ll
- L represents:
- length, used often in quantum mechanics as the size of an infinite square well[10]
- angular momentum[10]
- the unit of volume the litre
- the radiance
- the space of all integrable real (or complex) functions
- the space of linear maps, as in L(E,F) or L(E) = End(E)
- the likelihood function
- a formal language
- the lag operator in statistics
- a Lucas number
- the Lagrange function[10]
- l represents:
- the unit of volume the litre
- the length of a side of a rectangle or a cuboid (e.g. V = lwh; A = lw)
- the last term of a sequence or series (e.g. Sn = n(a+l)/2)
- the orbital angular momentum quantum number[22]
- ℒ () represents:
- the Lagrangian (sometimes just L)
- exposure (in particle physics)
Mm
- M represents:
- a manifold
- a metric space
- a matroid
- the unit prefix mega- (106)[10]
- the Madelung constant for crystal structures held by ionic bonding
- the moment of force[10]
- molar mass[10]
- molar mass constant, denoted Mu[10]
- relative molecular mass, denoted Mr [10]
- m represents:
Nn
- N represents
- the unit newton of force[10]
- the nine-point center of a triangle
- N represents
- the neutron number[10]
- The number of particles of a thermodynamical system[23]: 57
- NA represents the Avogadro constant
- represents the natural numbers.
- n represents
- n represents
- the number of columns in a matrix
- the "number of" in algebraic equations
- the number density of particles in a volume
- the index of the nth term of a sequence or series (e.g. tn = a + (n − 1)d)
- the principal quantum number[10]
- the amount of a given substance[10]
- the number concentration[10]
- the overall order of reaction[10]
Oo
- O represents
- the order of asymptotic behavior of a function (upper bound); see Big O notation
- — the origin of the coordinate system in Cartesian coordinates
- the circumcenter of a triangle or other cyclic polygon, or more generally the center of a circle
- o represents
- the order of asymptotic behavior of a function (strict upper bound); see Little o notation
- the order of an element in a group
Pp
- P represents:
- represents
- the prime numbers
- projective space
- a probability (as in P(E), which reads "the probability P of event E happening")
- p represents
- Q represents:
- heat energy[23]: 6
- electroweak charge, denoted QW[10]
- represents the rational numbers
- q represents:
- the deceleration parameter in cosmology
- electric charge of a particle
- a generalized coordinate[10]
Rr
- R represents:
- the Ricci tensor
- the circumradius of a cyclic polygon such as a triangle
- an arbitrary relation
- represents the set of real numbers and various algebraic structures built upon the set of real numbers, such as .
- r represents:
- the radius of a circle or sphere[10]
- the inradius of a triangle or other tangential polygon
- the ratio of a geometric series (e.g. arn−1)
- the separation of two objects, for example in Coulomb's law
- a position vector[10]
- the rate of concentration change of B (due to chemical reaction) denoted rB [24]
Ss
- S represents
- a sum
- the unit siemens of electric conductance[10]
- the unit sphere (with superscript denoting dimension)
- the scattering matrix
- entropy
- action in joule-seconds[10]
- s represents:
- an arclength[10]
- a path length[10]
- the displacement in mechanics equations
- the unit second of time[10]
- a complex variable s = σ + i t in analytic number theory
- the semiperimeter of a triangle or other polygon
- 𝒮 () represents a system's action in physics
Tt
- T represents:
- the top element of a lattice
- a tree (a special kind of graph)
- temperature in physics equations[23]: 4
- the unit tesla of magnetic flux density[10]
- the unit prefix tera (1012)[10]
- the stress–energy tensor
- tension in physics
- an arbitrary monad
- the time it takes for one oscillation[10]
- kinetic energy[10]
- Torque[10]
- t represents:
- time in graphs, functions or equations[10]
- a term in a sequence or series (e.g. tn = tn−1 + 5)
- the imaginary part of the complex variable s = σ + it in analytic number theory
- the sample statistic resulting from a Student's t-test
- the half life of a quantity, denoted as t1⁄2[10]
Uu
- U represents:
- a U-set which is a set of uniqueness
- a unitary operator
- in thermodynamics, the internal energy of a system
- a forgetful functor
- U(n) represents the unitary group of degree n
- ∪ represents the union operator
- u represents the initial velocity in mechanics equations[10][25]
Vv
- V represents:
- the unit volt of voltage[10]
- the set of vertices in a graph
- a vector space
- potential energy[10]
- molar volume denoted by Vm[10]
- v represents
- the final velocity in mechanics equations[10][25]
- frequency,[10] especially when referring to electromagnetic waves[26]
- a specific volume in classical mechanics[10]
- the rate of concentration change of B (due to chemical reaction) denoted vB[24]
- the rate of reaction based on amount concentration denoted v or vc
- the rate of reaction based on number concentration denoted v or vC
Ww
- W represents:
- the unit watt of power[10]
- work, both mechanical and thermodynamical[23]: 8–9
- in thermodynamics, the number of possible quantum states in Boltzmann's entropy formula
- weight measured in newtons[10]
- w represents:
- the coordinate on the fourth axis in four-dimensional space
- work in classical mechanics
Xx
- X represents
- Ẋ represents
- the rate of change of quantity X[10]
- x represents
- a realized value of a random variable
- an unknown variable, most often (but not always) from the set of real numbers, while a complex unknown would rather be called z, and an integer by a letter like m from the middle of the alphabet
- the coordinate on the first or horizontal axis in a Cartesian coordinate system,[10] or the viewport in a graph or window in computer graphics
- a mole fraction[10]
Yy
- Y represents:
- Y represents:
- a second random variable
- y represents:
- the unit prefix yocto- (10−24)[10]
- a realized value of a second random variable
- a second unknown variable
- the coordinate on the second or vertical axis (backward axis in three dimensions) in a Cartesian coordinate system,[10] or in the viewport of a graph or window in computer graphics
- a mole fraction[10]
Zz
- Z represents:
- the unit prefix zetta (1021)[10]
- the atomic number or proton number of an element in chemistry[10]
- a standardized normal random variable in probability theory and statistics
- The partition function in statistical mechanics[23]: 111
- in meteorology, the radar reflectivity factor
- represents the integers
- z represents:
- the unit prefix zepto (10−21)[10]
- the coordinate on the third or vertical axis in three dimensional space[10]
- the view depth in computer graphics, see also "z-buffering"
- the argument of a complex function, or any other variable used to represent a complex value
- in astronomy, wavelength redshift[27]: 9
- a third unknown variable
- the collision frequency of A with A is denoted zA(A)[28]
- the collision frequency factor is denoted zAB[10]
See also
- Blackboard bold letters used in mathematics
- Greek letters used in mathematics
- List of letters used in mathematics and science
- Mathematical alphanumeric symbols
- Table of mathematical symbols
References
- ^ a b c Weisstein, Eric W. "Triangle". mathworld.wolfram.com. Retrieved 2022-03-21.
