Plane and Solid Analytic Geometry.

On the Relationship between plane and solid Geometry

Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and...

Plane Curves and Contact Geometry

We apply contact homology to obtain new results in the problem of distinguishing immersed plane curves without dangerous selftangencies.

Fuzzy plane geometry: triangles

A fuzzy triangle T (with a discrete-valued membership function) can be regarded as a nest of parallel-sided triangles T i with successively higher membership values. Such a nest is determined by its max projections on any two of its \sides". The area (perimeter) of T is a weighted sum of the areas (perimeters) of the T i 's. The side lengths and altitudes of T can also be deened as weighted sum...

Formalizing Complex Plane Geometry

Deep connections between complex numbers and geometry had been well known and carefully studied centuries ago. Fundamental objects that are investigated are the complex plane (usually extended by a single infinite point), its objects (points, lines and circles), and groups of transformations that act on them (e.g., inversions and Möbius transformations). In this paper we treat the geometry of c...

Analytic Center Cutting-Plane Method