Common Geometry Terminology – SolveForce Fiber Internet, Cloud Computing & Telecommunications

Algebraic Geometry: A branch of mathematics that deals with the properties and relations of algebraic varieties, which are sets of solutions to polynomial equations, using the tools of algebra, geometry, and topology.
Altitude: A line segment that connects a vertex of a triangle to the opposite side, such that it is perpendicular to the side.
Analytic Geometry: A branch of mathematics that deals with the representation of geometric shapes using algebraic equations and manipulating these equations to solve geometric problems.
Angle: The measure of the amount of turn between two rays with the same endpoint
Arc: A part of the circumference of a circle
Area: The amount of space inside a shape.
Chord: A line segment that connects two points on a circle
Circle: A set of points in a plane that are the same distance from a center point
Computational Conformal Geometry: A branch of mathematics and computer science that deals with the design, analysis, and implementation of algorithms for solving problems related to conformal geometry, such as conformal mapping and the uniformization of Riemann surfaces.
Computational Geometry: A branch of mathematics and computer science that deals with the design, analysis, and implementation of algorithms for solving geometric problems, such as finding the intersection of two lines or the shortest path between two points.
Congruence: Two shapes are congruent when they are the same size and shape.
Congruent: Two shapes that have the same size and shape
Convex Geometry: A branch of mathematics that deals with the properties and relations of convex sets and convex functions, which are sets and functions that maintain their shape when a line segment is drawn between any two points within the set or function.
Coordinate Geometry: A branch of mathematics that deals with the representation of geometric shapes using coordinates and manipulating these coordinates to solve geometric problems.
Diameter: A line segment that passes through the center of a circle and has endpoints on the circumference
Differential Geometry of Bundles: A branch of mathematics that deals with the properties and relations of geometric structures called bundles, which are collections of geometric objects that are “glued” together consistently.
Differential Geometry of Curves: A branch of mathematics that deals with the properties and relations of curves in space, such as arc length, curvature, and torsion.
Differential Geometry of Fibrations: A branch of mathematics that deals with the properties and relations of fibrations, which are geometric structures that “glue” together different manifolds, and the manipulation of these properties and relations to solve geometric problems.
Differential Geometry of Lie Groups: A branch of mathematics that deals with the properties and relations of Lie groups, which are smooth manifolds that are also grouped under a smooth binary operation, and the manipulation of these properties and relations to solve geometric problems.
Differential Geometry of Manifolds: A branch of mathematics that deals with the properties and relations of smooth manifolds, which are topological spaces that locally resemble Euclidean space, and the manipulation of these manifolds to solve geometric problems.
Differential Geometry of Surfaces: A branch of mathematics that deals with the properties and relations of surfaces in the space, such as Gaussian curvature and mean curvature.
Differential Geometry: A branch of mathematics that deals with the properties and relations of points, lines, angles, surfaces and solids using calculus and manipulating these properties and relations to solve geometric problems.
Differential-Topological Geometry: A branch of mathematics that deals with the properties and relations of differentiable manifolds, which are smooth manifolds, and topological spaces, which are spaces that are “glued” together in a consistent way, using the tools of differential calculus and topology.
Discrete Geometry: A branch of mathematics that deals with the properties and relations of discrete geometric objects, such as polygons, graphs, and polyhedra, and the manipulation of these objects to solve geometric problems.
Euclidean Geometry: A branch of mathematics that deals with the properties and relations of points, lines, angles, surfaces and solids using Euclid’s postulates.
fields and industries.
Foliations and foliated geometry: A branch of mathematics that deals with the properties and relations of foliations, which are geometric structures that “cut” a manifold into a family of submanifolds called leaves and the manipulation of these properties and relations to solve geometric problems.
Fractal Geometry: A branch of mathematics that deals with the properties and relations of self-similar shapes, meaning they have the same pattern at different scales.
Geometric Algebra: A branch of mathematics that deals with the properties and relations of geometric objects using an algebraic system, which combines traditional vector algebra with the theory of projective geometry and the theory of orthogonal transformations.
Geometric Group Theory: A branch of mathematics that deals with the properties and relations of groups, which are sets of symmetries, using the tools of geometry, algebra, and topology.
