This is a text in basic mathematics with multiple uses for either high school or college level courses. The subject matter is clearly covered and the author develops concepts so the reader can see how one subject matter can relate and grow into another.
The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory;
Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of integers of a number field.
From the reviews: "A prominent research mathematician and a high school teacher have combined their efforts in order to produce a high school geometry course.