Geometry
Geometry is a branch of mathematics that deals with shapes, sizes, positions, and dimensions of objects. It studies properties of points, lines, angles, surfaces, and solids, and explores relationships between them. Geometry can be divided into various subfields, including Euclidean geometry, analytic geometry, differential geometry, and topology, each with its own set of tools and techniques for understanding spatial relationships. Euclidean geometry is based on the principles established by the ancient Greek mathematician Euclid and deals with flat surfaces and shapes in two dimensions. It involves proving theorems about points, lines, circles, triangles, and other polygons using a set of axioms or self-evident truths. Analytic geometry, also known as coordinate geometry, is the study of geometry using algebraic methods. It involves representing geometric shapes and relationships in terms of coordinates and equations in a Cartesian plane. This allows for the manipulation and analysis of geometric objects using algebraic techniques. Differential geometry is a branch of mathematics that uses calculus to study the properties and behavior of curves, surfaces, and other geometric objects. It deals with concepts such as curvature, tangent spaces, and differential forms, and is used in fields such as physics, engineering, and computer graphics. Topology is a branch of mathematics that studies the properties of geometric objects that are preserved under continuous deformations, such as stretching, bending, and twisting, but not tearing or gluing. It deals with concepts such as connectedness, compactness, and continuity, and is used in fields such as geometry, analysis, and algebra. Overall, geometry is a fundamental discipline that provides the tools and techniques for understanding and analyzing spatial relationships in various contexts. Its applications range from architecture and design to physics and engineering, making it a crucial area of study in mathematics and related fields.
External Links
- [geometryfactory.com] GeometryFactory | points, triangles, and more
- [GeometryGames.org] Topology and Geometry
- [geometryexpressions.com]
- [FractalGeometry.com] Welcome fractalgeometry.com - Hostmonster.com
- [ArchitecturalGeometry.org] Architectural Geometry - Architekturgeometrie
- [geometry101.com] Geometry Geometry 101
- [geometrydashlites.com] --
- [architecturalgeometry.at] www.geometrie.tuwien.ac.at
- [circulargeometry.net] CircularGeometry
- [Tilings.org] Tilings, Geometry and Automorphisms of Surfaces | Tilings, Automorphisms, Hyperbolic Geometry and Computational Group Theory
- [isgg.net] International Society for Geometry and Graphics (ISGG) | ISGG – International Society for Geometry and Graphics
- [aag2020.com] Architecture | Architectural Geometry Conference | Champs-sur-Marne
- [jmap.org] JMAP HOME - Free resources for Algebra I, Geometry, Algebra II, Precalculus, Calculus - worksheets, answers, lesson plans
- [ka-gold-jewelry.com] Ka Gold Jewelry - Authentic Sacred Geometry Jewelry and Talismans
- [walktheplanck.wordpress.com] Walk the Planck! | To Planck or Not To Planck, Is That The Question? A research project about an integrated Universe View for the National Science Fair, began in a high school geometry class in River Ridge, Louisiana.
- [AvantGardeArchitecture.com] Avant-garde architecture | Elevating geometry, envisioning future
- [MusicalForms.com] Musical Forms | Music and Geometry
- [0fps.net] 0 FPS – Mostly geometry
- [geup.net] GEUP.net: geometry software for math, science, engineering
- [cornellmath.wordpress.com] The Everything Seminar | Geometry, Topology, Categories, Groups, Physics, . . . Everything
- [1728.org] CALCULATOR CITY: Resource for Mathematics,Algebra, Geometry, Trigonometry, Calculus, Finance, Measurement, Chemistry, Physics, Astronomy
- [cgal.org] The Computational Geometry Algorithms Library
- [mehm.net] Geometry saves the Earth!
- [doublings.wordpress.com] Big Board - little universe | Start at the Planck Length, multiply by 2, and each result by 2, include all vertices and emergent geometries, until you are out to the Observable or Known Universe.