Curso De Geometria Metrica Puig Adam 25.pdf
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Curso De Geometria Metrica Puig Adam 25.pdf: A Comprehensive Guide to Metric Geometry
If you are looking for a reliable and comprehensive source of information on metric geometry, you might want to check out Curso De Geometria Metrica Puig Adam 25.pdf. This is a PDF file that contains the first volume of the classic textbook on metric geometry by Pedro Puig Adam, a renowned Spanish mathematician and educator.
Metric geometry is a branch of geometry that studies spaces in which a distance between points is defined, and the transformations that preserve this distance. Metric geometry has applications in many fields of mathematics, physics, engineering, computer science, and more.
Curso De Geometria Metrica Puig Adam 25.pdf covers the basic concepts and properties of metric spaces, such as distance, congruence, similarity, angles, triangles, circles, polygons, and polyhedra. It also introduces some advanced topics, such as non-Euclidean geometries, affine geometry, projective geometry, and differential geometry.
The book is written in a clear and rigorous style, with plenty of examples, exercises, and illustrations. It is suitable for students and teachers of geometry at various levels of education, as well as for anyone who wants to learn more about this fascinating subject.
You can download Curso De Geometria Metrica Puig Adam 25.pdf for free from Academia.edu[^1^], a platform for academics to share research papers. You will need to sign up with your email address to access the file. Alternatively, you can also find other sources of the book online by searching for its title on Bing.
Curso De Geometria Metrica Puig Adam 25.pdf is a valuable resource for anyone interested in metric geometry. It will help you understand the foundations and applications of this important branch of mathematics. Don't miss this opportunity to learn from one of the best experts in the field!
What is Metric Geometry
Metric geometry is a subfield of geometry that deals with spaces that have a notion of distance between points. A distance function, also called a metric, is a rule that assigns a non-negative real number to any pair of points in a space, such that the following properties hold:
The distance between two points is zero if and only if they are the same point.
The distance between two points is the same regardless of the order in which they are given.
The distance between two points does not exceed the sum of the distances between them and any third point. This is known as the triangle inequality.
A space that has a distance function is called a metric space. Examples of metric spaces include the Euclidean plane, the surface of a sphere, and the set of real numbers with the usual absolute value.
Metric geometry studies the properties and structures of metric spaces and the maps between them that preserve distances. These maps are called isometries or congruences. For example, translations, rotations, reflections, and scaling are isometries in the Euclidean plane.
Metric geometry also explores how different metrics can give rise to different geometries on the same space. For instance, on the surface of a sphere, there are at least three natural metrics: the Euclidean metric inherited from the three-dimensional space, the spherical metric based on the central angle between points, and the hyperbolic metric based on the logarithm of the cross-ratio of four points. Each of these metrics induces a different geometry with different properties and applications. ec8f644aee