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Geometry theorem relating to triangles
In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another
Hinge_theorem
Topics referred to by the same term
configuration to another in a reversible fashion Hinge functions in multivariate statistics Hinge theorem in geometry Hinge decomposition of hypergraphs, used when
Hinge_(disambiguation)
Ancient Greek mathematician (fl. 300 BC)
the later tradition of Alexandria. In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections
Euclid
Relates the length of a median of a triangle to the lengths of its sides
In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the
Apollonius's_theorem
Gauss–Wantzel theorem (geometry) Geometric mean theorem (geometry) Hinge theorem (geometry) Hjelmslev's theorem (geometry) Impossibility of angle trisection
List_of_theorems
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It
Ancient_Greek_mathematics
Problem of constructing equal-area shapes
proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi ( π {\displaystyle \pi } ) is a transcendental number
Squaring_the_circle
Hadwiger–Finsler inequality Hinge theorem Hitchin–Thorpe inequality Isoperimetric inequality Jordan's inequality Jung's theorem Loewner's torus inequality
List_of_inequalities
bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Hinge theorem Inscribed angle theorem Intercept theorem Intersecting
A History of Greek Mathematics
A_History_of_Greek_Mathematics
Ancient Greek spherical geometry treatise
astronomy as modeled by the celestial sphere. Primarily consisting of theorems which were known at least informally a couple centuries earlier, the Spherics
Theodosius'_Spherics
Geometric partition where pieces are connected by "hinged" points
the famous hinged dissection of a square into a triangle (pictured) in his 1907 book The Canterbury Puzzles. The Wallace–Bolyai–Gerwien theorem, first proven
Hinged_dissection
Certain dynamical systems will eventually return to (or approximate) their initial state
In mathematics and physics, the Poincaré recurrence theorem states that certain dynamical systems will, after a sufficiently long but finite time, almost
Poincaré_recurrence_theorem
Theorem on modular exponentiation
In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers
Euler's_theorem
Problem of finding unknown lengths and angles of a triangle
]}.} Here R is the Earth's radius. Congruence Hansen's problem Hinge theorem Lénárt sphere Snellius–Pothenot problem "Solving Triangles". Maths is
Solution_of_triangles
Theorem in mathematics
the inverse function theorem (see Generalizations below). An alternate proof in finite dimensions hinges on the extreme value theorem for functions on a
Inverse_function_theorem
Theorem in mathematical logic
compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important
Compactness_theorem
Ancient Greek mathematician
bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Hinge theorem Inscribed angle theorem Intercept theorem Intersecting
Leon_(mathematician)
Physics theorem about a swimmer's displacement
In physics, the scallop theorem states that a swimmer that performs a reciprocal motion cannot achieve net displacement in a low-Reynolds number Newtonian
Scallop_theorem
Rigidity theorem for convex polyhedra
Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding
Cauchy's_theorem_(geometry)
Theorem in dimensional analysis
Buckingham π theorem is a key theorem in dimensional analysis. It is a formalisation of Rayleigh's method of dimensional analysis. Loosely, the theorem states
Buckingham_pi_theorem
equality if and only if the two triangles are similar. The hinge theorem or open-mouth theorem states that if two sides of one triangle are congruent to
List_of_triangle_inequalities
Universality of construction using just a straightedge and a single circle with center
In Euclidean geometry, the Poncelet–Steiner theorem is a result about compass and straightedge constructions with certain restrictions. This result states
Poncelet–Steiner_theorem
Description of flat one-vertex origami
Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex
Kawasaki's_theorem
Concept in machine learning
the hinge loss quite attractive, as bounds can be placed on the difference between expected risk and the sign of hinge loss function. The Hinge loss
Loss functions for classification
Loss_functions_for_classification
between the creases can be colored with two colors. Kawasaki's theorem or Kawasaki-Justin theorem: at any vertex, the sum of all the odd angles (see image)
Mathematics_of_paper_folding
formation of plastic hinge in the structure. Engineers use limit states to define and check a structure's performance. Plastic limit theorems provide a way to
Limit_load_(physics)
Speeding up Turing machines by increasing tape symbol complexity
2 n + 3. {\displaystyle f(n)/c+2n+3.} The proof of the speedup theorem clearly hinges on the capability to compress storage by replacing the alphabet
Linear_speedup_theorem
Algebraic structure with addition, multiplication, and division
analysis, which are based on fields with additional structure. Basic theorems in analysis hinge on the structural properties of the field of real numbers. Most