Geometric Measure Theory: A branch of mathematics that deals with the properties and relations of geometric objects, such as sets and measures, using measure theory and the manipulation of these properties and relations to solve geometric problems.
Geometric Topology: A branch of mathematics that deals with the properties and relations of topological spaces and geometric objects, such as points, lines, and surfaces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Affine Manifolds: A branch of mathematics that deals with the properties and relations of affine manifolds, which are smooth manifolds that are also affine spaces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Algebraic Curves: A branch of mathematics that deals with the properties and relations of algebraic curves, which are the solutions of polynomial equations in two variables and the manipulation of these properties and relations to solve geometric problems.
Geometry of Algebraic Surfaces: A branch of mathematics that deals with the properties and relations of algebraic surfaces, which are the solutions of polynomial equations in three variables and the manipulation of these properties and relations to solve geometric problems.
Geometry of Algebraic Varieties: A branch of mathematics that deals with the properties and relations of algebraic varieties, which are the solutions of polynomial equations in any number of variables and the manipulation of these properties and relations to solve geometric problems.
Geometry of Arithmetic Geometry: A branch of mathematics that deals with the properties and relations of algebraic varieties over the integers and other number fields and the manipulation of these properties and relations to solve geometric problems.
Geometry of Cartan Manifolds: A branch of mathematics that deals with the properties and relations of Cartan manifolds, which are smooth manifolds that are also equipped with a Cartan connection, a way to measure parallel transport and curvature, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Complex Manifolds: A branch of mathematics that deals with the properties and relations of complex manifolds, which are smooth manifolds that are also complex spaces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Conformal Manifolds: A branch of mathematics that deals with the properties and relations of conformal manifolds, which are smooth manifolds that are also equipped with a conformal structure, a way to measure angles and angles preserving transformations and the manipulation of these properties and relations to solve geometric problems.
Geometry of CR Manifolds: A branch of mathematics that deals with the properties and relations of CR manifolds, which are smooth manifolds that are also equipped with a CR structure, a way to define a subbundle of tangent space that is invariant under a certain complex structure and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Equations: A branch of mathematics that deals with the properties and relations of differential equations, which is the study of solving and understanding differential equations in a geometric context and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Forms: A branch of mathematics that deals with the properties and relations of differential forms, which is the study of multivariable calculus and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Aerodynamics: A branch of mathematics that deals with the properties and relations of aerodynamics, which is the study of how gases or liquids interact with solid objects, such as aircraft, cars, and buildings, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Architectural Acoustics: A branch of mathematics that deals with the properties and relations of architectural acoustics, which is the study of how sound behaves in buildings and other structures, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Architecture: A branch of mathematics that deals with the properties and relations of architecture, which is the study of how to design and construct buildings and other structures, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Augmented Reality: A branch of mathematics that deals with the properties and relations of augmented reality, which is the study of how digital information can be overlaid on the real world, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Complex Analytic Manifolds: A branch of mathematics that deals with the properties and relations of complex analytic manifolds, which are complex manifolds equipped with additional analytic structures and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Computational Geometry: A branch of mathematics that deals with the properties and relations of computational geometry, which is the study of algorithms for solving geometric problems using techniques from differential geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Computer Graphics: A branch of mathematics that deals with the properties and relations of computer graphics, which is the study of how images can be generated, displayed, and animated using computer algorithms, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Computer Vision: A branch of mathematics that deals with the properties and relations of computer vision, which is the study of how computers can interpret and understand visual information, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Control Theory: A branch of mathematics that deals with the properties and relations of control theory, which is the study of controlling systems using techniques from differential geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Discrete Geometry: A branch of mathematics that deals with the properties and relations of discrete geometry, which is the study of discrete structures such as point sets, graphs, and polyhedra using techniques from differential geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Foliations: A branch of mathematics that deals with the properties and relations of foliations, which are partitions of a manifold into submanifolds called leaves and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Game Physics: A branch of mathematics that deals with the properties and relations of game physics, which is the study of how physical phenomena can be simulated in video games, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Geographic Information Systems: A branch of mathematics that deals with the properties and relations of geographic information systems, which is the study of how geographic data can be acquired, analyzed, and represented, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Geometric Mechanics: A branch of mathematics that deals with the properties and relations of geometric mechanics, which is the study of mechanical systems using techniques from differential geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Hermitian Manifolds: A branch of mathematics that deals with the properties and relations of hermitian manifolds, which are smooth manifolds equipped with a Hermitian metric and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Homogeneous