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Surgery operation in minimal model program
In algebraic geometry, flips and flops are codimension-2 surgery operations arising in the minimal model program, given by blowing up along a relative
Flip_(algebraic_geometry)
Topics referred to by the same term
(Playboating) Flip (algebraic geometry) and flop, operations in algebraic geometry Flip-flop (politics), a sudden change of position on an issue Flip-flop hub
Flip-flop
Topics referred to by the same term
animation festival Flip (algebraic geometry), an operation in algebraic geometry Reflection (mathematics), sometimes called flip, an operation that preserves
Flip
theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory,
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
In algebraic geometry, the abundance conjecture is a conjecture in birational geometry, more precisely in the minimal model program, stating that for
Abundance_conjecture
Field of algebraic geometry
In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside
Birational_geometry
Effort to birationally classify algebraic varieties
In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational
Minimal_model_program
Algebra associated to any vector space
-blade. The wedge product was introduced originally as an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues:
Exterior_algebra
Japanese mathematician (born 1951)
February 23, 1951) is a Japanese mathematician, known for his work in algebraic geometry, particularly in relation to the classification of three-folds. He
Shigefumi_Mori
Russian mathematician (born 1950)
May 1950) is a Russian mathematician best known for his research in algebraic geometry. The proof of the Noether–Enriques–Petri theorem, the cone theorem
Vyacheslav_Shokurov
Classification of computer problems
idea behind the approach is to adopt and develop advanced tools in algebraic geometry and representation theory (i.e., geometric invariant theory) to prove
Geometric_complexity_theory
In algebraic geometry, a contraction morphism is a surjective projective morphism f : X → Y {\displaystyle f:X\to Y} between normal projective varieties
Contraction_morphism
Basic concepts of algebra
relationships in science and mathematics are expressed as algebraic equations. In mathematics, a basic algebraic operation is a mathematical operation similar to
Elementary_algebra
Geometric object that has length and direction
the direction refers to the direction of displacement from A to B. Many algebraic operations on real numbers such as addition, subtraction, multiplication
Euclidean_vector
Group of symmetries of a regular polygon
in group theory, geometry, and chemistry. The notation for the dihedral group differs in geometry and abstract algebra. In geometry, Dn or Dihn refers
Dihedral_group
Topics referred to by the same term
album by the band And One Flop (album), by Maurizio Pisciottu Flop (algebraic geometry), a birational transformation Flop-transition, in the string theory
Flop
Concept in algebraic geometry
Kleiman-Mori cone) of an algebraic variety X {\displaystyle X} is a combinatorial invariant of importance to the birational geometry of X {\displaystyle X}
Cone_of_curves
Mathematical structure in abstract algebra
(such as the imaginary unit √−1) is a *-algebra over the original field, considered as a trivially-*-ring. The * flips the sign of that square root. A quadratic
*-algebra
Branch of mathematics concerned with the movement of shapes and sets
mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups
Transformation_geometry
Physical quantity that changes sign with improper rotation
vectors and bivectors in 3-D". Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (2nd ed.). Morgan Kaufmann. p. 82. ISBN 978-0-12-374942-0
Pseudovector
Graph that encodes local operations in mathematics
by an elementary operation called a flip. Flip graphs are special cases of geometric graphs. Among notable flip graphs, one finds the 1-skeleton of polytopes
Flip_graph
Mathematical conjecture
Mirror Symmetry - Clay Mathematics Institute ebook Mirror Symmetry and Algebraic Geometry - Cox, Katz On the work of Givental relative to mirror symmetry Equivariant
Mirror_symmetry_conjecture
Kurdish mathematician
modern birational geometry. In 2010 he received the Leverhulme Prize in mathematics and statistics for his contributions to algebraic geometry, and in 2016
