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Topics referred to by the same term
g. x·d/dx quantum white noise conservation or QWN-Euler operator Euler operator (digital geometry), a local operation on a mesh which preserves topology
Euler_operator
In solid modeling and computer-aided design, the Euler operators modify the graph of connections to add or remove details of a mesh while preserving its
Euler operator (digital geometry)
Euler_operator_(digital_geometry)
Branch of mathematics
Leonhard Euler, originally a student of Johann Bernoulli, provided many significant contributions not just to the development of geometry, but to mathematics
Differential_geometry
Branch of mathematics
under noncommutative geometry developed from several areas, including operator algebra theory, index theory, algebraic geometry, quantum mechanics and
Noncommutative_geometry
Number, approximately 3.14
confirming a conjecture made by both Legendre and Euler. The first recorded use of the symbol π in circle geometry is in Oughtred's Clavis Mathematicae (1648)
Pi
Branch of geometry that studies combinatorial properties and constructive methods
geometry, combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology. Polyhedra
Discrete_geometry
Geometric model of the physical space
surface, beginning the theory of intrinsic geometry upon which modern geometric ideas are based. In 1760, Euler proved a theorem expressing the curvature
Three-dimensional_space
Number divisible only by 1 and itself
the sum of two primes, in a 1742 letter to Euler. Euler proved Alhazen's conjecture (now the Euclid–Euler theorem) that all even perfect numbers can be
Prime_number
Topological space that locally resembles Euclidean space
projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures
Manifold
Area of mathematics
a connection between geometry and (discrete) differential operators. Introductory text: K. Crane, "Discrete Differential Geometry: An Applied Introduction
Discrete differential geometry
Discrete_differential_geometry
Relation between sides of a right triangle
theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of
Pythagorean_theorem
Maximal and minimal curvature at a point of a surface
radius#Principal sections Euler's theorem (differential geometry) Surface Curvature Struik, D. J. (1933). "Outline of a History of Differential Geometry: I". Isis. 19
Principal_curvature
Branch of mathematics
Global questions of Riemannian geometry are often studied. One example is the spectral geometry of the Laplace–Beltrami operator, which generalizes the problem
Mathematical_analysis
Conjecture on zeros of the zeta function
{1}{n^{s}}}={\frac {1}{1^{s}}}+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+\cdots } Leonhard Euler considered this series in the 1730s for real values of s {\displaystyle
Riemann_hypothesis
Branch of mathematics
the algebraic character of coordinate geometry was subsumed by the calculus of infinitesimals of Lagrange and Euler. It took the simultaneous 19th-century
Algebraic_geometry
Branch of mathematics
Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
Property of a mathematical space
back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William
Dimension
Branch of computer science
Computational geometry is a branch of computer science devoted to the study of algorithms that can be stated in terms of geometry. Some purely geometrical
Computational_geometry
Research topic in computational geometry
Laplace operator, geometric smoothing might be achieved by convolving a surface geometry with a blur kernel formed using the Laplace-Beltrami operator. Applications
Geometry_processing
Straight path on a curved surface or a Riemannian manifold
In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points
Geodesic
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
versions of the Kronecker delta have found applications in differential geometry and modern tensor calculus, particularly in formulations of gauge theory
Kronecker_delta
Proofs of Fermat's little theorem Fermat quotient Euler's totient function Noncototient Nontotient Euler's theorem Wilson's theorem Primitive root modulo
List_of_number_theory_topics
Overview of and topical guide to discrete mathematics
Digital geometry – Deals with digitized models or images of objects of the 2D or 3D Euclidean space Digital topology – Properties of 2D or 3D digital
Outline of discrete mathematics
Outline_of_discrete_mathematics
Combinatorial approach of studying the topology of a manifold