Spaces: A branch of mathematics that deals with the properties and relations of homogeneous spaces, which are Riemannian manifolds that are transitive under a group of isometries and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Hydrodynamics: A branch of mathematics that deals with the properties and relations of hydrodynamics, which is the study of how liquids interact with solid objects, such as ships and offshore structures, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Industrial Design: A branch of mathematics that deals with the properties and relations of industrial design, which is the study of how to design and create products and other manufactured goods, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Integrable Systems: A branch of mathematics that deals with the properties and relations of integrable systems, which are dynamical systems that can be solved exactly using techniques from differential geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Kahler Manifolds: A branch of mathematics that deals with the properties and relations of Kahler manifolds, which are complex manifolds equipped with a Kahler form, a closed, non-degenerate 2-form and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Knot Invariants: A branch of mathematics that deals with the properties and relations of knot invariants, which are mathematical quantities that are used to distinguish different knots and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Knot Theory: A branch of mathematics that deals with the properties and relations of knots, which are closed loops in 3-dimensional space, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Landscape Architecture: A branch of mathematics that deals with the properties and relations of landscape architecture, which is the study of how to design and construct outdoor spaces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Lie Algebroids: A branch of mathematics that deals with the properties and relations of Lie algebroids, which are generalizations of Lie algebras that have some additional algebraic data and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Lie Groupoids: A branch of mathematics that deals with the properties and relations of Lie groupoids, which are generalizations of Lie groups that have some additional algebraic data and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Manifolds with Singularities: A branch of mathematics that deals with the properties and relations of manifolds with singularities, which are smooth manifolds that have some singular points or loci, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Mechanics: A branch of mathematics that deals with the properties and relations of mechanics, which is the study of motion and forces using techniques from differential geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Medical Imaging: A branch of mathematics that deals with the properties and relations of medical imaging, which is the study of how medical images can be acquired, analyzed, and interpreted, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Metric Geometry: A branch of mathematics that deals with the properties and relations of metric geometry, which is the study of geometric spaces equipped with a metric, a way to measure distance, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Optimal Control: A branch of mathematics that deals with the properties and relations of optimal control, which is the study of finding the optimal control for systems using techniques from differential geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Orbifolds: A branch of mathematics that deals with the properties and relations of orbifolds, which are generalizations of manifolds that have some singular points or loci, but with a specific type of local geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Poisson Manifolds: A branch of mathematics that deals with the properties and relations of Poisson manifolds, which are smooth manifolds equipped with a Poisson bracket, a way to measure the algebraic relations of functions on the manifold, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Product Design: A branch of mathematics that deals with the properties and relations of product design, which is the study of how to design and create products and other manufactured goods, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Riemannian Manifolds: A branch of mathematics that deals with the properties and relations of Riemannian manifolds, which are smooth manifolds equipped with a Riemannian metric, a way to measure distance and angles, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Aerial Robotics: A branch of mathematics that deals with the properties and relations of robotics aerial robotics, which is the study of how robotic systems can be used in aerial applications, such as drones, aerial survey, and aerial photography, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Affective Robotics: A branch of mathematics that deals with the properties and relations of robotics affective robotics, which is the study of how robotic systems can recognize and respond to human emotions, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Agriculture Robotics: A branch of mathematics that deals with the properties and relations of robotics agriculture robotics, which is the study of how robotic systems can be used to assist farmers in crop planting, harvesting, and maintenance, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Assistive Robotics: A branch of mathematics that deals with the properties and relations of robotics assistive robotics, which is the study of how robotic systems can be used to help people with disabilities, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Biomechanics: A branch of mathematics that deals with the properties and relations of robotics biomechanics, which is the study of how robotic systems can mimic and replicate the movement and behavior of living organisms, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Biomedical Robotics: A branch of mathematics that deals with the properties and relations of robotics biomedical robotics, which is the study of how robotic systems can be used in medical applications, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Cognitive architectures: A branch of mathematics that deals with the properties and relations of cognitive architectures, which is the study of how robotic systems can mimic and replicate the cognitive processes of human, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Cognitive Robotics: A branch of mathematics that deals with the properties and relations of robotics cognitive robotics, which is the study of how robotic systems can mimic human cognitive processes, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Computer Vision: A branch of mathematics that deals with the properties and relations of computer vision, which is the study of how robotic systems can process and interpret visual information, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Control: A branch of mathematics that deals with the properties and relations of robotics control, which is the study of how robotic systems can be controlled to achieve specific tasks and goals, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Dynamics: A branch of mathematics that deals with the properties and relations of robotics dynamics, which is the study of how robotic systems move and interact with their environment, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Emotion Robotics: A branch of mathematics that deals with the properties and relations of robotics emotion robotics, which is the study of how robotic systems can recognize and express emotions, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Entertainment Robotics: A branch of mathematics that deals with the properties and relations of robotics entertainment robotics, which is the study of how robotic systems can be used in entertainment applications, such as interactive displays, theme park attractions, and robotic pets, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Environmental Robotics: A branch of mathematics that deals with the properties and relations of robotics environmental robotics, which is the study of how robotic systems can be used to monitor, protect, and preserve the environment, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Exoskeletons: A branch of mathematics that deals with the properties and relations of robotics exoskeletons, which is the study of how robotic systems can be used to enhance human strength and mobility, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Food Robotics: A branch of mathematics that deals with the properties and relations of robotics food robotics, which is the study of how robotic systems can be used in the food industry, such as food processing, packaging, and delivery, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Grasping: A branch of mathematics that deals with the properties and relations of robotics grasping, which is the study of how robotic systems can pick up and manipulate objects, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Human-Robot Interaction: A branch of mathematics that deals with the properties and relations of robotics human-robot interaction, which is the study of how robotic systems can interact and communicate with humans, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Industrial Robotics: A branch of mathematics that deals with the properties and relations of robotics industrial robotics, which is the study of how robotic systems can be used in industrial applications, such as manufacturing, assembly, and inspection, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Intelligence: A branch of mathematics that deals with the properties and relations of robotics intelligence, which is the study of how robotic systems can exhibit intelligent behavior, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Kinematics: A branch of mathematics that deals with the properties and relations of robotics kinematics, which is the study of how robotic systems move, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Learning: A branch of mathematics that deals with the properties and relations of robotics learning, which is the study of how robotic systems can learn and improve their performance over time, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Localization: A branch of mathematics that deals with the properties and relations of robotics localization, which is the study of how robotic systems can determine their position and orientation in their environment, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Manipulation: A branch of mathematics that deals with the properties and relations of robotics manipulation, which is the study of how robotic systems can move and manipulate objects, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Mapping: A branch of mathematics that deals with the properties and relations of robotics mapping, which is the study of how robotic systems can create maps of their environment, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Marine Robotics: A branch of mathematics that deals with the properties and relations of robotics marine robotics, which is the study of how robotic systems can be used in marine applications, such as undersea exploration, oceanography, and oil and gas exploration, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Medical Robotics: A branch of mathematics that deals with the properties and relations of robotics medical robotics, which is the study of how robotic systems can be used to assist doctors and surgeons in medical procedures, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Micro-Robotics: A branch of mathematics that deals with the properties and relations of robotics micro-robotics, which is the study of how small-scale robotic systems can be designed, built and controlled, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Military Robotics: A branch of mathematics that deals with the properties and relations of robotics military robotics, which is the study of how robotic systems can be used in military applications, such as reconnaissance, weapons delivery, and mine clearing, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Mining Robotics: A branch of mathematics that deals with the properties and relations of robotics mining robotics, which is the study of how robotic systems can be used in the mining industry, such as exploration, excavation, and ore processing, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Multi-Robotics: A branch of mathematics that deals with the properties and relations of robotics multi-robotics, which is the study of how multiple robotic systems can work together to achieve a common goal, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Nano-Robotics: A branch of mathematics that deals with the properties and relations of robotics nano-robotics, which is the study of how small-scale robotic systems can be designed, built and controlled, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Natural Language Processing: A branch of mathematics that deals with the properties and relations of natural language processing, which is the study of how robotic systems can process, understand, and generate human language, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Navigation: A branch of mathematics that deals with the properties and relations of robotics navigation, which is the study of how robotic systems can navigate and move through their environment, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Neuro-mechanics: A branch of mathematics that deals with the properties and relations of robotics neuro-mechanics, which is the study of how robotic systems can mimic and replicate the movement and behavior of living organisms, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Neurorobotics: A branch of mathematics that deals with the properties and relations of robotics neurorobotics, which is the study of how robotic systems can mimic the function and structure of the nervous system, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Nuclear Robotics: A branch of mathematics that deals with the properties and relations of robotics nuclear robotics, which is the study of how robotic systems can be used in nuclear applications, such as nuclear power plants, nuclear waste management, and radiation detection, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Orthotics: A branch of mathematics that deals with the properties and relations of robotics orthotics, which is the study of how robotic systems can be used to correct or enhance human movement and posture, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Perception: A branch of mathematics that deals with the properties and relations of robotics perception, which is the study of how robotic systems can perceive and interpret their environment, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Planning: A branch of mathematics that deals with the properties and relations of robotics planning, which is the study of how robotic systems can plan and execute actions to achieve specific tasks and goals, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Prosthetics: A branch of mathematics that deals with the properties and relations of robotics prosthetics, which is the study of how robotic systems can be used to replace or enhance human limbs the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Rehabilitation Robotics: A branch of mathematics that deals with the properties and relations of robotics rehabilitation robotics, which is the study of how robotic systems can be used to help patients recovering from injuries or illnesses, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Robotics Control: A branch of mathematics that deals with the properties and relations of robotics control, which is the study of how robotic systems can be controlled and manipulated, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Robotics Dynamics: A branch of mathematics that deals with the properties and relations of robotics dynamics, which is the study of how robotic systems move and respond to forces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Robotics Perception: A branch of mathematics that deals with the properties and relations of robotics perception, which is the study of how robotic systems can sense and interpret their environment, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Robotics Planning: A branch of mathematics that deals with the properties and relations of robotics planning, which is the study of how robotic systems can make decisions and plan actions, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Search and Rescue Robotics: A branch of mathematics that deals with the properties and relations of robotics search and rescue robotics, which is the study of how robotic systems can be used in search and rescue operations, such as disaster response, exploring hazardous areas, and finding missing people, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Security Robotics: A branch of mathematics that deals with the properties and relations of robotics security robotics, which is the study of how robotic systems can be used in security applications, such as surveillance, border control, and law enforcement, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Self-awareness: A branch of mathematics that deals with the properties and relations of robotics self-awareness, which is the study of how robotic systems can autonomously perceive and understand their own state, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Self-healing: A branch of mathematics that deals with the properties and relations of robotics self-healing, which is the study of how robotic systems can autonomously detect and repair damages or malfunctions, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Self-learning: A branch of mathematics that deals with the properties and relations of robotics self-learning, which is the study of how robotic systems can autonomously learn and improve their own performance, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Self-optimization: A branch of mathematics that deals with the properties and relations of robotics self-optimization, which is the study of how robotic systems can autonomously optimize their performance and adapt to changing environments, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Self-organization: A branch of mathematics that deals with the properties and relations of robotics self-organization, which is the study of how robotic systems can autonomously organize themselves to achieve a common goal, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Self-replication: A branch of mathematics that deals with the properties and relations of robotics self-replication, which is the study of how robotic systems can autonomously replicate themselves or create new robotic systems, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Service Robotics: A branch of mathematics that deals with the properties and relations of robotics service robotics, which is the study of how robotic systems can be used to provide services, such as customer service, cleaning, and maintenance, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Smart Robotics: A branch of mathematics that deals with the properties and relations of robotics smart robotics, which is the study of how robotic systems can be used in smart cities, smart homes, and other smart environments, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Social Robotics: A branch of mathematics that deals with the properties and relations of robotics social robotics, which is the study of how robotic systems can interact and communicate with humans, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Soft Robotics: A branch of mathematics that deals with the properties and relations of robotics soft robotics, which is the study of how robotic systems can be made soft and flexible, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Space Robotics: A branch of mathematics that deals with the properties and relations of robotics space robotics, which is the study of how robotic systems can be designed, built and controlled for use in space, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Swarm Robotics: A branch of mathematics that deals with the properties and relations of robotics swarm robotics, which is the study of how multiple robotic systems can work together to achieve a common goal, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Transportation Robotics: A branch of mathematics that deals with the properties and relations of robotics transportation robotics, which is the study of how robotic systems can be used in transportation applications, such as self-driving cars, drones, and autonomous ships, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics Underwater Robotics: A branch of mathematics that deals with the properties and relations of robotics underwater robotics, which is the study of how robotic systems can be designed, built and controlled for use underwater, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Robotics: A branch of mathematics that deals with the properties and relations of robotics, which is the study of how machines can mimic human actions and movements, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Schemes: A branch of mathematics that deals with the properties and relations of schemes, which are algebraic varieties with added data and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Shape Analysis: A branch of mathematics that deals with the properties and relations of shapes, which are geometric objects that points can represent, curves, surfaces, and volumes, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Stacky manifolds: A branch of mathematics that deals with the properties and relations of stacky manifolds, which are generalizations of manifolds that have some additional algebraic data and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Super Lie Algebras: A branch of mathematics that deals with the properties and relations of super Lie algebras, which are generalizations of Lie algebras that include anticommuting coordinates, known as Grassmann numbers, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Superconnections: A branch of mathematics that deals with the properties and relations of superconnections, which is a generalization of connections on vector bundles that include anticommuting coordinates, known as Grassmann numbers, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Supergeometry: A branch of mathematics that deals with the properties and relations of supergeometry, which is a generalization of geometry that includes anticommuting coordinates, known as Grassmann numbers, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Supergravity: A branch of mathematics that deals with supergravity’s properties and relations, a theory that combines supersymmetry and general relativity and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Supergroups: A branch of mathematics that deals with the properties and relations of supergroups, which are generalizations of Lie groups that include anticommuting coordinates, known as Grassmann numbers, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Supermanifolds: A branch of mathematics that deals with the properties and relations of supermanifolds, which are generalizations of smooth manifolds that include anticommuting coordinates, known as Grassmann numbers, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Supermanifolds: A branch of mathematics that deals with the properties and relations of supermanifolds, which is a generalization of manifolds that include anticommuting coordinates, known as Grassmann numbers, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Superspaces: A branch of mathematics that deals with the properties and relations of superspaces, which are generalizations of vector spaces that include anticommuting coordinates, known as Grassmann numbers, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Superstring theory: A branch of mathematics that deals with the properties and relations of superstring theory, which is a theoretical framework in physics that unifies quantum mechanics and general relativity using supersymmetry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Supersymmetry: A branch of mathematics that deals with the properties and relations of supersymmetry, which is a symmetry between bosons and fermions in particle physics and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Symmetric Spaces: A branch of mathematics that deals with the properties and relations of symmetric spaces, which are Riemannian manifolds that are invariant under a group of isometries and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Symplectic Manifolds: A branch of mathematics that deals with the properties and relations of symplectic manifolds, which are smooth manifolds equipped with a closed, non-degenerate 2-form and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Textile Design: A branch of mathematics that deals with the properties and relations of textile design, which is the study of how to design and create fabrics and other textile products, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Topological Data Analysis: A branch of mathematics that deals with the properties and relations of topological data analysis, which is the study of using topological techniques to analyze data and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Urban Planning: A branch of mathematics that deals with the properties and relations of urban planning, which is the study of how to design and organize cities and other urban areas, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Geometry of Virtual Reality: A branch of mathematics that deals with the properties and relations of virtual reality, which is the study of how immersive digital environments can be created, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Differential Inclusions: A branch of mathematics that deals with the properties and relations of differential inclusions, which is the study of systems of differential equations involving inequalities and the manipulation of these properties and relations to solve geometric problems.
Geometry of Finsler Manifolds: A branch of mathematics that deals with the properties and relations of Finsler manifolds, which are smooth manifolds that are also equipped with a Finsler metric, a way to measure distance that allows for different speeds in different directions, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Flag manifolds: A branch of mathematics that deals with the properties and relations of flag manifolds, which are certain types of homogeneous spaces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Grassmannians: A branch of mathematics that deals with the properties and relations of Grassmannians, which are certain types of homogeneous spaces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Homogeneous Spaces: A branch of mathematics that deals with the properties and relations of homogeneous spaces, which are spaces that are “glued” together in a consistent way, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Hyperkähler Manifolds: A branch of mathematics that deals with the properties and relations of hyperkähler manifolds, which are complex manifolds that are also equipped with a hyperkähler metric, a more general way to measure distance and angles, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Information Geometry: A branch of mathematics that deals with the properties and relations of information geometry, which is the study of statistical models and probability distributions using tools from Riemannian geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Information Manifolds: A branch of mathematics that deals with the properties and relations of information manifolds, which are smooth manifolds that are also equipped with information geometry structures, a way to study probability distributions and statistical models and the manipulation of these properties and relations to solve geometric problems.