Field_(mathematics)
Linkages of different dimensions with the same output motion
cognate linkages together. The theorem states, for a given coupler curve produced by a four-bar linkage with four revolute (hinge) joints, there exist three
Cognate_linkage
Average solution cost is the same with any method
In computational complexity and optimization the no free lunch theorem is a result that states that for certain types of mathematical problems, the computational
No free lunch in search and optimization
No_free_lunch_in_search_and_optimization
Combinatorial theory of mechanics and discrete geometry
graphs. Cauchy's theorem states that a three-dimensional convex polyhedron constructed with rigid plates for its faces, connected by hinges along its edges
Structural_rigidity
Mathematically obvious
that an example or a solution is not simple, or that a statement or a theorem is not easy to prove. Triviality does not have a rigorous definition in
Triviality_(mathematics)
Property of mathematical objects
plane. The Schwarz lemma is an example of such a rigidity theorem. By the fundamental theorem of algebra, polynomials in C are rigid in the sense that
Rigidity_(mathematics)
fitting the training set data in a way that minimizes the average of the hinge-loss function and L2 norm of the learned weights. This strategy avoids overfitting
Regularization perspectives on support vector machines
Regularization_perspectives_on_support_vector_machines
Tiling puzzle where pieces can be assembled in different ways
situations, such as ensuring that every piece connects to another with a hinge. Dissection puzzles are an early form of geometric puzzle. The earliest
Dissection_puzzle
Theorem about diagonalizing matrices
the context of linear algebra and symplectic geometry, the Williamson theorem concerns the diagonalization of positive definite matrices through symplectic
Williamson_theorem
Ability to readily identify logical or mathematical truth
challenges efficiently. Humans apply logical intuition in proving mathematical theorems, validating logical arguments, developing algorithms and heuristics, and
Logical_intuition
Theorem
at the point and vice versa.) Among the corollaries of this theorem are the identity theorem that two holomorphic functions that agree at every point of
Analyticity of holomorphic functions
Analyticity_of_holomorphic_functions
Curved structure that spans a space and may support a load
therefore the two-hinged arch is also statically indeterminate, although not as much as the fixed arch. The three-hinged arch is not only hinged at its base
Arch
British philosopher (born 1942)
Wittgenstein's hinge epistemology, introduced in Wittgenstein's On Certainty as a response to radical skepticism. According to hinge epistemology, there
Crispin_Wright
Historical critique of quantum mechanics
physicist Edward Condon, who said, "Of course, a great deal of the argument hinges on just what meaning is to be attached to the word 'reality' in physics
Einstein–Podolsky–Rosen paradox
Einstein–Podolsky–Rosen_paradox
Optical imaging rule
axis of rotation has been given many different names: "counter axis", "hinge line", and "pivot point". Refer to Figure 4; if a lens with focal length
Scheimpflug_principle
Unique point and line of a conic section
the polar p {\displaystyle p} of point P {\displaystyle P} . (La Hire's theorem) If a point P {\displaystyle P} moves along a line l {\displaystyle l}
Pole_and_polar
Branch of geometry that studies combinatorial properties and constructive methods
rigid bodies connected by flexible linkages or hinges. Topics in this area include: Cauchy's theorem Flexible polyhedra Incidence structures generalize
Discrete_geometry
Logic error due to ignoring the base rate
or liability that are not analyzable as errors in base rates or Bayes's theorem. An example of the base rate fallacy is the false positive paradox (also
Base_rate_fallacy
Mathematical method in functional analysis
}({\mathfrak {A}})J={\cal {R}}_{\lambda }({\mathfrak {A}})^{\prime }.} The proof hinges on evaluating the operator integral: e s / 2 Δ 1 / 2 ( Δ + e s ) − 1 = ∫
Tomita–Takesaki_theory
Method for load calculation in construction
frequency ω n {\displaystyle \omega _{n}} . The boundary conditions of a hinged-hinged beam of length L {\displaystyle L} (fixed at x = 0 {\displaystyle x=0}
Euler–Bernoulli_beam_theory
Type of folding using rigid materials
is concerned with folding structures using flat rigid sheets joined by hinges. That is, unlike in traditional origami, the panels of the paper cannot
Rigid_origami
Family of shellfish, many edible
(i.e., upper) valve, which in many species is actually concave. With the hinge of the two valves oriented towards the top, one side corresponds to the
Scallop
Universal C*-algebra
{\displaystyle \textstyle \sum s_{i}s_{i}^{*}=1} . The proof of the theorem hinges on the following fact: any C*-algebra generated by n {\displaystyle
Cuntz_algebra
Graph in engineering
When determining the moment caused by at some point B along the beam, a hinge will be placed at point B, releasing it to moments but resisting shear.