of σ {\displaystyle \sigma } to τ {\displaystyle \tau } . The boundary operator is the endomorphism ∂ {\displaystyle \partial } of the free abelian group
Discrete_Morse_theory
Branch of elementary mathematics
Napier. In the 18th and 19th centuries, mathematicians such as Leonhard Euler and Carl Friedrich Gauss laid the foundations of modern number theory. Another
Arithmetic
Arithmetic operation
right of the base as bn. Sometimes an up arrow or caret is used as the operator, e.g. b ↑ n {\displaystyle b\uparrow n} or b^n. In abstract algebra, when
Exponentiation
Used to count, measure, and label
would later be named Euler's number (e). Irrational numbers began to be studied systematically in the 18th century, with Leonhard Euler who proved that the
Number
Number used for counting
Bernard de (1727). Eléments de la géométrie de l'infini [Elements of geometry of infinity] (in French). p. 3. Arithmetices principia: nova methodo (in
Natural_number
Computer-based generation of digital images
computer-based generation of digital images—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques
2D_computer_graphics
Theory of gravitation as curved spacetime
seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity
General_relativity
Analysis and solving of problems that involve fluid flows
be simplified by removing terms describing viscous actions to yield the Euler equations. Further simplification, by removing terms describing vorticity
Computational_fluid_dynamics
Interdisciplinary field of biology
which holds. The operator A {\displaystyle A} is the generalized moment of inertia or inertial operator. Classical calculation of the Euler–Lagrange equation
Computational_anatomy
Set of principles for modeling solid geometry
frame modelling Free-surface modelling Computational geometry Computer graphics Engineering drawing Euler boundary representation PLaSM – Programming Language
Solid_modeling
American mathematician (b. 1949)
President Fefferman, Charles L. (April 14, 1984). "Twentieth Century Geometry". Bard Digital Commons. Wikiquote has quotations related to Charles Fefferman
Charles_Fefferman
input is an equation. In digital geometry it is a method of drawing a curve pixel by pixel. Here input is an array (digital image). damped sine wave Is
Glossary_of_calculus
Inverse of a finite difference
derivative. The notation for indefinite summation goes back to Leonhard Euler, who in his 1755 Institutiones calculi differentialis introduced the symbol
Indefinite_sum
methods need to solve an equation at every step Backward Euler method — implicit variant of the Euler method Trapezoidal rule — second-order implicit method
List of numerical analysis topics
List_of_numerical_analysis_topics
Detects a given configuration (or pattern) in a binary image
configuration (or pattern) in a binary image, using the morphological erosion operator and a pair of disjoint structuring elements. The result of the hit-or-miss
Hit-or-miss_transform
test Sieve of Atkin Sieve of Eratosthenes Sieve of Sundaram Backward Euler method Euler method Linear multistep methods Multigrid methods (MG methods), a
List_of_algorithms
Roughly, the number of k-dimensional holes on a topological surface
}(-1)^{i}b_{i}(K,F),\,} where χ ( K ) {\displaystyle \chi (K)} denotes Euler characteristic of K and any field F. For any two spaces X and Y we have
Betti_number
Branch of mathematics
used by Gauss in 1805 for trigonometric interpolation of asteroid orbits. Euler and Lagrange both discretized the vibrating string problem, using what would
Fourier_analysis
All points in the topological closure not belonging to the interior
S=\partial \partial \partial S} for any set S . {\displaystyle S.} The boundary operator thus satisfies a weakened kind of idempotence. In discussing boundaries
Boundary_(topology)
Michelsohn (born 1941), American researcher on complex geometry, spin manifolds, the Dirac operator, and algebraic cycles Ruth I. Michler (1967–2000), American
List_of_women_in_mathematics
Mathematical transform that expresses a function of time as a function of frequency
how easily the rectangular form was deduced by an application of Euler's formula. Euler's formula introduces the possibility of negative ξ {\displaystyle
Fourier_transform
Branch of physics describing the motion of objects without considering forces
Kinematics is a subfield of physics and a branch of geometry. In physics, kinematics studies the geometrical aspects of motion of physical objects independent
Kinematics
German polymath (1646–1716)
