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One of several theorems linking the sizes of different ideal class groups
theory, a reflection theorem or Spiegelungssatz (German for reflection theorem – see Spiegel and Satz) is one of a collection of theorems linking the
Reflection_theorem
Kind of proposition in mathematics
forms of the reflection principle depending on exactly what is meant by "resemble". Weak forms of the reflection principle are theorems of Zermelo–Fraenkel
Reflection_principle
Scripps National Spelling Bee winner
mathematics from Princeton University, with a dissertation titled "Reflection theorems for number rings". He held a two-year post-doctoral position at the
Evan_O'Dorney
Discrete group type in group theory
Coxeter groups. While the orthogonal group is generated by reflections (by the Cartan–Dieudonné theorem), it is a continuous group (indeed, Lie group), not a
Reflection_group
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Topics referred to by the same term
function f and a constant a Reflection theorem, one of a collection of theorems about the sizes of class groups Schwarz reflection principle, a way to extend
Reflection principle (disambiguation)
Reflection_principle_(disambiguation)
Theorem in mathematical logic
logic, the Paris–Harrington theorem states that a certain claim in Ramsey theory, namely the strengthened finite Ramsey theorem, which is expressible in
Paris–Harrington_theorem
Mathematical rule for inverting probabilities
Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting conditional probabilities
Bayes'_theorem
Continued fraction closely related to the Rogers–Ramanujan identities
And therefore following result appears: In the next step we use the reflection theorem for the continued fraction R again: R [ exp ( − π ) ] ⊕ R [ exp
Rogers–Ramanujan continued fraction
Rogers–Ramanujan_continued_fraction
Geometrical theorem relating the lengths of two segments that divide a triangle
In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that
Angle_bisector_theorem
equations) Reflection theorem (algebraic number theory) Ribet's theorem (elliptic curves) Robin's theorem (number theory) Rosser's theorem (number theory)
List_of_theorems
Well-quasi-ordering of finite trees
In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under
Kruskal's_tree_theorem
Invariance under simultaneous charge conjugation, parity transformation and time reversal
explicit proofs, so this theorem is sometimes known as the Lüders–Pauli theorem. At about the same time, and independently, this theorem was also proved by
CPT_symmetry
Theorem in differential topology
The hairy ball theorem of algebraic topology (formally, the Sphere Vector Field Theory, sometimes called the hedgehog theorem) states that there is no
Hairy_ball_theorem
Euclidean Wightman distributions
taking a reflection and complex conjugating all the fields, then the previous quantity has to be nonnegative. The Osterwalder–Schrader theorem states that
Schwinger_function
Theorems that help decompose a finite group based on prime factors of its order
specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow
Sylow_theorems
Theorem in Euclidean geometry
theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. This theorem refers
Mohr–Mascheroni_theorem
Group of geometric symmetries with at least one fixed point
Dihedral groups Dn of n-fold rotation and reflection groups Applying the crystallographic restriction theorem restricts n to values 1, 2, 3, 4, and 6 for
Point_group
German mathematician (1810–1893)
conjecture Kummer's transformation of series Ideal number Regular prime Reflection theorem Principalization McElroy, Tucker (2005). A to Z of Mathematicians
Ernst_Kummer
Characterization by prime factors of sums of two squares
In number theory, the sum of two squares theorem relates the prime decomposition of any integer n > 1 to whether it can be written as a sum of two squares
Sum_of_two_squares_theorem
Mapping from a Euclidean space to itself
Cartan–Dieudonné theorem. Similarly the Euclidean group, which consists of all isometries of Euclidean space, is generated by reflections in affine hyperplanes
Reflection_(mathematics)
Theorem in computability theory
recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions. The theorems were first
Kleene's_recursion_theorem
Mathematics principle in complex analysis
In mathematics, the Schwarz reflection principle is a way to extend the domain of definition of a complex analytic function, i.e., it is a form of analytic
Schwarz_reflection_principle
