Significant progress has been accomplished during the past decades about geometric
constraint solving, in particular thanks to its applications in industrial fields like CAD and …

We investigate how projective plane geometry can be formalized in a proof assistant such as
Coq. Such a formalization increases the reliability of textbook proofs whose details and …

In this paper we consider geometrical construction problems and their role in mathematical
education. Owing to the main features of construction problems (accuracy in making …

This paper presents some important issues and potential research tracks for Geometric
Constraint Solving: the use of the simplicial Bernstein base to reduce the wrapping effect in …

Formalizing geometry theorems in a proof assistant like Coq is challenging. As emphasized
in the literature, the non-degeneracy conditions leads to technical proofs. In addition, when …

Over the last sixty years, a number of methods for automated theorem proving in geometry,
especially Euclidean geometry, have been developed. Almost all of them focus on …

In the area of Computer Aided Design (CAD), the main feature of geometric constraint
systems lies in their invariance under the direct isometry group. Several researchers have …

Robust computations have been haunting CAD system builders for decades. The common
belief among researchers is that the source of the problem lies in rounded arithmetic and …

Over the last sixty years, a number of methods for automated theorem proving in geometry,
especially Euclidean geometry, have been developed. Almost all of them focus on …

Accounting for geometric variability in mechanical assemblies is a key component of modern
design methodologies. This paper presents a framework for worst case analysis of the …