Axiomatic Thinking Ferreira

Singer, guitarist, composer, arranger and music producer, Sid Ferreira in his fourth album "Kinda Brazilian Jazz" mixes Brazilian musical genres such as samba, samba-rock, marcha-rancho, choro and bossa nova, to various genres of Latin American music such as rumba, salsa, ballad, jazz, cumbia, waltz, bolero, fado, flamenco and chachacha, making clear his diverse influences in authorial songs and partnerships in English and Portuguese.

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia.

Focusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomatic geometry: Euclidean, non-Euclidean and projective. Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all, several parallels) has led to the emergence of mathematical theories based on an arbitrary system of axioms, an essential feature of contemporary mathematics.