Real algebraic geometry

quantity along a continuous line

the absence of infinitesimals in a mathematical system

{| class="wikitable" style="margin-left:1em" align="right" |- |50px |50px |50px |50px |50px |50px |- | colspan="6" | A polyhedron is a 3-dimensional polytope |} thumb|400px|right|A polygon is a 2-dimensional polytope. Polygons can be characterised according to various criteria. Some examples are: open (excluding its boundary), bounding circuit only (ignoring its interior), closed (including both its boundary and its interior), and self-intersecting with varying densities of different regions.

homogeneous polynomial of degree two in a number of variables

field together with a total ordering of its elements such that the set of positive elements is translation-invariant and multiplicatively closed

Count of the roots of a polynomial in an interval, without computing them

ring with a compatible total order

On topology of algebraic curves and surfaces

When are rational functions sums of quotients of squares

subfield of convex optimization

trying to map moments to a measure that generates them

mathematical algorithm for eliminating variables from a system of linear inequalities

subset of n-space defined by a finite sequence of polynomial equations and inequalities

number of connected components an algebraic curve can have

upper bound and parity of the number of real roots of a polynomial in an interval