Influence_line
Toeplitz algebra. Theorem (Coburn) C*(V) is isomorphic to the Toeplitz algebra and V is the isomorphic image of Tz. The proof hinges on the connections
Wold's_decomposition
Natural number, composite number
a single flexible polyhedron, called a 2-dof flexible polyhedron, each hinge will only have a total range of motion of 14 degrees.p.139 14 is also the
14_(number)
Overview of and topical guide to machine learning
Markov model Higher-order factor analysis Highway network Hinge loss Holland's schema theorem Hopkins statistic Hoshen–Kopelman algorithm Huber loss IRCF360
Outline_of_machine_learning
Size of a set in mathematics
The term cardinality originates from the post-classical Latin cardo ("to hinge"), which referred to something central or pivotal, both literally and metaphorically
Cardinality
C*-algebra
Effros-Handelman-Shen theorem is the fact that every Riesz group is the direct limit of Zk 's, each with the canonical order structure. This hinges on the following
Approximately finite-dimensional C*-algebra
Approximately_finite-dimensional_C*-algebra
Engineering method deriving slope and displacement of a beam
Essentially, it requires the same amount of computation as the moment-area theorems to determine a beam's slope or deflection; however, this method relies
Conjugate_beam_method
convex polyhedra as a set of rigid plates, i.e., as a variant of a body-bar-hinge framework, then the framework is rigid. The next result, by Bricard in 1897
Geometric_rigidity
Algebraic structure
whereas the remaining two hinge on important facts in commutative algebra, the going-up theorem and Krull's principal ideal theorem. A ring homomorphism or
Commutative_ring
German civil engineer and civil servant
Schwedler truss and the Schwedler cupola. He is an author of Schwedler's theorem, a formula defining relation between shear force and bending moment. Schwedler
Johann_Wilhelm_Schwedler
Deep learning method
estimation, even though GAN cannot perform maximum likelihood estimation itself. Hinge loss GAN: L D = − E x ∼ p ref [ min ( 0 , − 1 + D ( x ) ) ] − E x ∼ μ
Generative adversarial network
Generative_adversarial_network
known assertions. A theorem of such a theory is either an axiom or an assertion that can be obtained from previously known theorems by the application
Philosophy_of_mathematics
Physical object which does not deform when forces or moments are exerted on it
that the translational motion is zero or simplified, e.g. on an axle or hinge, at the center of a ball and socket joint, etc. When the center of mass
Rigid_body
Topics referred to by the same term
speedup theorem, in computational complexity theory Blum (surname), including a list of people with the name Julius Blum, a company manufacturing hinges in
Blum
Type of motion
such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time
Rotation_around_a_fixed_axis
Physics of the cause–effect relation
theories, causality is closely related to the principle of locality. Bell's Theorem shows that conditions of "local causality" in experiments involving quantum
Causality_(physics)
Covering by shapes without overlaps or gaps
tessellation in recreational mathematics. For example, Dudeney invented the hinged dissection, while Gardner wrote about the "rep-tile", a shape that can be
Tessellation
Geometric problems involving the partition of a figure
restricted to being the closures of disjoint open sets. The Bolyai–Gerwien theorem states that any polygon may be dissected into any other polygon of the
Dissection_problem
Number, approximately 1.618
golden ratio with the Pythagorean theorem. Kepler said of these: Geometry has two great treasures: one is the theorem of Pythagoras, the other the division
Golden_ratio
Cutting a square into pieces which rearrange into 3 identical squares
used his dissection to demonstrate the Pythagorean theorem. This geometrical proof of Pythagoras' theorem would be rediscovered in the years 1835 - 1840 by
Square_trisection
Principle in statistical learning theory
