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In proof theory, the Geometry of Interaction (GoI) was introduced by Jean-Yves Girard shortly after his work on linear logic. In linear logic, proofs
Geometry_of_interaction
French logician (born 1947)
of "reducibility candidate" ("candidat de réductibilité"). He is also credited with the discovery of Girard's paradox, linear logic, the geometry of interaction
Jean-Yves_Girard
Graphical model of computation
proof structures of linear logic. An interaction net system is specified by a set of agent types and a set of interaction rules. Interaction nets are an inherently
Interaction_nets
British computer scientist
calculus, strictness analysis, concurrency theory, interaction categories and geometry of interaction, game semantics and quantum computing. Notably, he
Samson_Abramsky
Branch of mathematics
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is
Geometry
Mathematical methods
several constructions, such as geometry of interaction models, ludics, and interaction graphs models. Realizability is one of the methods used in proof mining
Realizability
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
Resource-sensitive logic allowing each assumption to be used at most once
introduced the name as part of the geometry of interaction semantics of linear logic, which characterizes linear logic in terms of linear algebra; here he
Affine_logic
Most basic type of physical force
interactions known to exist: gravity, electromagnetism, weak interaction, and strong interaction. The gravitational and electromagnetic interactions produce
Fundamental_interaction
by Jean-Yves Girard. Linear logic Ludics Geometry of interaction Coherent space Deep inference Interaction nets Girard, Jean-Yves. Linear logic, Theoretical
Proof_net
Programming language evaluation rules
maint: deprecated archival service (link) The interactive on-line Geometry of Interaction visualiser, implementing a graph-based machine for several common
Evaluation_strategy
Model for predicting molecular geometry
və-SEP-ər) is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It
VSEPR_theory
System of resource-aware logic
Philosophy portal Chu spaces Computability logic Game semantics Geometry of interaction Intuitionistic logic Linear logic programming Linear type system
Linear_logic
Theory in number theory
mono-anabelian, and combinatorial versions) and with multiple interactions with number theory, algebraic geometry, and low-dimensional topology. The "anabelian question"
Anabelian_geometry
Intermolecular forces between oppositely-charged sites on molecules
chemistry, sigma hole interactions (or σ-hole interactions) are a family of intermolecular forces that can occur between several classes of molecules and arise
Sigma_hole_interactions
Academic journal
Journal of Geometry and Physics is a scientific journal in mathematical physics. Its scope is to stimulate the interaction between geometry and physics
Journal of Geometry and Physics
Journal_of_Geometry_and_Physics
Topics referred to by the same term
as another linkage of a different geometry Cognate interaction, in immunology denotes the specific, contact-dependent interaction between two cells. Connation
Cognate_(disambiguation)
Classical theory of gravitation
framework of Riemann–Cartan geometry, which possesses a locally gauged Lorentz symmetry, while general relativity is formulated within the framework of Riemannian
Einstein–Cartan_theory
Hypothetical physical concept
the concept of a "theory of everything" varies. The original technical concept referred to unification of the four fundamental interactions: electromagnetism
Theory_of_everything
Contribution to magnetic exchange interaction
known as the Dzyaloshinskii–Moriya interaction (DMI), is a contribution to the total magnetic exchange interaction between two neighboring magnetic spins
Antisymmetric_exchange
Base pairs in molecular genetics
intrinsic geometries and interaction energies of the isolated models. This procedure, however, sometimes leads to optimized geometries of base pairs
Non-canonical_base_pairing
Noncovalent molecular interaction
cation, solvation effects, the nature of the π system, and the geometry of the interaction. From electrostatics (Coulomb's law), smaller and more positively
Cation–π_interaction
Geometric structure used in certain particle interactions
Arkani-Hamed and Jaroslav Trnka. It enables simplified calculation of particle interactions in some quantum field theories. In planar N = 4 supersymmetric
Amplituhedron
Parameter used to characterize molecular geometry
interactions within coordination sphere. For example, in complexes of mercury(II), the Hg···π interactions were found this way. Selected geometries and
Geometry_index
Chemical bonding involving attraction between ions
