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Notation for mathematical knots
Gauss notation (also known as a Gauss code or Gauss words) is a notation for mathematical knots. It is created by enumerating and classifying the crossings
Gauss_notation
Mathematical notation for describing the structure of knots
different number sequences possible in this notation. Alexander–Briggs notation Conway notation Gauss notation Dowker, C. H.; Thistlethwaite, Morwen B. (1983-07-01)
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite_notation
Algorithm for solving systems of linear equations
algebra textbooks by the end of the 18th century. Carl Friedrich Gauss in 1810 devised a notation for symmetric elimination that was adopted in the 19th century
Gaussian_elimination
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field
Divergence_theorem
Notation used to describe knots based on operations on tangles
exist. Conway knot Dowker notation Alexander–Briggs notation Gauss notation "Conway notation", mi.sanu.ac.rs. "Conway Notation", The Knot Atlas. Conway
Conway_notation_(knot_theory)
Study of mathematical knots
polyhedra, there are nonstandard choices available. Gauss code, similar to the Dowker–Thistlethwaite notation, represents a knot with a sequence of integers
Knot_theory
special notation invented by Carl Friedrich Gauss to represent the convergents of a simple continued fraction in the form of a simple fraction. Gauss used
Gaussian_brackets
Shorthand notation for tensor operations
differential geometry, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies
Einstein_notation
Mathematical algorithm
The Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It
Gauss–Newton_algorithm
Theorem related to ordinary least squares
In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest
Gauss–Markov_theorem
Method for representing or encoding numbers
Positional notation, also known as place-value notation, is the property of a numeral system that the value represented by each symbol in a written numeral
Positional_notation
Constant used in orbital mechanics
Do not confuse μ the gravitational parameter with Gauss's notation for the mass of the body. Gauss, Carl Friedrich; Davis, Charles Henry (1857). Theory
Gaussian gravitational constant
Gaussian_gravitational_constant
mathematical notation History of the Hindu–Arabic numeral system Glossary of mathematical symbols List of mathematical symbols by subject Mathematical notation Mathematical
Table of mathematical symbols by introduction date
Table_of_mathematical_symbols_by_introduction_date
Tensor index notation for tensor-based calculations
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with
Ricci_calculus
Nearest integers from a number
his proof of the Legendre's formula. Carl Friedrich Gauss introduced the square bracket notation [x] in his third proof of quadratic reciprocity (1808)
Floor_and_ceiling_functions
Equations describing classical electromagnetism
Maxwell's microscopic equations are written as (top to bottom: Gauss's law, Gauss's law for magnetism, Faraday's law, Ampère-Maxwell law) ∇ ⋅ E = ρ ε
Maxwell's_equations
Function defined by a hypergeometric series
Euler, but the first full systematic treatment was given by Carl Friedrich Gauss (1813). Studies in the nineteenth century included those of Ernst Kummer (1836)
Hypergeometric_function
Mathematical Concept
associated names for this idea: Mandel notation, Mandel–Voigt notation and Nye notation are others found. Kelvin notation is a revival by Helbig of old ideas
Voigt_notation
Branch of mathematics
surface onto a flat plane, a consequence of the later Theorema Egregium of Gauss. The first systematic or rigorous treatment of geometry using the theory
Differential_geometry
Graphical notation for multilinear algebra calculations
In mathematics and physics, Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions
Penrose_graphical_notation
Type of non-Euclidean geometry
a new geometry. Gauss wrote in an 1824 letter to Franz Taurinus that he had constructed it, but Gauss did not publish his work. Gauss called it "non-Euclidean
Hyperbolic_geometry
Array of numbers
including solving linear equations and finding matrix inverses with Gauss elimination and Gauss–Jordan elimination, respectively. A submatrix of a matrix is
Matrix_(mathematics)
Origin and evolution of the symbols used to write equations and formulas
than from notations. — Carl Friedrich Gauss, writing about the proof of Wilson's theorem At the turn of the 19th century, Carl Friedrich Gauss developed
