distances

Measuring lengths is one of the oldest human activities. This task is concretely based on mathematics, in particular on many results of geometry, so powerful that they have spread to all sciences: today, one can measure anything... or almost, and even in several ways! Geographic distance can be Euclidean or spherical, the gap between two numbers can be measured by their difference or their 'p-adic distance'. The notion of distance can apply, more surprisingly, to deviations from the mean of a statistical series, to linguistic proximity between words, to ways of connecting two cities (with many units such as kilometers covered, hours spent in a vehicle, energy cost...). But the formal notion of distance, even if it took centuries to emerge, is also an intuitive and accessible concept, leading to many visual puzzles, present in this book.
The dossiers
• Surveying and measuring • At the heart of geometry • Various metrics • Distances to solve problems