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Special mathematical function
]^{4}\}} Lemniscatic example for the fifth power theorem: A next example for the fifth power theorem: If two positive numbers a {\displaystyle a} and
Nome_(mathematics)
Interactive theorem prover software
computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs
Proof_assistant
Geometric symmetry operation
transforms as direct sums of rotations and reflections, which follows from the spectral theorem, for instance. "Reflections in Lines". new.math.uiuc.edu. Retrieved
Point_reflection
an effort to avoid naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them after Euler. Euler's
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
Distribution result for probability mathematics
distribution as the reflection of the subsequent path about the value a. More formally, the reflection principle refers to a theorem concerning the distribution
Reflection principle (Wiener process)
Reflection_principle_(Wiener_process)
Every rigid motion is a screw displacement
In kinematics, Chasles' theorem, or Mozzi–Chasles' theorem, says that the most general rigid body displacement can be produced by a screw displacement
Chasles'_theorem_(kinematics)
Distance-preserving mathematical transformation
motion (translation or rotation), or a composition of a rigid motion and a reflection. Isometries are often used in constructions where one space is embedded
Isometry
Group of symmetries of a regular polygon
Algebraically, this is an instance of the conjugate Sylow theorem (for n odd): for n odd, each reflection, together with the identity, form a subgroup of order
Dihedral_group
Equality of areas of a sliced disk
"Reflection groups and the pizza theorem", Algebra i Analiz (in Russian), 33 (6): 1–8 Brailov, Yury (2022), "Reflection groups and the pizza theorem"
Pizza_theorem
Theorem in electrical engineering
between two cylinders, the transmission and reflection of light at the boundary between two media. The theorem was originally misunderstood (notably by Joule)
Maximum power transfer theorem
Maximum_power_transfer_theorem
Proof assistant
of the four color theorem, which was completed in 2002. Their work led to the development of the SSReflect ("Small Scale Reflection") package, which was
Rocq
Relationship between derivatives and integrals
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Mathematic theorem
composition of at most n reflections. Indefinite orthogonal group Coordinate rotations and reflections Householder reflections Chasles' theorem Gallier, Jean H
Cartan–Dieudonné_theorem
Mathematical concept
The following table gives examples of rotation and reflection matrix : Cartan–Dieudonné theorem Dihedral group Euclidean plane isometry Euclidean symmetries
Rotations and reflections in two dimensions
Rotations_and_reflections_in_two_dimensions
Symmetry-based invariance to continuous group action
viewing some symmetries as motions, as opposed to discrete symmetry, e.g. reflection symmetry, which is invariant under a kind of flip from one state to another
Continuous_symmetry
Theorem in optics that explains light propagation in a medium
well as refraction, reflection, and diffraction). It is named after Paul Peter Ewald and Carl Wilhelm Oseen, who proved the theorem in crystalline and
Ewald–Oseen extinction theorem
Ewald–Oseen_extinction_theorem
Theorem in plane geometry
In geometry, Hjelmslev's theorem, named after Johannes Hjelmslev, is the statement that if points P, Q, R... on a line are isometrically mapped to points
Hjelmslev's_theorem
Generalized scaling operation in geometry
gets the identity mapping; for k = − 1 {\displaystyle k=-1} one gets the reflection at the center; for 1 / k {\displaystyle 1/k} one gets the inverse mapping
Homothety
Theorem in geometrical optics
through an arbitrary amount of reflections and refractions, then let it emerge in some other homogenous medium. The theorem states that the resulting pencil
Malus–Dupin_theorem
Meromorphic function
Laplace transform of (−1)m+1 tm/1 − e−t. It follows from Bernstein's theorem on monotone functions that, for m > 0 and x real and non-negative, (−1)m+1
Polygamma_function
Functional programming language
Vreeswijk, which is about a hen named Agda. This alludes to the name of the theorem prover Rocq, which was originally named Coq after Thierry Coquand. The
Agda_(programming_language)
Theorem concerning spontaneous symmetry breaking
In theoretical physics, the Vafa–Witten theorem, named after Cumrun Vafa and Edward Witten, is a theorem that shows that vector-like global symmetries