History of mathematical notation
History_of_mathematical_notation
Mathematical notation for tensors and spinors
Abstract index notation (also referred to as slot-naming index notation) is a mathematical notation for tensors and spinors that uses indices to indicate
Abstract_index_notation
How many integer lattice points there are in a circle
In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and
Gauss_circle_problem
Algebraic object with geometric applications
concepts of later tensor analysis arose from the work of Carl Friedrich Gauss in differential geometry, and the formulation was much influenced by the
Tensor
5-sided star shaped polygon
and E T S {\displaystyle ETS} are rotations of one another. Gauss introduced the notation ( α , β , γ , δ , ε ) = ( tan 2 T P , tan 2 P Q , tan 2
Pentagramma_mirificum
In mathematics, in number theory, Gauss composition law is a rule, invented by Carl Friedrich Gauss, for performing a binary operation on integral binary
Gauss_composition_law
Mathematics of smooth surfaces
investigated is the Gaussian curvature, first studied in depth by Carl Friedrich Gauss, who showed that curvature was an intrinsic property of a surface, independent
Differential geometry of surfaces
Differential_geometry_of_surfaces
Specification of a derivative along a tangent vector of a manifold
language and using a local coordinate system and the traditional index notation. The covariant derivative of a tensor field is presented as an extension
Covariant_derivative
Number of integers coprime to and less than n
now-standard notation φ ( A ) {\displaystyle \varphi (A)} comes from Gauss's 1801 treatise Disquisitiones Arithmeticae, although Gauss did not use parentheses
Euler's_totient_function
Gives conditions for the solvability of quadratic equations modulo prime numbers
before its modern form: Euler and Legendre did not have Gauss's congruence notation, nor did Gauss have the Legendre symbol. In this article p and q always
Quadratic_reciprocity
Formulation in classical mechanics
variational formulation of classical mechanics enunciated by Carl Friedrich Gauss in 1829, equivalent to all other formulations of analytical mechanics. Intuitively
Gauss's principle of least constraint
Gauss's_principle_of_least_constraint
Mathematical functions
by Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually
Lemniscate_elliptic_functions
How many times curves wind around each other
fractions or just not exist at all). The linking number was introduced by Gauss in the form of the linking integral. It is an important object of study
Linking_number
Array of numbers describing a metric connection
reminder that these are defined to be equivalent notation for the same concept. The choice of notation is according to style and taste, and varies from
Christoffel_symbols
Symbol with multiple meanings
identical. In number theory, it has been used beginning with Carl Friedrich Gauss (who first used it with this meaning in 1801) to mean modular congruence:
Triple_bar
Ways of writing certain laws of physics
inhomogeneous Maxwell's equations, Gauss's law and Ampère's law (with Maxwell's correction) combine into (with (+ − − −) metric): Gauss–Ampère law ∂ α F α β = μ
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Exterior algebraic map taking tensors from p forms to n-p forms
}(dy\wedge dz)&=dt\wedge dx\,.\end{aligned}}} These are summarized in the index notation as ⋆ ( d x μ ) = η μ λ ε λ ν ρ σ 1 3 ! d x ν ∧ d x ρ ∧ d x σ , ⋆ ( d x
Hodge_star_operator
Integral of the Gaussian function, equal to sqrt(π)
the entire real line. Named after the German mathematician Carl Friedrich Gauss, the integral is ∫ − ∞ ∞ e − x 2 d x = π . {\displaystyle \int _{-\infty
Gaussian_integral
Assignment of a tensor continuously varying across a region of space
curvature tensors built from them are. The notation for tensor fields can sometimes be confusingly similar to the notation for tensor spaces. Thus, the tangent
Tensor_field
Isomorphism between the tangent and cotangent bundles of a manifold
the use of the musical notation symbols ♭ {\displaystyle \flat } (flat) and ♯ {\displaystyle \sharp } (sharp). In the notation of Ricci calculus and mathematical
Musical_isomorphism
Operation in mathematics
2x2; often 3x3 or 4x4 are used, but any size is allowed. In simple index notation, this is written ∑ j = 1 2 a i j × b j k = c i k {\textstyle \sum _{j=1}^{2}a_{ij}\times
Tensor_contraction
