Tag: Euclidean

Free Download Problem-Solving and Selected Topics in Euclidean Geometry: In the Spirit of the Mathematical Olympiads By Sotirios E. Louridas, Michael Th. Rassias (auth.)
2013 | 235 Pages | ISBN: 1461472725 | PDF | 3 MB
"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO’s are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.

Free Download A. C. Paseau, "The Euclidean Programme "
English | ISBN: 1009494406 | 2024 | 75 pages | PDF | 2 MB
The Euclidean Programme embodies a traditional sort of epistemological foundationalism, according to which knowledge – especially mathematical knowledge – is obtained by deduction from self-evident axioms or first principles. Epistemologists have examined foundationalism extensively, but neglected its historically dominant Euclidean form. By contrast, this book offers a detailed examination of Euclidean foundationalism, which, following Lakatos, the authors call the Euclidean Programme. The book rationally reconstructs the programme’s key principles, showing it to be an epistemological interpretation of the axiomatic method. It then compares the reconstructed programme with select historical sources: Euclid’s Elements, Aristotle’s Posterior Analytics, Descartes’s Discourse on Method, Pascal’s On the Geometric Mind and a twentieth-century account of axiomatisation. The second half of the book philosophically assesses the programme, exploring whether various areas of contemporary mathematics conform to it. The book concludes by outlining a replacement for the Euclidean Programme.

Free Download Analysis in Euclidean Space (578 Pages)
by Joaquim Bruna
English | 2023 | ISBN: 1800611714 | 579 pages | True PDF | 13.52 MB