Caucher_Birkar
Motion of a certain space that preserves at least one point
Matrices, versors (quaternions), and other algebraic things: see the section Linear and Multilinear Algebra Formalism for details. A general rotation in
Rotation_(mathematics)
Matrix operation which flips a matrix over its diagonal
In linear algebra, transposition is an operation that flips a matrix over its diagonal; that is, transposition switches the row and column indices of
Transpose
complex geometry, spin manifolds, the Dirac operator, and algebraic cycles Ruth I. Michler (1967–2000), American commutative algebraist and algebraic geometer
List_of_women_in_mathematics
Non-orientable surface with one edge
flip" is a difficult acrobatic skiing trick, involving a full flip with a twist. In The Moebius Flip, a 1969 experimental short ski film, skiers flip
Möbius_strip
Largest distance between two points
have also been studied in computational geometry; see diameter (computational geometry). In differential geometry, the diameter is an important global Riemannian
Diameter_of_a_set
British mathematician
birational geometry of algebraic varieties in dimension greater than three, in particular, for [an] inductive proof of the existence of flips." In 2009
Christopher_Hacon
Mapping from a Euclidean space to itself
hyperplane. Some mathematicians use "flip" as a synonym for "reflection". In a plane (or, respectively, 3-dimensional) geometry, to find the reflection of a point
Reflection_(mathematics)
Partition of a simple polygon into triangles
graph Flip graph Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf (2000), "3: Polygon Triangulation", Computational Geometry (2nd ed
Polygon_triangulation
British mathematician (born 1964)
"contributions to algebraic geometry, in particular his proof of the finite generation of the canonical ring, the existence of flips and the boundedness
James_McKernan
Orthogonal symmetric polynomial family
by proving the n! conjecture. It is still a central open problem in algebraic combinatorics to find a combinatorial formula for the qt-Kostka coefficients
Macdonald_polynomials
Theorem in algebraic geometry
maps and the category of non-singular complex projective algebraic curves with the algebraic morphisms. (Richter) Note each face in the polyhedron consist
Hurwitz's automorphisms theorem
Hurwitz's_automorphisms_theorem
Exact solution for the Einstein field equations
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical
Kerr_metric
Complexity class of problems
Determining whether the rotation distance between two binary trees or the flip distance between two triangulations of the same convex polygon is below a
NP-intermediate
Collection of random variables
Stochastic Geometry and Its Applications. John Wiley & Sons. p. 108. ISBN 978-1-118-65825-3 – via Google Books. Haenggi, Martin (2013). Stochastic Geometry for
Stochastic_process
Smallest convex set containing a given set
1016/0020-0190(79)90072-3 Artin, Emil (1967), "2.5. Newton's Polygon", Algebraic Numbers and Algebraic Functions, Gordon and Breach, pp. 37–43, MR 0237460 Auel, Asher
Convex_hull
Area interpreted positively or negatively
Just as negative numbers simplify the solution of algebraic equations by eliminating the need to flip signs in separately considered cases when a quantity
Signed_area
Mathematical concept
with connected fibers to an algebraic curve such that almost all fibers are smooth curves of genus 1. (Over an algebraically closed field such as the complex
Elliptic_surface
Mathematical description of spacetime used in relativity
Riemannian geometries with intrinsic curvature, those exposed by the model spaces in hyperbolic geometry (negative curvature) and the geometry modeled by
Minkowski_spacetime
Topics referred to by the same term
or hyperbola Linear equivalence, a concept related to divisors in algebraic geometry Linear fractional transformation, an (invertible) homography based
Linear_(disambiguation)
global structures, especially in its interactions with algebraic geometry; etc. Affine geometry of curves Affine focal set Affine sphere Affine maximal
Affine_differential_geometry
Formula for the "volume" of an n-simplex
was a young geometry professor at the University of Vienna and Arthur Cayley was a British mathematician who specialized in algebraic geometry. Menger extended