Mathematical object that describes the electromagnetic field in spacetime
into two tensor field equations. In electrostatics and electrodynamics, Gauss's law and Ampère's circuital law are respectively: ∇ ⋅ E = ρ ε 0 , ∇ × B
Electromagnetic_tensor
Mathematical notation
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory
Multi-index_notation
Affine connection on the tangent bundle of a manifold
Transport phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad
Levi-Civita_connection
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
i = j ] . {\displaystyle \delta _{ij}=[i=j].} Often, a single-argument notation δ i {\displaystyle \delta _{i}} is used, which is equivalent to setting
Kronecker_delta
Group of units of the ring of integers modulo n
all other values of n the group is not cyclic. This was first proved by Gauss. This means that for these n: ( Z / n Z ) × ≅ C φ ( n ) , {\displaystyle
Multiplicative group of integers modulo n
Multiplicative_group_of_integers_modulo_n
equation was proven in 1997 by the Russian mathematician Sergey Bobkov. Notation: Let γ n ( d x ) = ( 2 π ) − n / 2 e − ‖ x ‖ 2 / 2 d n x {\displaystyle
Bobkov's_inequality
Complex number whose real and imaginary parts are both integers
Gaussian integers are named after the German mathematician Carl Friedrich Gauss. The Gaussian integers are the set Z [ i ] = { a + b i ∣ a , b ∈ Z } , where
Gaussian_integer
Integer that is a perfect square modulo some integer
Gauss used R and N to denote residuosity and non-residuosity, respectively; for example, 2 R 7 and 5 N 7, or 1 R 8 and 3 N 8. Although this notation is
Quadratic_residue
Tensor in differential geometry
The second fundamental form, which determines the full curvature via the Gauss–Codazzi equation, is itself determined by the Ricci tensor and the principal
Ricci_curvature
Mathematical operation on vector spaces
differentiable, then a */ b is differentiable. However, these kinds of notation are not universally present in array languages. Other array languages may
Tensor_product
contrast, a dyad is specifically a dyadic tensor of rank one. Einstein notation This notation is based on the understanding that whenever a multidimensional array
Glossary_of_tensor_theory
Conditions in number theory
Lemmermeyer, p. 172 Gauss, BQ § 2 Gauss, BQ § 3 Gauss, BQ §§ 4–7 Gauss, BQ § 8 Gauss, BQ § 10 Gauss, DA Art. 182 Gauss, DA, Art. 182 Gauss BQ §§ 14–21 Dirichlet
Quartic_reciprocity
Natural number
also the original representation of 3 in the Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the Gupta Empire
3
Method for specifying point positions
Transport phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad
Coordinate_system
Probability distribution
In his notation φΔ is the probability density function of the measurement errors of magnitude Δ. Not knowing what the function φ is, Gauss requires
Normal_distribution
German physicist (1804–1891)
23 June 1891) was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph. Weber was born in Schlossstrasse
Wilhelm_Eduard_Weber
Theorem on prime numbers
integers less than n is one less than a multiple of n. That is (using the notations of modular arithmetic), the factorial ( n − 1 ) ! = 1 × 2 × 3 × ⋯ × (
Wilson's_theorem
Matrix operation which flips a matrix over its diagonal
another matrix, called the transpose of A and often denoted AT (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician
Transpose
Swiss mathematician (1707–1783)
calculus. He also introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is known for his work
Leonhard_Euler
Expression that may be integrated over a region
dependent is zero. A common notation for the wedge product of elementary k {\displaystyle k} -forms is so called multi-index notation: in an n {\displaystyle
Differential_form
Notation used for Weyl spinors
In theoretical physics, Van der Waerden notation refers to the usage of two-component spinors (Weyl spinors) in four spacetime dimensions. This is standard
Van_der_Waerden_notation
Structure defining distance on a manifold
notion of a metric tensor was known in some sense to mathematicians such as Gauss from the early 19th century, it was not until the early 20th century that
Metric_tensor
Property of a mathematical space
Transport phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad
Dimension
Continuous surjection satisfying a local triviality condition
Transport phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad
Fiber_bundle
Algebraic operation on coordinate vectors