Geometry of Integrable Systems: A branch of mathematics that deals with the properties and relations of integrable systems, which are systems that can be solved using the methods of algebraic geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Kähler Manifolds: A branch of mathematics that deals with the properties and relations of Kähler manifolds, which are complex manifolds that are also equipped with a Kähler metric, a way to measure distance and angles, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Kinematic Manifolds: A branch of mathematics that deals with the properties and relations of kinematic manifolds, which are smooth manifolds that are also equipped with kinematic structures, a way to study the motion of mechanical systems and the manipulation of these properties and relations to solve geometric problems.
Geometry of Lie groups: A branch of mathematics that deals with the properties and relations of Lie groups, which are smooth manifolds that are also groups under a smooth binary operation.
Geometry of Moduli Spaces: A branch of mathematics that deals with the properties and relations of moduli spaces, which are spaces that parametrize certain classes of geometric objects, such as Riemann surfaces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Non-Euclidean Geometry: A branch of mathematics that deals with the properties and relations of non-Euclidean geometry, which is the study of geometries that differ from Euclidean geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Octonionic Manifolds: A branch of mathematics that deals with the properties and relations of octonionic manifolds, which are smooth manifolds that are also octonionic spaces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Optimal Transport: A branch of mathematics that deals with the properties and relations of optimal transport, which is the study of finding the most efficient way to move mass from one place to another using tools from geometry and partial differential equations and the manipulation of these properties and relations to solve geometric problems.
Geometry of Orbifolds: A branch of mathematics that deals with the properties and relations of orbifolds, which are generalizations of smooth manifolds that allow for singularities, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Principal Bundles: A branch of mathematics that deals with the properties and relations of principal bundles, which are geometric structures that “glue” together different spaces under the action of a group, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Projective Manifolds: A branch of mathematics that deals with the properties and relations of projective manifolds, which are smooth manifolds that are also projective spaces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Quantum Field Theory: A branch of mathematics that deals with the properties and relations of quantum field theory, which is the study of quantum systems and the manipulation of these properties and relations to solve geometric problems.
Geometry of Quantum Manifolds: A branch of mathematics that deals with the properties and relations of quantum manifolds, which are smooth manifolds that are also equipped with quantum structures, a way to study quantum systems and the manipulation of these properties and relations to solve geometric problems.
Geometry of Quaternionic Manifolds: A branch of mathematics that deals with the properties and relations of quaternionic manifolds, which are smooth manifolds that are also quaternionic spaces, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Quotients: A branch of mathematics that deals with the properties and relations of quotients, which are spaces that are formed by “gluing” together different spaces under certain equivalence relations, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Representations: A branch of mathematics that deals with the properties and relations of representations, which are ways of representing geometric objects, such as groups and Lie algebras, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Schemes: A branch of mathematics that deals with the properties and relations of schemes, which are generalizations of algebraic varieties that include data such as multiplicities and the manipulation of these properties and relations to solve geometric problems.
Geometry of Shape Analysis: A branch of mathematics that deals with the properties and relations of shapes, which is the study of geometric properties of shapes using tools from Riemannian geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Shape Matching: A branch of mathematics that deals with the properties and relations of shape matching, which is the study of matching and comparing shapes using tools from Riemannian geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Shape Optimization: A branch of mathematics that deals with the properties and relations of shapes optimization, which is the study of optimizing geometric properties of shapes using tools from Riemannian geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Shape Registration: A branch of mathematics that deals with the properties and relations of shape registration, which is the study of aligning and registering shapes using tools from Riemannian geometry and the manipulation of these properties and relations to solve geometric problems.
Geometry of Submanifolds: A branch of mathematics that deals with the properties and relations of submanifolds, which are subsets of a given manifold that have additional structure, such as being a subgroup or subalgebra.
