A Brief Journey from Euclidean to Smarandachean Geometry

The aim of this book is straightforward: to illustrate the true essence of geometry and justify the necessity for the existence of Smarandache geometry. This goal is accomplished by narrating the history of this mathematical field from its origins, akin to a captivating tale featuring characters fixated on depicting spatial forms throughout millennia. The mathematicians portrayed in this narrative exemplify that talent is not solely an intellectual attribute but also demands audacity for transcendence. The first chapter summarizes the book's content, aiming to captivate the reader. The second chapter covers Euclidean Geometry, while the third chapter explores hyperbolic and elliptical geometries, as well as Taxicab and finite geometries. Chapter 4 delves into Smarandache geometries and NeutroGeometries, presenting known and new models. Lastly, the Appendix provides access to Julia language code utilized for generating three-dimensional figures showcased in the book, with the intention of inspiring adept readers to develop software enabling exploration of these spaces virtually. It is hoped that this narrative will engross readers and leave them eager for more at its conclusion.