Related papers: GeoGebra Tools with Proof Capabilities
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
In our contribution we describe some on-going improvements concerning the Automated Reasoning Tools developed in GeoGebra Discovery, providing different examples of the performance of these new features. We describe the new ShowProof…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
We introduce a system of software tools that can automatically prove or discover geometric inequalities. The system, called GeoGebra Discovery, consisting of an extended version of GeoGebra, a controller web service realgeom, and the…
We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools. The project includes formal…
The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…
We describe a prototype of a new experimental GeoGebra command and tool, Discover, that analyzes geometric figures for salient patterns, properties, and theorems. This tool is a basic implementation of automated discovery in elementary…
We describe a prototype of a new experimental GeoGebra command and tool Discover that analyzes geometric figures for salient patterns, properties, and theorems. This tool is a basic implementation of automated discovery in elementary planar…
Understanding geometric relationships with little mathematical knowledge can be challenging for today's students and teachers. A new toolset is introduced that is able to create a proof without words by combining the benefits of the…
Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly…
Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…
Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous…
The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other…
This paper presents an intelligent tutoring system, GeoTutor, for Euclidean Geometry that is automatically able to synthesize proof problems and their respective solutions given a geometric figure together with a set of properties true of…
GeoGebra is an open source mathematics education software tool being used in thousands of schools worldwide. Since version 4.2 (December 2012) it supports symbolic computation of locus equations as a result of joint effort of mathematicians…
Comparison of geometric quantities usually means obtaining generally true equalities of different algebraic expressions of a given geometric figure. Today's technical possibilities already support symbolic proofs of a conjectured theorem,…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects.…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…