Vafa–Witten_theorem
Solution to a stochastic differential equation
Optional stopping theorem Prokhorov's theorem Quadratic variation Reflection principle Skorokhod integral Skorokhod's representation theorem Skorokhod space
Diffusion_process
Theorem concerning ratios of line segments
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry
Intercept_theorem
Principle in compass and straightedge constructions
In geometry, the compass equivalence theorem is an important statement in compass and straightedge constructions. The tool advocated by Plato in these
Compass_equivalence_theorem
generated by transpositions (ij), which act by reflections on V. On the other hand, by the main theorem of symmetric functions, the algebra of invariants
Chevalley–Shephard–Todd theorem
Chevalley–Shephard–Todd_theorem
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no procedure for group
Arrow's_impossibility_theorem
pseudoreflection generalizes the concepts of reflection and complex reflection and is simply called reflection by some mathematicians. It plays an important
Pseudoreflection
Movement with a fixed point is rotation
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the body remains
Euler's_rotation_theorem
Formula for number of orbits of a group action
sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma, or the orbit-counting theorem, is a result in group theory that is often
Burnside's_lemma
Relationship between two figures of the same shape and size, or mirroring each other
combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but
Congruence_(geometry)
1970s automated theorem prover
Logic for Computable Functions (LCF) is an interactive automated theorem prover developed at Stanford and Edinburgh by Robin Milner and collaborators
Logic for Computable Functions
Logic_for_Computable_Functions
Mathematical transformation that preserves distances
transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid
Rigid_transformation
Adjusting input/output impedances of an electrical circuit for some purpose
desired value is selected to maximize power transfer or minimize signal reflection. For example, impedance matching typically is used to improve power transfer
Impedance_matching
Election result probability theorem
is popularly known as André's reflection method, although André did not use any reflections. Bertrand's ballot theorem is related to the cycle lemma.
Bertrand's_ballot_theorem
Apparent force in a rotating reference frame
In physics, the Coriolis force is a pseudo-force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame
Coriolis_force
Subgroup of a root system's isometry group
group is this: Theorem: If Δ {\displaystyle \Delta } is base for Φ {\displaystyle \Phi } , then the Weyl group is generated by the reflections s α {\displaystyle
Weyl_group
Relates the length of a median of a triangle to the lengths of its sides
Theorem via Ptolemy's Theorem". Mathematics Magazine. doi:10.1080/0025570X.2024.2385255. Rose, Mike (2007). "27. Reflections on Apollonius' Theorem"
Apollonius's_theorem
Plane curve
equation for t = t 0 . {\displaystyle t=t_{0}\;.} Area From Apollonios theorem (see below) one obtains: The area of an ellipse x → = f → 0 + f → 1 cos
Ellipse
Matrix decomposition
with reflections, or both rotations without reflections.[citation needed] If the determinant is negative, exactly one of them will have a reflection. If
Singular_value_decomposition
Law Field Person(s) Named After Abel's theorem Calculus Niels Henrik Abel Ariadne's thread Computer science Ariadne Amdahl's law Computer science Gene
List of scientific laws named after people
List_of_scientific_laws_named_after_people
On distances between points on a circle
Applications of the three-gap theorem include the study of plant growth and musical tuning systems, and the theory of light reflection within a mirrored square
Three-gap_theorem
Concept in mathematics
vector space is a complex reflection group if and only if its ring of invariants is a polynomial ring (Chevalley–Shephard–Todd theorem). For ℓ {\displaystyle
Complex_reflection_group
Counting polynomial roots in an interval
JSTOR 2330245. S2CID 154334522. Akritas, Alkiviadis G. (1982). "Reflections on a pair of theorems by Budan and Fourier". Math. Mag. 55 (5): 292–298. doi:10
Sturm's_theorem
Mathematical theorem
property's reflection. In other words, the Lie derivative of one coordinate with respect to another is zero. The Clairaut-Schwarz theorem is the key fact
Symmetry of second derivatives
Symmetry_of_second_derivatives
Type of group in mathematics
