Ricerc@Sapienza

The history of the geometric thought evolution derives only in small part from direct written sources. A lot of news has come down to us for successive transcriptions, often reworked, or for random discoveries of autograph texts whose existence was unknown.
Many recent studies have shown that in the pre-Hellenistic period the knowledge of geometry was certainly greater than imagined until a few decades ago. Geometry was one of the main components of a multidisciplinary knowledge that also included arithmetic, music and astronomy, as well as grammar, rhetoric and dialectics.
For a long period, at least until the fifth century AD, there have been studies and discoveries that constitute, even today, the foundation of this scientific discipline and of mathematical knowledge in general.
In the spirit of research, summarized in this volume, here we want to retrace this wonderful journey studded with scientific discoveries with a specific focus on curved lines.
A parallel analysis is also proposed in the practical application of architecture (necessarily limited to a few but significant examples). If in fact, as mentioned, the written sources are few and often difficult to attribute, a significant help to the understanding of the geometric thought evolution can undoubtedly arrive analyzing the innumerable traces that architects and engineers of the time have left us in their formidable works.