An artificial-intelligence (AI) tool can rigorously prove whether geometric facts — statements about two-dimensional shapes such as triangles or polygons — are true, just as well as competitors in the ...

This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and ...

ABSTRACT: While the use of three-dimensional (3D) geographical information system (GIS) is becoming in rapid development and being used in various fields such as urban and regional planning, disaster ...

ABSTRACT: Node localization is commonly employed in wireless networks. For example, it is used to improve routing and enhance security. Localization algorithms can be classified as range-free or range ...

J. R. Brown, Philosophy of mathematics: an introduction to the world of proofs and pictures, Routledge (1999). 2. R. B. Nelsen, Proofs without words I: exercises in ...

THE opening sentence of the Preface—“The author has attempted to bring together all the well-known theorems and examples connected with Harmonics, Anharmonics, Involution, Projection (including ...

The authors investigated how secondary mathematics teachers check student geometry proofs. From video records of geometry teachers checking proofs, they conjectured that teachers have different ...