Cayley–Menger_determinant
aspect of computational geometry. Mathematical visualization is used throughout mathematics, particularly in the fields of geometry and analysis. Notable
Mathematical_visualization
Branch of applied probability theory
random event is affected by previous isolated random events. For example, if flips of a fair coin give repeated tails, the coin still has the same probability
Decision_theory
Mathematics award
birational geometry of algebraic varieties in dimension greater than three, in particular, for their inductive proof of the existence of flips" "For their
Clay_Research_Award
Technique of illustration
Modern orthographic projection is derived from Gaspard Monge's descriptive geometry. Monge defined a reference system of two viewing planes: horizontal H ("ground")
Multiview orthographic projection
Multiview_orthographic_projection
Limitative results in mathematical logic
necessary axioms have been discovered or included. For example, Euclidean geometry without the parallel postulate is incomplete, because some statements in
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
2026 Android mobile operating system
with Android 17 are the Samsung Galaxy Z Fold 8 series, and the Galaxy Z Flip 8. Since Android 14 QPR2 shifted the development process to a trunk-based
Android_17
Number, approximately 1.618
frequent appearance in geometry; the division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams
Golden_ratio
Algebraic object with an ordered structure
ordered topological space Preorder field – Algebraic concept in measure theory, also referred to as an algebra of setsPages displaying short descriptions
Ordered_field
Path in a graph that visits each vertex exactly once
dodecahedron. Hamilton solved this problem using the icosian calculus, an algebraic structure based on roots of unity with many similarities to the quaternions
Hamiltonian_path
Quantum error correction code
overcome this difficulty. Algebraic-geometry codes provide another source of stabilizer constructions. Matsumoto used algebraic curves to obtain asymptotically
Stabilizer_code
Online news aggregator from Google
Google Fast Flip was an online news aggregator from Google Inc. that mimicked the experience of flicking through a newspaper or magazine, allowing visual
Google_Fast_Flip
Fundamental operation on complex numbers
Frank Morley's book Inversive Geometry (1933), written with his son Frank Vigor Morley. The other planar real unital algebras, dual numbers, and split-complex
Complex_conjugate
Polytope associated with combinatorial problems
In geometry, the cyclohedron is a d-dimensional polytope where d can be any non-negative integer. It was first introduced as a combinatorial object by
Cyclohedron
2025 Android mobile operating system
devices to ship with Android 16 are the Samsung Galaxy Z Fold 7, Galaxy Z Flip 7, and its FE model. As of July 2026[update], 25.49% of Android devices run
Android_16
Formula for systems of linear equations
equal, which is implied by the property that the sign of the determinant flips if you switch two columns. Fix the index j of a column, and consider that
Cramer's_rule
Four-dimensional analogue of the cube
MR 0304504. Pournin, Lionel (2013). "The flip-Graph of the 4-dimensional cube is connected". Discrete & Computational Geometry. 49 (3): 511–530. arXiv:1201.6543
Tesseract
Computational geometry problem
of points problem or closest pair problem is a problem of computational geometry: given n {\displaystyle n} points in metric space, find a pair of points
Closest pair of points problem
Closest_pair_of_points_problem
(2023-11-05), "An 𝒪(3.82^k) Time FPT Algorithm for Convex Flip Distance", Discrete & Computational Geometry, Springer Science and Business Media LLC: 44:1–44:14
Rotation_distance
Convex polytope of parenthesizations
of a regular polygon with n + 1 sides, and the edges correspond to edge flips in which a single diagonal is removed from a triangulation and replaced
Associahedron
Serpent-like curve
generalization of the curve is given by the flipped curve when a = 2 {\displaystyle a=2} , resulting in the flipped curve equation y 2 ( x 2 + 1 ) 2 = x 2
Serpentine_curve
Shape with six sides
In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon. The total of the internal
Hexagon
Possibility of a consistent definition of "clockwise" in a mathematical space
