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e. Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2] Geometry is, along with arithmetic, one of the ...
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ( arithmetic ). Classic geometry was focused in compass and straightedge constructions.
In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it. Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two- dimensional surface of a sphere [a] or the n -dimensional surface of higher dimensional spheres .
Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint.
Information geometry. Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. [1] It studies statistical manifolds, which are Riemannian manifolds whose points correspond to probability distributions .
In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection.
e. Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity.
Geometry. Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally, this has meant using only the first four of Euclid's postulates. [1] The term was introduced by János Bolyai in 1832. [2]