Differential geometry (nonfiction): Difference between revisions
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[[File:Hyperbolic_triangle.svg|thumb|A triangle immersed in a saddle-shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines.]]'''Differential geometry''' is a [[Mathematics|mathematical]] discipline that uses the techniques of [[Differential calculus (nonfiction)|differential calculus]], [[Integral (nonfiction)|integral calculus]], [[Linear algebra (nonfiction)|linear algebra]], and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. | [[File:Hyperbolic_triangle.svg|thumb|A triangle immersed in a saddle-shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines.]]'''Differential geometry''' is a [[Mathematics|mathematical]] discipline that uses the techniques of [[Differential calculus (nonfiction)|differential calculus]], [[Integral (nonfiction)|integral calculus]], [[Linear algebra (nonfiction)|linear algebra]], and [[Multilinear algebra (nonfiction)|multilinear algebra]] to study problems in [[Geometry (nonfiction)|geometry]]. The [[Differential geometry of curves (nonfiction)|theory of plane and space curves]] and [[Differential geometry of surfaces (nonfiction)|surfaces]] in the three-dimensional [[Euclidean space (nonfiction)|Euclidean space]] formed the basis for development of differential geometry during the 18th century and the 19th century. | ||
Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds. Differential geometry is closely related to differential topology and the geometric aspects of the theory of differential equations. The differential geometry of surfaces captures many of the key ideas and techniques endemic to this field. | Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds. Differential geometry is closely related to differential topology and the geometric aspects of the theory of differential equations. The differential geometry of surfaces captures many of the key ideas and techniques endemic to this field. | ||
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* [[Differential calculus (nonfiction)]] | * [[Differential calculus (nonfiction)]] | ||
* [[Differential geometry of curves (nonfiction)]] | |||
* [[Differential geometry of surfaces (nonfiction)]] | |||
* [[Euclidean space (nonfiction)]] | |||
* [[Integral (nonfiction)]] | * [[Integral (nonfiction)]] | ||
* [[Linear algebra (nonfiction)]] | * [[Linear algebra (nonfiction)]] | ||
Revision as of 15:57, 29 December 2018
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra, and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century.
Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds. Differential geometry is closely related to differential topology and the geometric aspects of the theory of differential equations. The differential geometry of surfaces captures many of the key ideas and techniques endemic to this field.
In the News
Fiction cross-reference
Nonfiction cross-reference
- Differential calculus (nonfiction)
- Differential geometry of curves (nonfiction)
- Differential geometry of surfaces (nonfiction)
- Euclidean space (nonfiction)
- Integral (nonfiction)
- Linear algebra (nonfiction)
- Mathematics (nonfiction)
External links:
- Differential geometry @ Wikipedia