Euler's rotation theorem, which asserts that every (non-identity) element of SO(3) is a rotation about a unique axis–angle pair. Reflections are the elements
Orthogonal_group
German mathematician (1843–1921)
Schwarz theorem (also known as Clairaut's theorem) Schwarz integral formula Schwarz–Christoffel mapping Schwarz–Ahlfors–Pick theorem Schwarz reflection principle
Hermann_Schwarz
Calculation technique for classical electrostatics
of the method of image charges rests upon a corollary of the uniqueness theorem, which states that the electric potential in a volume V is uniquely determined
Method_of_image_charges
Stochastic volatility model used in derivatives markets
Optional stopping theorem Prokhorov's theorem Quadratic variation Reflection principle Skorokhod integral Skorokhod's representation theorem Skorokhod space
SABR_volatility_model
Set with associative invertible operation
order of the reflection elements f v {\displaystyle f_{\mathrm {v} }} etc. is 2. Both orders divide 8, as predicted by Lagrange's theorem. The groups F
Group_(mathematics)
Group that admits a formal description in terms of reflections
n} goes to infinity. Artin–Tits group Chevalley–Shephard–Todd theorem Complex reflection group Coxeter element Isomorphism problem of Coxeter groups Iwahori–Hecke
Coxeter_group
French mathematician and lawyer (1601–1665)
for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy
Pierre_de_Fermat
Shape with four equal sides and angles
number of equal-area triangles, a result of Monsky's theorem. Cross's theorem or Vecten's theorem states that, for a triangle formed by the sides of three
Square
Mathematical group that can be generated as the set of powers of a single element
Golubitsky 2010, pp. 47–48). (Cox 2012, p. 294, Theorem 11.1.7). (Cox 2012, p. 295, Corollary 11.1.8 and Theorem 11.1.9). (Aluffi 2009, pp. 82–84, 6.4 Example:
Cyclic_group
Branch of mathematics that studies abstract algebraic structures
over fields of characteristic zero) include finite groups (see Maschke's theorem), compact groups, and semisimple Lie algebras. In cases where complete
Representation_theory
Mathematical models of strategic interactions
von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard
Game_theory
Theorem in classical electromagnetism
classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources)
Reciprocity (electromagnetism)
Reciprocity_(electromagnetism)
Branch of mathematics
historic interest. Bressoud, David M. (2011). "Historical Reflections on Teaching the Fundamental Theorem of Integral Calculus". The American Mathematical Monthly
Calculus
Theorem on the orders of subgroups
In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is
Lagrange's theorem (group theory)
Lagrange's_theorem_(group_theory)
Measure of the "spread" of light in an optical system
case of a reflection at a surface dS, in which case nΣ = nS and θΣ = θS. A consequence of the conservation of etendue is the brightness theorem, which states
Etendue
Formula for number of orbits of a group action
The Pólya enumeration theorem, also known as the Redfield–Pólya theorem and Pólya counting, is a theorem in combinatorics that both follows from and ultimately
Pólya_enumeration_theorem
Flat-sided three-dimensional shape
results on polyhedral concepts, like Hilbert's third problem, Steinitz's theorem, and stellation of Platonic solids. Polyhedra are used in many fields,
Polyhedron
Mathematical theorem
In mathematics, Ramanujan's master theorem, named after Srinivasa Ramanujan, is a technique that provides an analytic expression for the Mellin transform
Ramanujan's_master_theorem
Probability distribution
distributions are not known. Their importance is partly due to the central limit theorem. It states that the average of many statistically independent samples (observations)
Normal_distribution
Geometric theorem regarding circles and triangles
and the Reflection Triangle" (PDF). Forum Geometricorum. 3: 105–111. John Rigby (1997). "Brief notes on some forgotten geometrical theorems". Mathematics
Kosnita's_theorem
reflection, across another line with the same end. Based on this "three reflections theorem", given any two ends x and y in H, Hilbert defines the sum x + y
Hilbert's_arithmetic_of_ends
Swiss mathematician (1707–1783)
properties of this function, he generalized Fermat's little theorem to what is now known as Euler's theorem. He contributed significantly to the theory of perfect
Leonhard_Euler
illuminating it with probing waves and recording the reflections. It is based on the diffraction slice theorem and assumes that the scatterer is weak. It is