Geometry of Symmetric Spaces: A branch of mathematics that deals with the properties and relations of symmetric spaces, which are homogeneous spaces that possess a certain type of symmetry, and the manipulation of these properties and relations to solve geometric problems.
Geometry of Thermodynamic Manifolds: A branch of mathematics that deals with the properties and relations of thermodynamic manifolds, which are smooth manifolds that are also equipped with thermodynamic structures, a way to study thermodynamic systems and the manipulation of these properties and relations to solve geometric problems.
Geometry of Variational Problems: A branch of mathematics that deals with the properties and relations of variational problems, which is the study of finding extrema of functionals, or functions of functions, using tools from calculus of variations and the manipulation of these properties and relations to solve geometric problems.
Geometry of Weyl Manifolds: A branch of mathematics that deals with the properties and relations of Weyl manifolds, which are smooth manifolds that are also equipped with a Weyl connection, a way to measure parallel transport, and the manipulation of these properties and relations to solve geometric problems.
Hyperbolic Geometry: A branch of non-Euclidean geometry that deals with the properties and relations of points, lines, angles, surfaces, and solids in a hyperbolic space, where the sum of the angles in a triangle is less than 180 degrees.
Integral Geometry: A branch of mathematics that deals with the properties and relations of geometric objects, such as sets and measures, using integral calculus and the manipulation of these properties and relations to solve geometric problems.
Line segment: A part of a line with two endpoints
Line: A straight path that extends infinitely in both directions
Median: A line segment that connects the midpoint of a side of a triangle to the opposite vertex.
Metric Geometry: A branch of mathematics that deals with the properties and relations of points, lines, angles, surfaces, and solids using a metric, which is a way to measure distance between points in a space.
Non-Euclidean Geometry: A branch of mathematics that deals with the properties and relations of points, lines, angles, surfaces and solids that do not necessarily satisfy Euclid’s postulates.
Parallel: Two lines or segments that are the same distance apart and never intersect
Perimeter: The distance around the outside of a shape
Perpendicular: Two lines or segments that form a right angle
Point: A location in space with no size or shape
Polygon: A closed figure made up of straight line segments
Projective Geometry: A branch of mathematics that deals with the properties and relations of points, lines, angles, surfaces, and solids using the principles of projection. It also involves the study of cross-ratios and duality, and the manipulation of these concepts to solve geometric problems.
Pythagorean Theorem: A theorem that states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Quadrilateral: A polygon with four sides and four angles
Radius: A line segment that connects the center of a circle to any point on the circumference
Ray: A part of a line that starts at one endpoint and extends infinitely in one direction
Riemannian Geometry: A branch of mathematics that deals with the properties and relations of points, lines, angles, surfaces and solids in a Riemannian manifold, a type of non-Euclidean space.
Riemannian Geometry: A branch of mathematics that deals with the properties and relations of Riemannian manifolds, which are smooth manifolds equipped with a Riemannian metric to measure distance and angles.
Similar: Two shapes that have the same shape but not necessarily the same size
Similarity: Two shapes are similar when they have the same shape but not necessarily the same size.
Spherical Geometry: A branch of non-Euclidean geometry that deals with the properties and relations of points, lines, angles, surfaces, and solids on a sphere, where the sum of the angles in a triangle is greater than 180 degrees.
Surface Area: The total area of the surface of a 3D shape.
Symmetry: A shape is symmetrical when there is a line of symmetry or a point of symmetry
Symplectic Geometry: A branch of mathematics that deals with the properties and relations of symplectic manifolds, which are smooth manifolds that are equipped with a symplectic form, a certain type of closed, non-degenerate 2-form.
Tensor Analysis: A branch of mathematics that deals with the properties and relations of geometric objects using tensors, which are multi-dimensional arrays of numbers, and the manipulation of these tensors to solve geometric problems.
Topology: A branch of mathematics that deals with the properties and relations of points, lines, angles, surfaces, and solids that remain unchanged under certain transformations, such as stretching or bending.
Transformation: A change in a shape’s position, size, or orientation.
Triangle: A polygon with three sides and three angles
Volume: The amount of space inside a 3D shape.

This list is not exhaustive, and new branches or variations of geometry are constantly being developed and studied, as the field of mathematics is constantly evolving.

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