electronegativities, and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding, along with covalent bonding and
Ionic_bonding
Mathematical treatise by Euclid
13 books of definitions, postulates, geometric constructions, and theorems with their proofs that covers plane and solid Euclidean geometry, elementary
Euclid's_Elements
Cylinder with hemispherical ends
(May 1949). "The effects of shape on the interaction of colloidal particles". Annals of the New York Academy of Sciences. 51 (4): 627–659. Bibcode:1949NYASA
Capsule_(geometry)
Mathematics of smooth surfaces
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most
Differential geometry of surfaces
Differential_geometry_of_surfaces
Mathematical model for modelling chemical reactions
destabilizing as it represents the distortion of a molecule from the equilibrium geometry. The interaction term, Δ E i n t {\displaystyle \Delta E_{\mathrm
Activation_strain_model
Property of a mathematical space
compact extra dimensions is equivalent to gauge interactions at long distances. In particular when the geometry of the extra dimensions is trivial, it reproduces
Dimension
Physical interaction in post-classical physics
Landau levels in the quantum treatment of a charged particle in a magnetic field. In this geometry, the interaction energy can be written E = ( a 1 a 2 2
Static forces and virtual-particle exchange
Static_forces_and_virtual-particle_exchange
Area of mathematics
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there
Discrete differential geometry
Discrete_differential_geometry
Number of "holes" of a surface
Riemann surface of X {\displaystyle X} (its manifold of complex points). For example, the definition of elliptic curve from algebraic geometry is connected
Genus_(mathematics)
Physical interaction of charged particles
Coulomb scattering is the elastic scattering of charged particles by the Coulomb interaction. The physical phenomenon was used by Ernest Rutherford in
Coulomb_scattering
2018 studio album by Tomeka Reid, Kyoko Kitamura, Taylor Ho Bynum, and Joe Morris
Geometry of Caves is an album by cellist Tomeka Reid, vocalist Kyoko Kitamura, cornetist and trumpeter Taylor Ho Bynum, and guitarist Joe Morris. It was
Geometry_of_Caves
Field of knowledge
the structures they form), geometry (the study of shapes and spaces that contain them), analysis (the quantitative study of approximation and convergence)
Mathematics
limitation of a workpiece. In general, there are three key ingredients in most of self assembly applications: geometry (order), interaction, energy. To
Self-assembly based manufacturing
Self-assembly_based_manufacturing
Invariant in quantum mechanics
^{2}(t){\hat {q}}^{2}\right].} The Ermakov–Lewis invariant for this type of interaction is I ^ = 1 2 [ ( q ^ ρ ) 2 + ( ρ p ^ − ρ ˙ q ^ ) 2 ] , {\displaystyle
Ermakov–Lewis_invariant
Ancient Greek mathematician (fl. 300 BC)
Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated
Euclid
Description of gravity using discrete values
interaction, and the weak interaction; this leaves gravity as the only interaction that has not been fully accommodated. The current understanding of
Quantum_gravity
System of connected p-orbitals with delocalized electrons in a molecule
constrained geometries favoring interaction to produce significant degrees of homoconjugation. In the example below, the carbonyl stretching frequencies of the
Conjugated_system
Model to predict the geometry of molecules
in first-principle vibronic coupling interactions. It enables prediction and explication of molecular geometries that are not necessarily satisfactorily
Second-order Jahn-Teller distortion in main-group element compounds
Second-order_Jahn-Teller_distortion_in_main-group_element_compounds
Theory of gravitation as curved spacetime
predictions concern the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light, and include gravitational
General_relativity
polyquinane polycyclic compound consisting of fused five-membered hydrocarbon rings. If the compound is unsaturated instead of saturated, it is called a polyquinene
Polyquinane
Short story by John Cheever
"The Geometry of Love" is a work of short fiction by John Cheever which first appeared in The Saturday Evening Post on January 1, 1966. The story was collected
The_Geometry_of_Love
British mathematician (born 1973)
manifolds and their interaction with algebraic geometry, low-dimensional topology, and dynamics. He is a professor at the University of Cambridge. Smith
Ivan_Smith_(mathematician)
Set of mathematical concepts in quantum gravity
In quantum gravity, quantum geometry is the set of mathematical concepts that generalize geometry to describe physical phenomena at distance scales comparable
Quantum_geometry
Israeli mathematician
Zeév; Sarnak, Peter (1995). "On Selberg's Eigenvalue Conjecture". Geometries in Interaction. Basel: Birkhäuser Basel. doi:10.1007/978-3-0348-9102-8_9.