either by employing a convex approximation to the 0–1 loss function (like hinge loss for SVM), which is easier to optimize, or by imposing assumptions on
Empirical_risk_minimization
Times. 6 June 1985. "Behind the Batus-Farmers Deal : $5.2-Billion Merger Hinged on Chemistry Between Chairmen". Los Angeles Times. 26 August 1988. Sims
List of largest mergers and acquisitions
List_of_largest_mergers_and_acquisitions
Lowest possible energy of a quantum system or field
at University of Colorado has highlighted that he believes such devices hinge on the assumption that the Casimir force is a nonconservative force. He
Zero-point_energy
Albert Einstein's hypothetical situations to argue scientific points
and/or natural particulars (demons sorting molecules, cats whose lives hinge upon a radioactive disintegration, men in enclosed elevators) in an idealized
Einstein's thought experiments
Einstein's_thought_experiments
Algebra with unique prime factorization
requirement that a Dedekind domain not be a field. Many more authors state theorems for Dedekind domains with the implicit proviso that they may require trivial
Dedekind_domain
Topological group with compact topology
the exceptional Lie groups: G2, F4, E6, E7, and E8. The classification theorem of compact Lie groups states that up to finite extensions and finite covers
Compact_group
Mathematical model used for classification or regression
dimension. Empirical risk minimization Common loss functions (log loss, hinge loss, squared loss) Regularization (L1/L2) Optimization methods (gradient
Discriminative_model
Mathematical relation assigning a probability event to a cost
Bayesian regret Loss functions for classification Discounted maximum loss Hinge loss Scoring rule Statistical risk Hastie, Trevor; Tibshirani, Robert; Friedman
Loss_function
2023 film by Christopher Nolan
of This Century', Raves Paul Schrader: 'This One Blows the Door Off the Hinges'". Variety. Archived from the original on January 18, 2024. Retrieved January
Oppenheimer_(film)
Concept in regression analysis mathematics
class of algorithms named Tikhonov regularization. For instance, using the hinge loss leads to the support vector machine algorithm, and using the epsilon-insensitive
Regularized_least_squares
Statistical method
which may occur at the same age. The identification of causal effects hinges on the crucial assumption that there is indeed a sharp cut-off, around which
Regression discontinuity design
Regression_discontinuity_design
Genevan philosopher, writer, and composer (1712–1778)
because it was too big. Much subsequent controversy about Rousseau's work has hinged on disagreements concerning his claims that citizens constrained to obey
Jean-Jacques_Rousseau
Mathematical structure
decomposed into edge-disjoint spanning trees via the Tutte and Nash-Williams theorem. There is a family of efficient algorithms, known as pebble games, for
Sparsity_matroid
Time reversal symmetry in physics
converted into hypotheses of the physical sciences. The current consensus hinges upon the Boltzmann–Shannon identification of the logarithm of phase space
T-symmetry
Mechanical linkage transforming rotary motion into linear
the Peaucellier–Lipkin linkage by 11 years and consists of a series of hinged rectangular plates, two of which remain parallel but can be moved normally
Peaucellier–Lipkin_linkage
Non-native organism causing damage to an established environment
with high species diversity were more susceptible to invasion. This debate hinged on the spatial scale of invasion studies. Small-scale studies tended to
Invasive_species
Mechanisms and evolution of insect flight
muscles", these muscles attach directly to the sclerites that make up the wing hinge and are contracted with 1:1 impulses from motor neurons. Recent work has
Insect_flight
Non-parametric statistic used to estimate the survival function
censoring does not take place; so whether an improvement is possible critically hinges upon whether censoring is in place. By elementary calculations, S ( t )
Kaplan–Meier_estimator
Regression analysis for modeling ordinal data
models by adapting common loss functions from classification (such as the hinge loss and log loss) to the ordinal case. ORCA (Ordinal Regression and Classification
Ordinal_regression
Logical paradox from vague predicates
question of perception; this may be seen to be relevant when the argument hinges on each change being "imperceptible". Another formulation is to start with
Sorites_paradox
Problem in network theory
Probabilistic soft logic (PSL) is a probabilistic graphical model over hinge-loss Markov random field (HL-MRF). HL-MRFs are created by a set of templated
Link_prediction
Device used to secure a vessel to the seabed
shank's weight from disrupting the fluke's orientation while setting. The hinge can wear out and may trap a sailor's fingers. Some later plough anchors
Anchor
Mathematical instrument consisting of two hinged rulers
It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various
Sector_(instrument)
Fringe hypothesis
were, oblivious to quantum effects. They don't amplify them; they don't hinge on them." Artificial consciousness Bohm interpretation of quantum mechanics
Quantum_mind
Mechanical analog computer
calculator Sector (instrument) – Mathematical instrument consisting of two hinged rulers Slide calculator – Mechanical calculator Slide chart – Hand-held
Slide_rule
Extension of superfactorials to the complex numbers
z}{\pi }}\right)+\operatorname {Cl} _{2}(2\pi z)} The proof of this result hinges on the following evaluation of the cotangent integral: introducing the notation
Barnes_G-function
Strain caused by an external load
becomes non-linear, and ductile materials will eventually enter a plastic hinge state where the magnitude of the stress is equal to the yield stress everywhere
Bending
Symmetrical transformations of the cuboctahedron into related uniform polyhedra
connected along the edges by hinges, the cuboctahedron is a rigid structure, as are all convex polyhedra, by Cauchy's theorem. However, when the faces are
Kinematics of the cuboctahedron
Kinematics_of_the_cuboctahedron
Vectors with given pattern of independence
ends by flexible hinges. A linkage of this type may be described as a graph, with an edge for each bar and a vertex for each hinge, and for one-dimensional
Matroid_representation
city its name. Cardea Mythical Rome Fertile Goddess Roman goddess of door hinges, conflated by Ovid with another deity, Carna, whose festival, the Bean-Kalends
List of women in the Heritage Floor
List_of_women_in_the_Heritage_Floor
HINGE THEOREM
HINGE THEOREM
Female
Norwegian
Norwegian unisex short form of longer names containing the element ing, INGE means "foremost one."Â
Surname or Lastname
English
English : variant of Mingy (see Mingee).German : from a pet form of the personal name Meinhardt.German : altered form of French Munier ‘miller’.Norwegian : habitational name from a farm name in Østfold, of obscure etymology.
Surname or Lastname
English
English : variant of Lingard.French : occupational name for a maker of or dealer in linen goods, from Old French linge ‘linen (goods)’ (see Linge 1).
Girl/Female
Teutonic Swedish Scandinavian
Hero's daughter.
Male
Norwegian
Norwegian unisex short form of longer names containing the name Ing, INGE means "Lord of the Inguins."Â
Surname or Lastname
English
English : variant spelling of Hind.
Surname or Lastname
English
English : habitational name from either of two places in Staffordshire and Shropshire named Hints, from Welsh hynt ‘road’, ‘path’.
Surname or Lastname
English
English : variant of Ingle.
Surname or Lastname
Americanized spelling of German Henz.English
Americanized spelling of German Henz.English : possibly a variant of Hince.
Girl/Female
German
From the Kettle Shaped Hollow
Surname or Lastname
English
English : variant spelling of Carnell.French : metonymic occupational name for a maker of latches and hinges, from Old Picard carnel, Old French charnel ‘hinge’.