Manifolds. HarperCollins. ISBN 978-0-8053-9021-6. Hatcher, Allen (2001). Algebraic Topology. Cambridge University Press. ISBN 978-0-521-79540-1. Hatcher
Orientability
Distance function defined between probability distributions
is the case where c ( x , y ) = x y {\displaystyle c(x,y)=xy} with a sign flip. We say that a function ψ {\displaystyle \psi } is c-convex iff ψ = φ c {\displaystyle
Wasserstein_metric
Unified field theory
given by the curvature (field strength) of the gauge connection. On the flip side, the action is stationary against variations of the gauge connection
Kaluza–Klein_theory
Generalization of tensor fields
In differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor
Tensor_density
Matrix representing a Euclidean rotation
Rotation matrices provide an algebraic description of such rotations, and are used extensively for computations in geometry, physics, and computer graphics
Rotation_matrix
Vector field on a pseudo-Riemannian manifold that preserves the metric tensor
"Riemmanian Geometry and Geometric Analysis" (Third edition) Springer. (See section 5.2 pages 241-251.) Carroll, Sean (2004). Spacetime and Geometry: An Introduction
Killing_vector_field
Lie group of complex numbers of unit modulus; topologically a circle
group of symmetries of the circle which preserve its orientation (do not flip it). Composition of two rotations is the ordinary multiplication of complex
Circle_group
Symmetry of physical laws under a charge-conjugation transformation
representation chosen for the gamma group (the subgroup of the Clifford algebra capturing the algebraic properties of the gamma matrices). This matrix is representation
C-symmetry
Mathematical use of "for all"
Conversely, for the logical connectives ↑, ↓, ↛, and ←, the quantifiers flip: P ( x ) ↑ ( ∃ y ∈ Y Q ( y ) ) ≡ ∀ y ∈ Y ( P ( x ) ↑ Q ( y ) ) P ( x )
Universal_quantification
Logic formula
represent objects, but in a specific algebraic system these objects do not have meanings. Thus work inside the algebra becomes an exercise in obeying certain
Propositional_formula
Correspondence between quaternions and 3D rotations
their associated arc-lengths, which is also defines an algebra for points in Elliptic geometry. The normalized rotation axis, removing the cos γ 2 {\textstyle
Quaternions and spatial rotation
Quaternions_and_spatial_rotation
Scheme for controlling errors in data over noisy communication channels
classical block codes apply the algebraic properties of finite fields. Hence classical block codes are often referred to as algebraic codes. There are many types
Error_correction_code
Image recognition tool developed by Google
Galaxy S25, and foldable models such as the Galaxy Z Fold 6 and Galaxy Z Flip 6. Google officially launched Google Lens on October 4, 2017, with app previews
Google_Lens
Geometric representation of the complex numbers
real algebras, and hence “complex planes”. These are the quadratic algebras over the real number field. Complex coordinate space Complex geometry Complex
Complex_plane
Chatbot developed by Google
July 2025, and subsequently expanded to models including the Z Fold 7 and Z Flip 7, where it became part of the Galaxy AI suite. In February 2025, Google
Google_Gemini
Proof assistant
proof of a lemma which states that taking the successor of a natural number flips its parity. The fold-unfold tactic introduced by Danvy is used to help keep
Rocq
Average uncertainty in variable's states
for which one outcome is not expected over the other. In this case a coin flip has an entropy of one bit (similarly, one trit with equiprobable values contains
Entropy_(information_theory)
Number of bits that differ between two strings
This means that if one bit is flipped or two bits are flipped, the error can be detected. If three bits are flipped, then "000" becomes "111" and the
Hamming_distance
Complexity class used to classify decision problems
"spot-checks" a few places in the proof string, and using a limited number of coin flips can determine the correct answer with high probability. This allows several
NP_(complexity)
On tangency patterns of circles
from dessins d'enfant, a certain type of graph embedding used in algebraic geometry to study Riemann surfaces and the absolute Galois group. These automatically
Circle_packing_theorem
Mass shooting in Georgia, U.S.