Zeev_Rudnick
Concept in algebraic geometry
algebraic geometry as quotients of schemes parametrizing marked objects. In the 1970s and 1980s the theory developed interactions with symplectic geometry and
Geometric_invariant_theory
Physical theory with fields invariant under the action of local "gauge" Lie groups
the action of the SU(3) group on the color triplet of quarks. The Standard Model unifies the description of electromagnetism, weak interactions and strong
Gauge_theory
Class of chemical compounds
by 60° into an eclipsed geometry, the interaction between 2e and e" is minimized, which results in an increase in the energy of the HOMO in the complex
Trimethylenemethane_complexes
Analysis of the principal curvature is important, since a number of biological membranes possess shapes that are analogous to these common geometry staples
Membrane_curvature
Compound containing rings with delocalized pi electrons
well-defined pi stacking interaction with a T-shaped geometry, whereas the unfolded state had no aryl–aryl interactions. The NMR chemical shifts of the two conformations
Aromatic_compound
Earthwork sculpture by Charles Ross
Ottmann has described Star Axis as "a summary of Ross's lifelong pursuit of the dynamics of human interaction with light and the cosmos." Charles Ross (born
Star_Axis
Study of random spatial patterns
point of a Poisson point process. More complex versions allow interactions based in various ways on the geometry of objects. Different directions of application
Stochastic_geometry
Expression of force profile interaction between finite size bodies
root mean square roughness). Frequent geometries considered involve the interaction between two identical spheres of radius R where the effective radius
Derjaguin_approximation
Statistical approach
has become extensively used. In contrast to conventional methods, the interaction among process variables can be determined by statistical techniques.
Response_surface_methodology
Combinatorics problem proposed by Thomas Penyngton Kirkman
to Solution II. Both solutions could be embedded in PG(3,2) though that geometry was not known at the time. However, in publishing his solutions to the
Kirkman's_schoolgirl_problem
Three-dimensional geometry of track layouts and associated measurements
Track geometry is concerned with the properties and relations of points, lines, curves, and surfaces in the three-dimensional positioning of railroad track
Track_geometry
Constructing product by means of computer
research in computational geometry, computer graphics (both hardware and software), and discrete differential geometry. The design of geometric models for
Computer-aided_design
Installing wheels on a vehicle so that the wheels' faces are not completely parallel
angle that each wheel makes with the longitudinal axis of the vehicle, as a function of static geometry, and kinematic and compliant effects. This can be contrasted
Toe_(automotive)
Theory of gravity on antimatter
The gravitational interaction of antimatter with matter or antimatter has been observed by physicists. As was predicted by most physicists, the experiment
Gravitational interaction of antimatter
Gravitational_interaction_of_antimatter
Form of particle interferometry
splitter of different geometries for an atom-wave. The Ramsey–Bordé interferometer specifically uses two pairs of counter-propagating interaction waves,
Ramsey_interferometry
behavior of social life. In Black's own use and application of the idea, social geometry is an instance of Pure Sociology. While social geometry might entail
Social_geometry
crossroads of artificial intelligence and human–computer interaction. Recognition algorithms usually are gesture-based, appearance-based, geometry-based,
Sketch_recognition
Radicals centered on boron atoms
possible interactions summarized as synergistic interactions by Lu et al, are given below. It is a combination of these which ends up deciding the geometry, stability
Boryl_radicals
Video game 3D engine
composed mostly of solid geometry rendered without shading. Developed in-house by Incentive Software, Freescape is considered to be one of the first proprietary
Freescape
Prize awarded by the Royal Swedish Academy of Sciences and the Crafoord Foundation
wife Anna-Greta Crafoord following a donation to the Royal Swedish Academy of Sciences. It is awarded jointly by the academy and the Crafoord Foundation
Crafoord_Prize
BOINC based World Community Grid volunteer computing subproject
partner identification than surface geometry. Proteins: Structure, Function, and Bioinformatics (2017). Great interactions: How binding incorrect partners
Help_Cure_Muscular_Dystrophy
Equation in physics
differential geometry, involving Einstein warped product manifolds, explores cases where the warped function satisfies the homogeneous version of the screened
Screened_Poisson_equation
Bond arrangement in organic chemistry
factor in the antiperiplanar conformer is the interaction between molecular orbitals. Anti-periplanar geometry will put a bonding orbital and an anti-bonding
Anti-periplanar
Theory of subatomic structure
M-theory. Studies of string theory have also yielded a number of results on the nature of black holes and the gravitational interaction. There are certain
String_theory
Form of human-machine interaction
3D human–computer interaction refers to types of human–computer interaction where users are able to move and perform interaction in 3D space. Both the