Girl/Female
Latin
Protectress of hinges.
Surname or Lastname
English (southwestern)
English (southwestern) : occupational name for a servant, from Middle English hine ‘lad’, ‘servant’ (originally a collective term for a body of servants, from an Old English plural noun, hīwan ‘household’).Americanized spelling of German Hein.
Girl/Female
Australian, Chinese, Danish, Dutch, French, German, Scandinavian, Teutonic
Hero's Daughter; Beautiful; Foremost
Surname or Lastname
English
English : unexplained.East Asian : unexplained.
Surname or Lastname
English
English : perhaps a patronymic from Hine.
Surname or Lastname
English
English : variant of Ing.German : probably from the Germanic female personal name Inga.
Surname or Lastname
English
English : variant spelling of Ling 1.Norwegian : habitational name from any of several farmsteads in western Norway named with lyng ‘heather’, either on its own, or with the addition of vin ‘meadow’.Dutch (de Linge) and North German : habitational name from a place named with Old Low German linge ‘strip of land or water’, or possibly with the river name Linge (this river flows through the Betuwe). See also Lingen.Possibly French, from a metonymic occupational name from linge ‘linen goods’, but there is no evidence of surname in North America.
Boy/Male
Australian, Basque, German, Norwegian, Russian, Scandinavian, Swedish
Ing's Soldier; Guarded by Ing; Ing's Beauty; Foremost One
Female
German
Pet form of German Kunigunde, KINGE means "brave war."
HINGE THEOREM
HINGE THEOREM
Girl/Female
Christian & English(British/American/Australian)
Famous One
Girl/Female
Indian
Beautiful, Pretty, Charming, Graceful
Boy/Male
Hindu, Indian, Marathi
Worthy of Praise
Boy/Male
Arabic, Australian, Muslim
Very Knowledgeable; Wise; Entire
Male
Hebrew
(יָמִיר) Hebrew name YAMIR means "to change."
Girl/Female
Indian
Walking with proud, Swinging gait, Pretty
Girl/Female
Tamil
Mallika | மலà¯à®²à®¿à®•à®¾
Jasmine
Girl/Female
Indian
Most perfect, Complete
Boy/Male
Bengali, Hindu, Indian, Marathi, Punjabi, Sanskrit, Sikh
Charitable Prince; Cute Angel
Boy/Male
Indian, Telugu
Powerfull
HINGE THEOREM
HINGE THEOREM
HINGE THEOREM
HINGE THEOREM
HINGE THEOREM
n.
The hook with its eye, or the joint, on which a door, gate, lid, etc., turns or swings; a flexible piece, as a strip of leather, which serves as a joint to turn on.
v. t.
To singe.
v. t.
To attach by, or furnish with, hinges.
n.
The hinge of a bivalve shell.
imp. & p. p.
of Tinge
a.
Furnished with hinges.
v. t.
To burn slightly or superficially; to burn the surface of; to burn the ends or outside of; as, to singe the hair or the skin.
n.
The pivot pin of a hinge.
p. pr. & vb. n.
of Hinge
n.
An axis; hinge; a turning point.
p. pr. & vb. n.
of Tinge
n.
A hinge.
v. t.
To bend.
n.
One of the four cardinal points, east, west, north, or south.
imp. & p. p.
of Hinge
a.
Without a hinge or joint.
n.
That on which anything turns or depends; a governing principle; a cardinal point or rule; as, this argument was the hinge on which the question turned.
v. i.
To stand, depend, hang, or turn, as on a hinge; to depend chiefly for a result or decision or for force and validity; -- usually with on or upon; as, the argument hinges on this point.
v. & n.
See Singe.
v. t.
To imbue or impregnate with something different or foreign; as, to tinge a decoction with a bitter taste; to affect in some degree with the qualities of another substance, either by mixture, or by application to the surface; especially, to color slightly; to stain; as, to tinge a blue color with red; an infusion tinged with a yellow color by saffron.