Local property in the context of "Two-dimensional"

In biochemistry, metabolic control analysis (MCA) is a mathematical framework for describingmetabolic, signaling, and genetic pathways. MCA quantifies how variables, such as fluxes and species concentrations, depend on network parameters.In particular, it is able to describe how network-dependent properties,called control coefficients, depend on local properties called elasticities or elasticity coefficients.

MCA was originally developed to describe the control in metabolic pathwaysbut was subsequently extended to describe signaling and genetic networks. MCA has sometimes also been referred to as Metabolic Control Theory, but this terminology was rather strongly opposed by Henrik Kacser, one of the founders.

In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the entire plane. It maps circles on the sphere to circles or lines on the plane, and is conformal, meaning that it preserves angles at which curves meet and thus locally approximately preserves shapes. It is neither isometric (distance preserving) nor equiareal (area preserving).

The stereographic projection gives a way to represent a sphere by a plane. The metric induced by the inverse stereographic projection from the plane to the sphere defines a geodesic distance between points in the plane equal to the spherical distance between the spherical points they represent. A two-dimensional coordinate system on the stereographic plane is an alternative setting for spherical analytic geometry instead of spherical polar coordinates or three-dimensional cartesian coordinates. This is the spherical analog of the Poincaré disk model of the hyperbolic plane.

A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional spaces are often called planes, or, more generally, surfaces. These include analogs to physical spaces, like flat planes, and curved surfaces like spheres, cylinders, and cones, which can be infinite or finite. Some two-dimensional mathematical spaces are not used to represent physical positions, like an affine plane or complex plane.