The clothoid: a historical, literary and artistic introduction with applications to technology

In this work, we trace the history of the clothoid curve, a peculiar spiral with several technological applications. Starting from the bibliographic research by Levien, we deepen its history, focusing our attention on Cesáro's and Markov's studies of the curve. We also investigate the use of clothoids in modern times, highlighting its extension into three dimensions. Finally, we focus on the significance of the computation of the Fresnel integrals, which proved to be key for overcoming the historical bottleneck and paving the way for its practical use in applications.