specified with respect to an orthonormal basis, is defined, in summation notation, as: a ⋅ b = ∑ i = 1 n a i b i = a 1 b 1 + a 2 b 2 + ⋯ + a n b n {\displaystyle
Dot_product
Field of knowledge
fruition with the contributions of Adrien-Marie Legendre and Carl Friedrich Gauss. Many easily stated number problems have solutions that require sophisticated
Mathematics
Mathematical algorithm for calculating area of a simple polygon
The shoelace formula, also known as Gauss's area formula and the surveyor's formula, is a mathematical algorithm to determine the area of a simple polygon
Shoelace_formula
Type of derivative in differential geometry
=f{\mathcal {L}}_{X}\omega +df\wedge i_{X}\omega .} In local coordinate notation, for a type ( r , s ) {\displaystyle (r,s)} tensor field T {\displaystyle
Lie_derivative
Mathematical function
They were introduced by Carl Gustav Jakob Jacobi (1829). Carl Friedrich Gauss had already studied special Jacobi elliptic functions in 1797, the lemniscate
Jacobi_elliptic_functions
Tensor that describes the 4D geometry of spacetime
{\displaystyle g_{\mu \nu }} themselves as the metric (see, however, abstract index notation). With the quantities d x μ {\displaystyle dx^{\mu }} being regarded as
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
Figurate number
by induction. An apocryphal story claims that the German mathematician Gauss found this relationship in his early youth, by multiplying n/2 pairs of
Triangular_number
Topological space that locally resembles Euclidean space
first studied such geometries in 1733, but sought only to disprove them. Gauss, Bolyai and Lobachevsky independently discovered them 100 years later. Their
Manifold
Straight path on a curved surface or a Riemannian manifold
Transport phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad
Geodesic
Algebra associated to any vector space
Then any alternating tensor t ∈ Ar(V) ⊂ Tr(V) can be written in index notation with the Einstein summation convention as t = t i 1 i 2 ⋯ i r e i 1 ⊗ e
Exterior_algebra
Set of vectors used to define coordinates
j}y_{j},} for i = 1, ..., n. This formula may be concisely written in matrix notation. Let A be the matrix of the a i , j {\displaystyle a_{i,j}} , and X = [
Basis_(linear_algebra)
Mathematical function, in linear algebra
Transport phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad
Linear_map
Approximation method in statistics
Ceres were those performed by the 24-year-old Gauss using least-squares analysis. In 1810, after reading Gauss's work, Laplace, after proving the central limit
Least_squares
Study of curves from a differential point of view
Transport phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad
Differentiable_curve
Type of matrix factorization
errors. Hence alternative expression becomes PAQ = LU, where in formal notation permutation matrix factors P and Q indicate permutation of rows (or columns)
LU_decomposition
Algorithm used to solve non-linear least squares problems
especially in least squares curve fitting. The LMA interpolates between the Gauss–Newton algorithm (GNA) and the method of gradient descent. The LMA is more
Levenberg–Marquardt_algorithm
Finite sum formed using the exponential function
incomplete sum is the partial sum of the quadratic Gauss sum (indeed, the case investigated by Gauss). Here there are good estimates for sums over shorter
Exponential_sum
Function in number theory
introducing a convenient notation that recorded whether a is a residue or a non-residue modulo p. Gauss' original notation used aRp for ( a p ) = 1 {\displaystyle
Legendre_symbol
Sequence of words formed by specific rules
language which utilised pictographs. Later, Carl Friedrich Gauss investigated the problem of Gauss codes. In the mid-19th century, George Boole established
Formal_language
Tensor describing energy momentum density in spacetime
superscripted variables (not exponents; see Tensor index notation and Einstein summation notation). The four coordinates of an event of spacetime x are given
Stress–energy_tensor
Vector behavior under coordinate changes
opposed to those of covectors) are said to be contravariant. In Einstein notation (implicit summation over repeated index), contravariant components are
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Extension of the factorial function
function" notation Π ( z ) = z ! {\displaystyle \Pi (z)=z!} due to Gauss is sometimes encountered in older literature, but Legendre's notation is dominant
Gamma_function
