The Handbook of Geometric Constraint Systems Principles is an entry point to the currently
used principal mathematical and computational tools and techniques of the geometric …

An important development in geometric algebra in recent years is the new system known as
point geometry, which treats points as direct objects of operations and considerably …

We used computer proof-checking methods to verify the correctness of our proofs of the
propositions in Euclid Book I. We used axioms as close as possible to those of Euclid, in a …

This paper describes the formalization of the arithmetization of Euclidean plane geometry in
the Coq proof assistant. As a basis for this work, Tarski's system of geometry was chosen for …

We compare the pencil/paper proofs and formal proof of two traditional proofs in high school
geometry. We highlight the fact that slightly different formulations or proofs can lead to …

In this paper, we report on the formalization of a synthetic proof of Pappus' theorem. We
provide two versions of the theorem: the first one is proved in neutral geometry (without …

In contrast to common automated theorem proving approaches, in which the search space is
a set of some formulae and what is sought is again a (goal) formula, we propose an …

We present an automatic theorem prover for projective incidence geometry. This prover
does not consider coordinates. Instead, it follows a combinatorial approach based on the …

This paper starts with a survey of what is known regarding an axiom, referred to as the
Lotschnittaxiom, stating that the perpendiculars to the sides of a right angle intersect …

In this paper, we describe the formal proof using the Coq proof assistant that Tarski's axioms
for plane neutral geometry (excluding continuity axioms) can be derived from the …