In mathematics, synthetic differential geometry is a formalization of the theory of differential geometry in the language of topos theory. There are several...

Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic...

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...

mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus...

in the rational foundations of continuum physics and in the synthetic differential geometry that had evolved from the spatial part of Lawvere's categorical...

Cambridge University Press. ISBN 978-0-521-62401-5. Uses synthetic differential geometry and nilpotent infinitesimals. Boelkins, M. (2012). Active Calculus:...

This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics...

References Absolute differential calculus An older name of Ricci calculus Absolute geometry Also called neutral geometry, a synthetic geometry similar to Euclidean...

popular in algebraic geometry. Differentials in smooth models of set theory. This approach is known as synthetic differential geometry or smooth infinitesimal...

Synthetic-aperture radar (SAR) is a form of radar that is used to create two-dimensional images or three-dimensional reconstructions of objects, such...

geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry...

synthetic geometry. Another topic that developed from axiomatic studies of projective geometry is finite geometry. The topic of projective geometry is...

analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability...

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an...

methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc...

elastic deformations of solid objects. Euler formulated the partial differential equations for the motion of inviscid fluid, and laid the mathematical...

used in the initial development of calculus, and are used in synthetic differential geometry. Hyperreal numbers: The numbers used in non-standard analysis...

using the Exterior algebra of an n-dimensional vector space. Synthetic differential geometry or smooth infinitesimal analysis have roots in category theory...

Hence, it is a more primitive definition of the structure (see synthetic differential geometry). A final advantage of this approach is that it allows for...

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most...

inventor of "fluxions", roughly equivalent to the differentials of later versions of the differential calculus) as a genius while deriding his well-known...

In algebraic geometry and synthetic differential geometry, a Grothendieck connection is a way of viewing connections in terms of descent data from infinitesimal...

Ruppeiner geometry Solid geometry Spherical geometry Symplectic geometry Synthetic geometry Systolic geometry Taxicab geometry Toric geometry Transformation...

Geometria Recondita et analysi indivisibilium atque infinitorum" (On a hidden geometry and analysis of indivisibles and infinites), published in Acta Eruditorum...

vectors to a scheme. This allows notions from differential geometry to be imported into algebraic geometry. In detail: The ring of dual numbers may be thought...

In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical...

analysis. Complex geometry sits at the intersection of algebraic geometry, differential geometry, and complex analysis, and uses tools from all three areas...

Nonstandard analysis Nonstandard calculus Internal set theory Synthetic differential geometry Smooth infinitesimal analysis Constructive nonstandard analysis...

is not true. In the geometries where the concept of a line is a primitive notion, as may be the case in some synthetic geometries, other methods of determining...

parallelism of lines. Affine geometry can be developed in two ways that are essentially equivalent. In synthetic geometry, an affine space is a set of...