δ)-definition of limit Continuous function Derivative Notation Newton's notation for differentiation Leibniz's notation for differentiation Simplest rules Derivative
List_of_calculus_topics
Tensor equal to the negative of any of its transpositions
{\displaystyle U_{ijk\dots }=U_{(ij)k\dots }+U_{[ij]k\dots }.} A shorthand notation for anti-symmetrization is denoted by a pair of square brackets. For example
Antisymmetric_tensor
Variant of the metric system
mathematician Carl Friedrich Gauss to base a system of absolute units on the three fundamental units of length, mass and time. Gauss chose the units of millimetre
Centimetre–gram–second system of units
Centimetre–gram–second_system_of_units
Antisymmetric permutation object acting on tensors
lower case epsilon ε or ϵ, or less commonly the Latin lower case e. Index notation allows one to display permutations in a way compatible with tensor analysis:
Levi-Civita_symbol
Differential form of degree one or section of a cotangent bundle
Transport phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad
One-form
Theory of gravitation as curved spacetime
is the stress–energy tensor. All tensors are written in abstract index notation. Matching the theory's prediction to observational results for planetary
General_relativity
Third letter of the Greek alphabet
measure of magnetic flux density, sometimes used in geophysics, equal to 10−5 gauss (G), or 1 nanotesla (nT). The power by which the luminance of an image is
Gamma
Type of symmetry group
origins in the formulas for the pentagramma mirificum found by Carl Friedrich Gauss in 1843 and Harold Scott MacDonald Coxeter's study of symmetries in the
Frieze_group
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
\end{aligned}}} It is common in rigid body mechanics to use notation that explicitly identifies the x {\displaystyle x} , y {\displaystyle y}
Moment_of_inertia
Theorem in vector calculus
\Sigma } , written ∂ Σ {\displaystyle \partial \Sigma } With the above notation, if F {\displaystyle \mathbf {F} } is any smooth vector field on R 3 {\displaystyle
Stokes'_theorem
Tensor operator generalizes the notion of operators which are scalars and vectors
which applies for any wavefunction, ensures the above equality. In Dirac notation: ⟨ ψ ¯ | V ^ a | ψ ¯ ⟩ = ⟨ ψ | U ( R ) † V ^ a U ( R ) | ψ ⟩ = ∑ b R a
Tensor_operator
GAUSS NOTATION
GAUSS NOTATION
Girl/Female
American, British, English, French, German
Joyous; Medieval Male Name Adopted as a Feminine Name; A Member of the German Tribe; The Gauts
Girl/Female
African, American, Australian, British, Chinese, English, French, German, Hebrew, Jamaican, Latin
Joyce; Happy; Joyful; Tribal Name of the Gauts Name; A Member of the German Tribe; The Gauts; Supplanter; Cheerful; Lion of God
Girl/Female
American, British, English, French, German
Joyous; Medieval Male Name Adopted as a Feminine Name; A Member of the German Tribe; The Gauts
Boy/Male
Australian, Gaelic
Of the Strange Gauls
Girl/Female
American, British, Christian, English, German, Latin
Joyous; Playful; A Member of the German Tribe; The Gauts; Cheerful
Girl/Female
American, British, English, French, German, Hebrew, Latin
Joyous; Medieval Male Name Adopted as a Feminine Name; Tribal Name of the Gauts; Supplanter; God is My Salvation; Cheerful
Boy/Male
British, English, French, German, Jamaican
Medieval Male Name Adopted as a Feminine Name; Tribal Name of the Gauts
Surname or Lastname
South German, Swiss, and Jewish (Ashkenazic)
South German, Swiss, and Jewish (Ashkenazic) : topographic name for someone who lived in a street in a city, town, or village, Middle High German gazze, German Gasse, Yiddish gas ‘street’, ‘side street’.English : variant of Gash.Altered spelling of German Gast, found in the areas of Swiss settlement.
Girl/Female
American, Australian, British, English, French, German, Hebrew, Latin, Swiss
Playful; Medieval Male Name Adopted as a Feminine Name; A Member of the German Tribe; The Gauts; Cheerful; Happy; Joyful
Girl/Female
American, British, English, French, German, Latin
Joyous; Medieval Male Name Adopted as a Feminine Name; A Member of the German Tribe; The Gauts; Cheerful
Boy/Male
Gaelic
Of the strange Gauls.
Boy/Male
Australian, Latin
Worthy of Respect
Boy/Male
Gaelic
Of the strange Gauls.
Girl/Female
American, Australian, British, English, French, German, Hebrew, Latin
Joyous; Medieval Male Name Adopted as a Feminine Name; A Member of the German Tribe; The Gauts
Boy/Male
Scottish Gaelic
From the land of the Gauls.
