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What (who) is quotient geometry - definition

EXPRESSION IN CALCULUS

Newton's quotient; Newton's difference quotient; Difference Quotient; Newton quotient; Fermat's difference quotient

Quotient space (linear algebra)

VECTOR SPACE CONSISTING OF AFFINE SUBSETS

Linear quotient space; Quotient vector space

In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by "collapsing" N to zero. The space obtained is called a quotient space and is denoted V/N (read "V mod N" or "V by N").

https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra)

Synthetic geometry

STUDY OF GEOMETRY WITHOUT THE USE OF COORDINATES OR FORMULAS.

Synthetical geometry; Computational synthetic geometry; Pure geometry; Synthetic proof

Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is the study of geometry without the use of coordinates or formulae. It relies on the axiomatic method and the tools directly related to them, that is, compass and straightedge, to draw conclusions and solve problems.

https://en.wikipedia.org/wiki/Synthetic_geometry

Arithmetic geometry

BRANCH OF ALGEBRAIC GEOMETRY FOCUSED ON PROBLEMS IN NUMBER THEORY

Arithmetical algebraic geometry; Arithmetic Geometry; Arithmetic algebraic geometry; Arithmetic Algebraic Geometry

In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.

https://en.wikipedia.org/wiki/Arithmetic_geometry

Wikipedia

Difference quotient

In single-variable calculus, the difference quotient is usually the name for the expression

{\frac {f(x+h)-f(x)}{h}}

which when taken to the limit as h approaches 0 gives the derivative of the function f. The name of the expression stems from the fact that it is the quotient of the difference of values of the function by the difference of the corresponding values of its argument (the latter is (x + h) - x = h in this case). The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h).^: 237 The limit of the difference quotient (i.e., the derivative) is thus the instantaneous rate of change.

By a slight change in notation (and viewpoint), for an interval [a, b], the difference quotient

{\frac {f(b)-f(a)}{b-a}}

is called the mean (or average) value of the derivative of f over the interval [a, b]. This name is justified by the mean value theorem, which states that for a differentiable function f, its derivative f′ reaches its mean value at some point in the interval. Geometrically, this difference quotient measures the slope of the secant line passing through the points with coordinates (a, f(a)) and (b, f(b)).

Difference quotients are used as approximations in numerical differentiation, but they have also been subject of criticism in this application.

Difference quotients may also find relevance in applications involving Time discretization, where the width of the time step is used for the value of h.

The difference quotient is sometimes also called the Newton quotient (after Isaac Newton) or Fermat's difference quotient (after Pierre de Fermat).

https://en.wikipedia.org/wiki/Difference quotient