Euclidean geometry in nLab
Tarski's axioms. Tarski's theory EPG (Elementary Plane [Euclidean] Geometry) is a one-sorted theory in classical first-order logic with equality ...
The concept of Euclidean space in analysis, topology, differential geometry and specifically Euclidean geometry, and physics is a fomalization in modern terms.
“geometric logic”) of (higher) functorial geometry famously including algebraic geometry or supergeometry but also more exotic variants such as ...
A Euclidean domain is an integral domain which admits a form of the Euclidean quotient-and-remainder algorithm familiar from school mathematics.
differential geometry · Lie group/algebraic group G G · subgroup (monomorphism) H ↪ G H \hookrightarrow G ; examples, Euclidean group Iso ( d ) ...
The real numbers constructible as lengths (or their negatives) via straightedge and compass from rational numbers. 3. See also. square root.
What non-categorical applications are there of homotopical algebra?
... geometric developments of Riemann, Klein and Lie have done for the down-to-earth study of Euclidean geometry. Your "classifying line bundles ...
Euclid (Εὐκλείδης) of Alexandria was the ancient author of the Elements, a treatise consisting of thirteen books covering plane and solid geometry.
Advantages of diffeological spaces over general sheaves
... nlab/show/… for ... The examples are numerous: from Euclidean geometry to projective geometry via spheric or hyperbolic geometry and so on.
Is nLab a good source? : r/math - Reddit
I am learning category theory from Tom Leinster's "Basic Category Theory" (Cambridge University Press, 2014) and have stumbled across nLab while supplementing ...
Non-Euclidean geometry in nLab
Generally, geometry which is not Euclidean geometry. Specifically hyperbolic geometry and elliptic geometry violating the parallel postulate. 2.
nLab -- General Discussion | The n-Category Café - Welcome
But we are not planning to have an nLab page for every math paper in the world. ... Euclidean spaces, considered as probes for smooth sets.).
Confusion about nLab's definition of smooth ∞-groupoid
This nLab page defines (in Definition 2.6) a smooth ∞-groupoid as an (∞,1)-sheaf on the (∞,1)-category C=CartSpsmooth whose objects are ...
Equivalent definitions of mathematical structures - Wikipedia
First, within a particular mathematical theory (for example, Euclidean geometry), a notion (for example, ellipse or minimal surface) may have more than one ...
Some schools concentrated on the axiomatic construction of geometry, independent from the tools which were offered by the models with concrete ...
Michael Listrom on LinkedIn: nLab symplectic geometry
A wider branch including symplectic geometry is Poisson geometry and a sister branch in odd dimensions is contact geometry. A special and ...
Michael Listrom on LinkedIn: nLab multisymplectic geometry
A one-to-one continuously-differentiable mapping f:M→N of a differentiable manifold M( e.g. of a domain in a Euclidean space) into a ...
A Dual for Set? | The n-Category Café - Welcome
... Euclidean, and believed in the objective truth of Euclidean geometry. ... I added this to nlab:cocomplete well-pointed topos. Posted by ...
An Essay on the Foundations of Geometry in nLab
In metrical Geometry, on the contrary, we found an empirical element arising out of the alternatives of Euclidean and non-Euclidean space. … In ...
Every simplicial set gives rise to a "nice" topological space, known as its geometric realization. This realization consists of geometric simplices, glued ...
Analytic geometry
Field of studyIn 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.
Differential geometry
DisciplineDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension.
Projective geometry
Field of studyIn mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
Elliptic geometry
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect.