Ad Meskens - Böcker

In this book the author presents a comprehensive study of Diophantos’ monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail.

In this book the author presents a comprehensive study of Diophantos’ monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. Its author, Diophantos, is an enigmatic figure of whom we know virtually nothing.Starting with Egyptian, Babylonian and early Greek mathematics the author paints a picture of the sources the Arithmetika may have had. Life in Alexandria, where Diophantos lived, is described and, on the basis of the limited available evidence, his biography is outlined.Of Arithmetika’s 13 books only 6 survive in Greek. It was not until 1971 that these were complemented by the discovery of 4 other books in an Arab translation. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail. Furthermore it is shown that Diophantos had a remarkable skill to solve higher degree equations.In the second part, the author draws our attention to the survival of Diophantos’ work in both Arab and European mathematical cultures. Once Xylander’s critical 1575 edition reached its European public, the fame of the Arithmetika grew. It was studied, translated and modified by such authors as Bombelli, Stevin and Viète. It reached its pinnacle of fame in 1621 with the publication of Bachet’s translation into Latin. The marginal notes by Fermat in his copy of Diophantos, including his famous “Last Theorem”, were the starting point of a whole new research subject: the theory of numbers.

In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software (IGS). The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of IGS the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves.By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those students who are thinking of becoming a mathematics teacher and for mathematics teachers.

Describes the development and the ultimate demise of the practice of mathematics in sixteenth century Antwerp. Against the background of the violent history of the Religious Wars the story of the practice of mathematics in Antwerp is told through the lives of two protagonists Michiel Coignet and Peeter Heyns. The book touches on all aspects of practical mathematics from teaching  and instrument making to the practice of building fortifications of the practice of navigation.​