- ^ a b "Hexadecimal - Hexadecimal and character sets - GCSE Computer Science Revision". BBC Bitesize. Retrieved 2022-03-21.
- ^ a b "DECIMAL function". support.microsoft.com. Retrieved 2022-03-22.
- ^ "BIPM - SI base units". bipm.org. 2014-10-07. Archived from the original on 2014-10-07.
- ^ a b "BIPM - SI derived units". bipm.org. 2014-10-07. Archived from the original on 2014-10-07. Retrieved 2022-03-22.
- ^ Jensen, William B. (December 2005). "The Origins of the Symbols A and Z for Atomic Weight and Number". Journal of Chemical Education. 82 (12): 1764. Bibcode:2005JChEd..82.1764J. doi:10.1021/ed082p1764. ISSN 0021-9584.
- ^ "22.1: Helmholtz Energy". Chemistry LibreTexts. 2014-06-21. Retrieved 2022-03-23.
- ^ "The magnetic vector potential". farside.ph.utexas.edu. Retrieved 2022-03-21.
- ^ Weisstein, Eric W. "Glaisher-Kinkelin Constant". mathworld.wolfram.com. Retrieved 2022-03-21.
- ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw ax ay az ba bb bc bd be bf bg bh bi bj bk bl bm bn bo bp bq br bs bt bu bv bw bx by bz ca cb cc cd ce cf cg ch ci cj ck cl cm cn co cp cq cr cs ct cu cv cw cx cy cz da db dc dd Stohner, Jürgen; Quack, Martin (2011). "A Concise Summary of Quantities, Units, and Symbols in Physical Chemistry" (PDF). Chemistry International. 33 (4). De Gruyter: Centerfold.
- ^ "6.2.3.1: Arrhenius Equation". Chemistry LibreTexts. 2013-10-02. Retrieved 2022-04-03.
- ^ Weisstein, Eric W. "Algebraic Number". mathworld.wolfram.com. Retrieved 2022-03-22.
- ^ Liebscher, Dierck-Ekkehard (2005). Cosmology. Berlin: Springer. pp. 53–77. ISBN 9783540232612.
- ^ "Earliest Uses of Symbols from Geometry". Maths History. Retrieved 2022-03-24.
- ^ Conversion factors and tables. Part 1. Basis of tables. Conversion factors. British Standards Institution (3rd revision ed.). London: BSI. 1974. p. 7. ISBN 0-580-08471-X. OCLC 32212391.
{{cite book}}
: CS1 maint: others (link) - ^ Conversion factors and tables. Part 1. Basis of tables. Conversion factors. British Standards Institution (3rd revision ed.). London: BSI. 1974. p. 4. ISBN 0-580-08471-X. OCLC 32212391.
{{cite book}}
: CS1 maint: others (link) - ^ "Arithmetic Progression - Formula, Examples | AP Formula". Cuemath. Retrieved 2022-03-24.
- ^ Weisstein, Eric W. "Ball". mathworld.wolfram.com. Retrieved 2022-03-24.
- ^ Prasad, Paras N. (16 January 2004). Introduction to Biophotonics. John Wiley & Sons. p. 12. ISBN 978-0-471-46539-3.
- ^ Quantities, Units and Symbols in Physical Chemistry. International Union of Pure and Applied Chemistry. 1993. p. 20. ISBN 0-632-03583-8.
- ^ "6.4.1: Eyring equation". Chemistry LibreTexts. 2013-10-02. Retrieved 2022-04-03.
- ^ "Quantum Numbers for Atoms". Chemistry LibreTexts. 2013-10-02. Retrieved 2022-04-07.
- ^ a b c d e f g Kardar, Mehran (2007). Statistical Physics of Particles. Cambridge University Press. ISBN 978-0-521-87342-0. OCLC 860391091.
- ^ a b https://media.iupac.org/publications/analytical_compendium/Cha01sec39.pdf [bare URL PDF]
- ^ a b "Velocity, acceleration and distance - Motion - Edexcel - GCSE Physics (Single Science) Revision - Edexcel". BBC Bitesize. Retrieved 2022-03-26.
- ^ "frequency | Definition, Symbols, & Formulas | Britannica". www.britannica.com. Retrieved 2022-03-26.
- ^ Durrer, Ruth (2021). The cosmic microwave background (2nd ed.). Cambridge, United Kingdom: Cambridge University Press. ISBN 978-1-316-47152-4. OCLC 1182021387.
- ^ Quantities, Units and Symbols in Physical Chemistry. International Union of Pure and Applied Chemistry. 1993. p. 56. ISBN 0-632-03583-8.