Diffraction_tomography
Vertex algebra acted on by the monster group
prove the monstrous moonshine conjectures, by applying the Goddard–Thorn theorem of string theory to construct the monster Lie algebra, an infinite-dimensional
Monster_vertex_algebra
Overview of and topical guide to geometry
progression Geometric shape Pi Angular velocity Linear velocity De Moivre's theorem Similar triangles Unit circle Point Line and Ray Plane Bearing Angle Degree
Outline_of_geometry
Number of subsets of a given size
coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers n ≥
Binomial_coefficient
On when a function on convex body K does not decrease if K is translated inwards
In mathematics, Anderson's theorem is a result in real analysis and geometry which says that the integral of an integrable, symmetric, unimodal, non-negative
Anderson's_theorem
Type of logical argument that applies deductive reasoning
Logical consequence Model Theorem Theory Type theory Theorems (list), paradoxes Gödel's completeness – incompleteness theorems Tarski's undefinability Banach–Tarski
Syllogism
Mathematical logician and philosopher
theorem in 1929 as part of his dissertation to earn a doctorate at the University of Vienna, and the publication of Gödel's incompleteness theorems two
Kurt_Gödel
Isometry of the Eluclidean plane
as length. There are four types: translations, rotations, reflections, and glide reflections (see below § Classification). The set of Euclidean plane isometries
Euclidean_plane_isometry
Paper-and-pencil game for two players
successful landing and must be careful not to block themself. Hales–Jewett theorem m,n,k-game Number Scrabble Garcia, Dan. "GamesCrafters: Tic-Tac-Toe". gamescrafters
Tic-tac-toe
REFLECTION THEOREM
REFLECTION THEOREM
Boy/Male
Buddhist, Indian, Japanese
Ancient Reflection
Boy/Male
Bengali, Hindu, Indian
Image; Reflection
Boy/Male
Hindu, Indian
Our Reflection
Girl/Female
Tamil
Reflection, Image, Radiance
Girl/Female
Indian
Reflection, Image, Radiance
Boy/Male
Tamil
Reflection through study
Boy/Male
Hindu, Indian, Punjabi, Sanskrit, Sikh
Thought; Reflection
Girl/Female
Arabic, Assamese, Australian, Hindu, Indian, Marathi, Muslim, Sindhi
Mirror; Reflection
Girl/Female
Japanese
Mirror reflection.
Boy/Male
Indian
Reflection; Gnawing Reflection
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Tamil, Telugu
Reflection; Outlook; Reflection Reflection
Girl/Female
Indian, Malayalam
Reflection
Boy/Male
Tamil
Gunjik | கà¯à®¨à¯à®œà¯€à®•
Reflection
Gunjik | கà¯à®¨à¯à®œà¯€à®•
Boy/Male
Hindu
Reflection
Boy/Male
Hindu, Indian
Perception; Reflection
Girl/Female
Tamil
Reflection, Image, Radiance
Boy/Male
Tamil
Reflection
Boy/Male
Hindu
Reflection
Girl/Female
Bengali, Hindu, Indian
Reflection; Mirror
Girl/Female
Hindu, Indian
Reflection
REFLECTION THEOREM
REFLECTION THEOREM
Boy/Male
Tamil
Fulfilled
Girl/Female
Hindu
Boy/Male
Christian, Finnish, French, German, Hebrew, Hindu, Indian, Malayalam, Marathi, Swedish
Nectar
Boy/Male
Hebrew
Wreath.
Boy/Male
Biblical
Dwelling of death.
Boy/Male
Arabic, Muslim, Sindhi
External; Outside
Boy/Male
Muslim
The ancient king of persia
Female
African
slave.
Boy/Male
Indian
The majesty of religion
Male
Basque
, mountain-conqueror.
REFLECTION THEOREM
REFLECTION THEOREM
REFLECTION THEOREM
REFLECTION THEOREM
REFLECTION THEOREM
n.
Election a second time, or anew; as, the reelection of a former chief.
a.
Capable of, or pertaining to, flection or inflection.
a.
The act of choosing; choice; selection.
n.
A reflecting telescope.
n.
The return of rays, beams, sound, or the like, from a surface. See Angle of reflection, below.
n.
The variation of words by declension, comparison, or conjugation; inflection.
a.
Capable of exercising thought or judgment; as, reflective reason.
n.
A part reflected, or turned back, at an angle; as, the reflection of a membrane.
n.
A slide, modulation, or accent of the voice; as, the rising and the falling inflection.
n.
Election beforehand.
n.
The act of reflecting, or turning or sending back, or the state of being reflected.
n.
That which is produced by reflection.
n.
A device for reflecting sound.
n.
Want of reflection.
n.
A deviation of the rays of light toward the surface of an opaque body; inflection; diffraction.
a.
Addicted to introspective or meditative habits; as, a reflective person.
a.
Throwing back images; as, a reflective mirror.
n.
See Reflection.
a.
Given to reflection or serious consideration; reflective; contemplative; as, a reflecting mind.
n.
An image given back from a reflecting surface; a reflected counterpart.