Boy/Male
Gaelic
Of the strange Gauls.
Girl/Female
American, British, English, French, German, Hebrew, Latin
Medieval Male Name Adopted as a Feminine Name; A Member of the German Tribe; The Gauts; Joyful; Happy
GAUSS NOTATION
GAUSS NOTATION
Girl/Female
Gujarati, Hindu, Indian
Gift from the Divine
Girl/Female
Arabic, Islamic, Malaysian, Muslim, Pakistani, Romanian, Urdu
Shining; Beautiful; Great Fullness
Boy/Male
Tamil
Conqueror of the earth
Boy/Male
Arabic, Farsi, Gujarati, Hindu, Indian, Iranian, Kannada, Marathi, Muslim, Punjabi, Sikh, Sindhi
Concern Attention; Kindness; Loving; Bounty; Favour
Girl/Female
Bengali, Indian
Good Heart
Girl/Female
Muslim/Islamic
Lot Fate, Portion
Girl/Female
Australian, Greek
Goddess; Godly; Abbreviation of Names Like Althea and Dorothea
Boy/Male
Indian
Vine
Girl/Female
Afghan, Arabic, Danish, Dutch, French, German, Indian, Iranian, Japanese, Lebanese, Muslim, Parsi
Sun; Star; Name of a Constellation; The Pleiades
Girl/Female
Tamil
GAUSS NOTATION
GAUSS NOTATION
GAUSS NOTATION
GAUSS NOTATION
GAUSS NOTATION
a.
Representing sounds; as, phonetic characters; -- opposed to ideographic; as, a phonetic notation.
n.
According to the French notation, which is followed also upon the Continent and in the United States, a unit with fifteen ciphers annexed; according to the English notation, the number produced by involving a million to the fourth power, or the number represented by a unit with twenty-four ciphers annexed. See the Note under Numeration.
n.
Ornamental notes or short passages, either introduced by the performer, or indicated by the composer, in which case the notation signs are called grace notes, appeggiaturas, turns, etc.
n.
The act of specifying or determining by a mark or limit; notation of limits.
n.
The written and printed notation of a musical composition; the score.
n.
A method of notation for all spoken sounds, proposed by Mr. Sweet; -- so called because it is based on the common Roman-letter alphabet. It is like the palaeotype of Mr. Ellis in the general plan, but simpler.
v. t.
To bedeck gaudily; to decorate with gauds or showy trinkets or colors; to paint.
n.
According to the French notation, which is used on the Continent and in America, the cube of a million, or a unit with eighteen ciphers annexed; according to the English notation, a number produced by involving a million to the fifth power, or a unit with thirty ciphers annexed. See the Note under Numeration.
n.
A collar or neck chain, usually twisted, especially as worn by ancient barbaric nations, as the Gauls, Germans, and Britons.
n.
A method of analysis developed by Newton, and based on the conception of all magnitudes as generated by motion, and involving in their changes the notion of velocity or rate of change. Its results are the same as those of the differential and integral calculus, from which it differs little except in notation and logical method.
a.
Of or pertaining to Galatia or its inhabitants. -- A native or inhabitant of Galatia, in Asia Minor; a descendant of the Gauls who settled in Asia Minor.
n.
A table showing the notation, length, or duration of the several notes.
n.
One of an order of priests which in ancient times existed among certain branches of the Celtic race, especially among the Gauls and Britons.
n.
According to the French and American notation, a thousand octillions, or a unit with thirty ciphers annexed; according to the English notation, a million octillions, or a unit with fifty-four ciphers annexed. See the Note under Numeration.
n.
The act or practice of recording anything by marks, figures, or characters.
n.
The practice of using symbols, or the system of notation developed thereby.
n.
A species of gause, or very silk.
n.
According to the French notation, which is used upon the Continent generally and in the United States, the number expressed by a unit with twelve ciphers annexed; a million millions; according to the English notation, the number produced by involving a million to the third power, or the number represented by a unit with eighteen ciphers annexed. See the Note under Numeration.
n.
Any particular system of characters, symbols, or abbreviated expressions used in art or science, to express briefly technical facts, quantities, etc. Esp., the system of figures, letters, and signs used in arithmetic and algebra to express number, quantity, or operations.
n.
Literal or etymological signification.