3D_human–computer_interaction
Attraction of masses and energy
gravitas 'weight'), also known as gravitation or a gravitational interaction, is a fundamental interaction, which may be described as the force that draws material
Gravity
Geometric entity created by a 3D reconstruction technique
intersection of the two silhouette cones defines a visual hull. which is a bounding geometry of the actual 3D object. When the reconstructed geometry is only
Visual_hull
Branch of discrete mathematics
pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions
Combinatorics
Interactions between groups of atoms that do not arise from chemical bonds
der Waals' force) is a distance-dependent interaction between atoms or molecules and one of the category of intermolecular force. Unlike ionic or covalent
Van_der_Waals_force
Field theory in physics that aims to unify the fundamental forces and particles
expanded this theory of special relativity to a description of gravity, general relativity, using a field to describe the curving geometry of four-dimensional
Unified_field_theory
Manifold with Riemannian, complex and symplectic structure
In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a
Kähler_manifold
Chemical compound
hydrophobic, but exhibits high gas solubility with ideal liquid gas interactions. Since molecular oxygen is paramagnetic it causes 19F NMR spin lattice
Hexafluorobenzene
to geometries they do not regularly adopt. Porphyrin readily binds to transition metals, which are capable of octahedral or square planar geometries. Boron
Boron_porphyrins
calculus An older name of Ricci calculus Absolute geometry Also called neutral geometry, a synthetic geometry similar to Euclidean geometry but without the parallel
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Multiple diffraction of waves
The dynamical theory of diffraction describes the interaction of waves with a regular lattice. The wave fields traditionally described are X-rays, neutrons
Dynamical theory of diffraction
Dynamical_theory_of_diffraction
In differential geometry, affine differential geometry is the study of differential invariants of curves, surfaces, and higher-dimensional submanifolds
Affine_differential_geometry
Combined real-and-virtual environment
glasses Spatial computing – Computing paradigm emphasizing 3D spatial interaction with technology Wearable computer – Small computing device worn on the
Extended_reality
Framework of distances and directions
non-Euclidean geometries provide a better model for the shape of space.[citation needed] Debates concerning the nature, essence and the mode of existence of space
Space
Generalization of compactness
In topology and related branches of mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily
Totally_bounded_space
characteristics with a database. A scan of a person's iris, fingerprint, face, or other distinguishing feature is created, and a series of biometric points are drawn
Biometric_points
Navigation and surveillance technique
and difficult to site. Accuracy of a multilateration system is a function of several factors, including: The geometry of the receiver(s) and transmitter(s)
Pseudo-range_multilateration
(2025). "Direct evidence of trophic interaction between a crocodyliform and a large terror bird in the Middle Miocene of La Venta, Colombia". Biology
2025 in archosaur paleontology
2025_in_archosaur_paleontology
Metal-joining technique
surface of the same geometry. Another consideration is the effect of temperature and time on the quality of brazed joints. As the temperature of the braze
Brazing
Steric effect from the spatial arrangement of methyl groups in n-pentane
that would be expected based on gauche interactions alone. Pentane interference helps explain molecular geometries in many chemical compounds, product ratios
Pentane_interference
Book on sociological theory of law by Donald Black
introduced in the book is that of social geometry. This theory posits that law varies systematically with other aspects of social life, including stratification
The_Behavior_of_Law
Minimum amount of a physical entity involved in an interaction
quantum (pl.: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property
Quantum
Methods for snow ski construction
Ski geometry is the shape of the ski. Described in the direction of travel, the front of the ski, typically pointed or rounded, is the tip, the middle
Ski_geometry
Theory proposed by Roger Penrose
unification of general relativity (space-time geometry) and quantum mechanics (quantum theory) and has subsequently evolved into a widely studied branch of theoretical
Twistor_theory
Branch of mathematics
central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic
Linear_algebra
3D computer graphics software
such as generate and deform. A few examples of commonly used modifiers are generally subdivide surface, geometry nodes, solidify, and shrinkwrap. Blender
Blender_(software)
List of combinatorial computational geometry topics enumerates the topics of computational geometry that states problems in terms of geometric objects
List of combinatorial computational geometry topics
List_of_combinatorial_computational_geometry_topics
Biomolecule consisting of chains of amino acid residues
Linderstrøm-Lang, contributed an understanding of protein folding and structure mediated by hydrophobic interactions. The first protein to have its amino acid
Protein
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