desks after seeing the "Hard Lockdown" message. A geometry teacher in a separate classroom flipped their desk over to barricade its door. Other students
2024 Apalachee High School shooting
2024_Apalachee_High_School_shooting
Algebraic tool for computing topological spaces' invariants
In algebraic topology and homology theory, the Mayer–Vietoris sequence is an algebraic tool to help compute algebraic invariants of topological spaces
Mayer–Vietoris_sequence
Data transfer program by Samsung and Google
high-end Galaxy devices. The Galaxy S23 series, Galaxy Z Fold 5, Galaxy Z Flip 5, and mid-range devices in the Galaxy A, F, M, and Tab A series are not
Quick_Share
Method may be implemented using Monte-Carlo simulation, or in a simplified algebraic or other form (see the Range Option below). Using simulation, for each
Datar–Mathews method for real option valuation
Datar–Mathews_method_for_real_option_valuation
Infinitely many tasks in finite time
time t = 0 the lamp is off, and the switch is flipped on at t = 1/2; after that, the switch is flipped after waiting for half the time as before. Thomson
Supertask
Gamma matrices for arbitrary Clifford algebras
the article on Clifford algebra. Jost provides a standard reference for spinors in the general setting of Riemmannian geometry. Most of the properties
Higher-dimensional gamma matrices
Higher-dimensional_gamma_matrices
copy the result as an image to their device's clipboard. "flip a coin( see it )" will flip a coin: heads or tails. "fun facts( see it )" or "i'm feeling
List_of_Google_Easter_eggs
Comprehensive physical model
SU(2) × SU(2) Georgi–Glashow model – SU(5); and Flipped SU(5) – SU(5) × U(1) SO(10) model; and Flipped SO(10) – SO(10) × U(1) E6 model; and Trinification
Grand_Unified_Theory
Public high school in California, United States
aims to pursue. Students typically start in Algebra 1, Geometry, Geometry Enriched, Algebra 2, or Algebra 2/Trigonometry in ninth grade. There are honors
Cupertino_High_School
Symmetrical calligraphic or typographic visual pun
several ambigrams closely related to his realm, like the words "algebra", "geometry", "math", "maths", or "mathematics". Calculator spelling is an unintended
Ambigram
American consumer electronics company
At Mobile World Congress the company also announced the Motorola Gleam flip phone and Motorola Pro for GSM networks. In Q1 2011, the company reported
Motorola_Mobility
Scientific study of digital information
entropy is equal to the lack of information about an event. In the above coin flip example, the entropy in the case where you don't know the outcome is 1 bit
Information_theory
Mathematical transform that expresses a function of time as a function of frequency
formulas, some ordinary differential equations can be transformed into algebraic equations, which are much easier to solve. These formulas also give rise
Fourier_transform
Basic circuit in quantum computing
Toffoli gate alone forms a set of universal gates for reversible Boolean algebraic logic circuits, which encompasses all classical computation. A single-gate
Quantum_logic_gate
Research and scientific development company
Maurice Karnaugh developed the Karnaugh map, used for managing of Boolean algebraic expressions. In January 1954, Bell Labs built one of the first completely
Bell_Labs
travel, tourism, insurance
FLIP ALGEBRAIC-GEOMETRY
FLIP ALGEBRAIC-GEOMETRY
Boy/Male
Greek
Lover of horses.
Boy/Male
Russian Swedish
loves horses'.
Boy/Male
Australian, British, Czechoslovakian, Danish, Dutch, English, French, German, Greek, Polish, Russian, Spanish, Swedish
Russian Form of Philip; Horse Lover; Friend of Horses
Surname or Lastname
English
English : of uncertain derivation; possibly a metonymic occupational name for a dealer in old clothes, from a derivative of Old French frepe ‘rag’, from frip(i)er ‘to tear to rags’.
Female
Serbian
(Филипа) Feminine form of Serbian Filip, FILIPA means "lover of horses."
Boy/Male
Biblical
Rabbit, wild rat, their lip, their brink.
Surname or Lastname
English
English : variant spelling of Gravely.Possibly also a variant spelling of Swiss German Gräfli (see Gravely).
Male
Serbian
(Филип) Serbian form of Greek Philippos, FILIP means "lover of horses."
Boy/Male
Gaelic Irish
Son of the red haired one.
Boy/Male
Greek
Greek surname. Euclid was an early developer of geometry theories.
Boy/Male
Biblical
Rabbit, wild rat, their lip, their brink.
Biblical
Shaphan, rabbit; wild rat; their lip; their brink
FLIP ALGEBRAIC-GEOMETRY
FLIP ALGEBRAIC-GEOMETRY
FLIP ALGEBRAIC-GEOMETRY
FLIP ALGEBRAIC-GEOMETRY
FLIP ALGEBRAIC-GEOMETRY
FLIP ALGEBRAIC-GEOMETRY
FLIP ALGEBRAIC-GEOMETRY
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