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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]
Mathematical visualization is used throughout mathematics, particularly in the fields of geometry and analysis. Notable examples include plane curves , space curves , polyhedra , ordinary differential equations , partial differential equations (particularly numerical solutions, as in fluid dynamics or minimal surfaces such as soap films ...
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes.The shapes studied in geometric modeling are mostly two- or three-dimensional (solid figures), although many of its tools and principles can be applied to sets of any finite dimension.
Artists have used mathematics since the 4th century BC when the Greek sculptor Polykleitos wrote his Canon, prescribing proportions conjectured to have been based on the ratio 1: √ 2 for the ideal male nude. Persistent popular claims have been made for the use of the golden ratio in ancient art
Technology use can increase accuracy and speed of data collection and allow real-time visualization and experimentation. [14] It also supports collaboration. [15] Computer tools may be intrinsically interesting and motivating to students, and provide a familiar and comforting context students already use in their daily life.
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry . Analytic geometry is used in physics and engineering , and also in aviation , rocketry , space science , and spaceflight .
Lipschitz maps are particularly important in metric geometry, since they provide more flexibility than distance-preserving maps, but still make essential use of the metric. [14] For example, a curve in a metric space is rectifiable (has finite length) if and only if it has a Lipschitz reparametrization.
The Brown University Division of Applied Mathematics is the oldest applied math program in the U.S. [18] [19] Schools with separate applied mathematics departments range from Brown University , which has a large Division of Applied Mathematics that offers degrees through the doctorate , to Santa Clara University , which offers only the M.S. in ...