Geometry in a sentence

A geometry constraint engine may also be employed to manage the associative relationships between geometry, such as wireframe geometry in a sketch or components in an assembly.

Carnap, R, An introduction to the philosophy of science, p. 148 Since Euclidean geometry is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.

Consequently, hyperbolic geometry is called Bolyai-Lobachevskian geometry, as both mathematicians, independent of each other, are the basic authors of non-Euclidean geometry.

Shafarevich, Basic Algebraic Geometry volume 2 (Schemes and Complex Manifolds), p. 5, section V.1 Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory.

The fourth angle of a Lambert quadrilateral is acute if the geometry is hyperbolic, a right angle if the geometry is Euclidean or obtuse if the geometry is elliptic.

The summit angles of a Saccheri quadrilateral are acute if the geometry is hyperbolic, right angles if the geometry is Euclidean and obtuse angles if the geometry is elliptic.

This insight had the corollary that non-Euclidean geometry was consistent if and only if Euclidean geometry was, putting Euclidean and non-Euclidean geometries on the same footing, and ending all controversy surrounding non-Euclidean geometry.

This result may also be stated as: the defect of triangles in hyperbolic geometry is positive, the defect of triangles in Euclidean geometry is zero, and the defect of triangles in elliptic geometry is negative.

With direct modeling once a sketch is used to create geometry the sketch is incorporated into the new geometry and the designer just modifies the geometry without needing the original sketch.

Although the first attempts at an axiomatisation of geometry appear in the Mohist canon in 330 BC, Liu Hui developed algebraic methods in geometry in the 3rd century AD and also calculated pi to 5 significant figures.

A notable exception to modern algebraic geometry texts following the conventions of this article is Commutative algebra with a view toward algebraic geometry / David Eisenbud (1995), which uses "h A " to mean the covariant hom-functor.

Another formal generalization is possible to Universal algebraic geometry in which every variety of algebras has its own algebraic geometry.

Arithmetic geometry, on the other hand, is a contemporary term for much the same domain as that covered by the term Diophantine geometry.

Ball, p. 485 Since non-Euclidean geometry is provably relatively consistent with Euclidean geometry, the parallel postulate cannot be proved from the other postulates.

Discovery of non-Euclidean geometry The beginning of the 19th century would finally witness decisive steps in the creation of non-Euclidean geometry.

Einstein's theory of general relativity shows that the true geometry of spacetime is not Euclidean geometry.

Euclidean geometry Euclid's construction for proof of the triangle inequality for plane geometry.

Geometry Computational geometry applies computer algorithms to representations of geometrical objects.

His influence has led to the current usage of the term "non-Euclidean geometry" to mean either "hyperbolic" or "elliptic" geometry.

Hyperbolic geometry is the most prevalent geometry in this picture and also the most complicated.