between them and is altered if those distances are altered, his admirer Euler, in the famous 1736 paper solving the Königsberg Bridge Problem and its
Gottfried_Wilhelm_Leibniz
Error detection Ethernet Ethical code Euclidean geometry Euler–Lagrange equation Euler's formula Euler's identity Exponential stability Extended Kalman
Index of electrical engineering articles
Index_of_electrical_engineering_articles
Theory of interwoven space and time by Albert Einstein
relativity is the replacement of Euclidean geometry with Lorentzian geometry. Distances in Euclidean geometry are calculated with the Pythagorean theorem
Special_relativity
Average uncertainty in variable's states
} where b is the base of the logarithm used. Common values of b are 2, Euler's number e, and 10, and the corresponding units of entropy are the bits for
Entropy_(information_theory)
Theory of getting acceptably close inexact mathematical calculations
Anastassiou, George A. (ed.). The History of Approximation Theory: From Euler to Bernstein. Birkhauser. doi:10.1007/0-8176-4475-X. ISBN 0-8176-4353-2
Approximation_theory
Interpretation of quantum mechanics
analogy to hydrodynamics. The Madelung equations, being quantum analog of Euler equations of fluid dynamics, differ philosophically from the de Broglie–Bohm
De_Broglie–Bohm_theory
Analyzes the topology of a manifold by studying differentiable functions on that manifold
the cellular chain groups (see cellular homology) it is clear that the Euler characteristic χ ( M ) {\displaystyle \chi (M)} is equal to the sum ∑ (
Morse_theory
Mathematical approximation of a function
of tan x are the Bernoulli numbers. The Ek in the expansion of sec x are Euler numbers. The hyperbolic functions have Maclaurin series closely related
Taylor_series
Algebraic structure
and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. A finite field is a field
Finite_field
Association of one output to each input
function is essentially that of the founders of calculus, Leibniz, Newton and Euler. However, it cannot be formalized, since there is no mathematical definition
Function_(mathematics)
Triangular array of the binomial coefficients
Bell triangle Bernoulli's triangle Binomial expansion Cellular automata Euler triangle Floyd's triangle Gaussian binomial coefficient Hockey-stick identity
Pascal's_triangle
Branch of topology
X=\bigcup _{i\in J}U_{i}.} Some branches of mathematics such as algebraic geometry, typically influenced by the French school of Bourbaki, use the term quasi-compact
General_topology
Motion of a curve based on its curvature
its convergence rate. For an empirical comparison of the forward Euler, backward Euler, and more accurate Crank–Nicolson finite difference methods, see
Curve-shortening_flow
There are however three (or four) famous cases that are integrable, the Euler, the Lagrange, and the Kovalevskaya top. The Kovalevskaya top is a special
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
Use of a GPU for computations typically assigned to CPUs
Game of Life, cloth simulation, fluid incompressible flow by solution of Euler equations (fluid dynamics) or Navier–Stokes equations Statistical physics
General-purpose computing on graphics processing units
General-purpose_computing_on_graphics_processing_units
Philosophical question
and without invoking any divine beings. Christian scholars, like Leonhard Euler and Bernard d'Espagnat, disagree with that kind of skeptical argument. Dawkins'
Existence_of_God
be a range of plausible values (or vectors or functions). Euler–Bernoulli beam theory Euler–Bernoulli beam theory (also known as engineer's beam theory
Glossary_of_engineering:_A–L
Overview of the events of 2020 in science
Memorial. Retrieved 11 February 2022. "Indian Maths Genius Who Debunked Euler's Theory, Made it to NYT Front Page Dies at 103". News18. 8 May 2020. Retrieved
April–June_2020_in_science
Study of the propulsion of a projectile
7367[permanent dead link] Army 1965, p. 2-3 Ed Sandifer (December 2006). "How Euler Did It, Cannon Ball Curves" (PDF). MAA Online. Testing Firearms: Measuring
Internal_ballistics
Behavior of projectiles in flight
drag data. The vacuum trajectory, simplified aerodynamic, d'Antonio, and Euler drag law models are special cases. The Manges drag law thereby provides
External_ballistics
aether streams attract all bodies to one another. Newton (1717) and Leonhard Euler (1760) proposed a model in which the aether loses density near mass, leading
History of gravitational theory
History_of_gravitational_theory
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