Spatial orientation, perception of objects’ shapes, and minimization of commuting distances are among the many geometry-based skills which we use on a daily basis. Plato’s academy admitted only students who were familiar with geometry, a science that calls into play philosophical topics but also delivers practical solutions for an array of technological issues. Geometry theorems have always helped us to turn challenging tasks – from straight lines to curved spaces – into easy ones. This book tells the story of how the human mind explores the shape of things and succumbs to its charm. The journey stretches from Euclid and elementary geometry to Riemann and contemporary theories, which provide physics with the tools for understanding the universe and developing a “theory of everything”.

Marco Andreatta teaches Geometry at the University of Trento, where he heads the Department of Mathematics and the International Centre for Mathematical Research.