AccueilGroupesDiscussionsPlusTendances
Site de recherche
Ce site utilise des cookies pour fournir nos services, optimiser les performances, pour les analyses, et (si vous n'êtes pas connecté) pour les publicités. En utilisant Librarything, vous reconnaissez avoir lu et compris nos conditions générales d'utilisation et de services. Votre utilisation du site et de ses services vaut acceptation de ces conditions et termes.

Résultats trouvés sur Google Books

Cliquer sur une vignette pour aller sur Google Books.

Chargement...

Geometry and the imagination (1952)

par David Hilbert

Autres auteurs: Voir la section autres auteur(e)s.

MembresCritiquesPopularitéÉvaluation moyenneMentions
158Aucun175,234 (4.13)1
This remarkable book endures as a true masterpiece of mathematical exposition. The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. Geometry and the Imagination is full of interesting facts, many of which you wish you had known before. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $mathbb{{R}}^3$. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $pi/4 = 1 - 1/3 + 1/5 - 1/7 + - ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is ``Projective Configurations''. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the pantheon of great mathematics books.… (plus d'informations)
Aucun
Chargement...

Inscrivez-vous à LibraryThing pour découvrir si vous aimerez ce livre

Actuellement, il n'y a pas de discussions au sujet de ce livre.

» Voir aussi la mention 1

Aucune critique
aucune critique | ajouter une critique

» Ajouter d'autres auteur(e)s

Nom de l'auteurRôleType d'auteurŒuvre ?Statut
David Hilbertauteur principaltoutes les éditionscalculé
Nemenyi, P.Traducteurauteur secondairequelques éditionsconfirmé
Vous devez vous identifier pour modifier le Partage des connaissances.
Pour plus d'aide, voir la page Aide sur le Partage des connaissances [en anglais].
Titre canonique
Informations provenant du Partage des connaissances anglais. Modifiez pour passer à votre langue.
Titre original
Titres alternatifs
Date de première publication
Personnes ou personnages
Lieux importants
Évènements importants
Films connexes
Épigraphe
Dédicace
Premiers mots
Citations
Derniers mots
Notice de désambigüisation
Directeur de publication
Courtes éloges de critiques
Langue d'origine
DDC/MDS canonique
LCC canonique
This remarkable book endures as a true masterpiece of mathematical exposition. The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. Geometry and the Imagination is full of interesting facts, many of which you wish you had known before. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $mathbb{{R}}^3$. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $pi/4 = 1 - 1/3 + 1/5 - 1/7 + - ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is ``Projective Configurations''. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the pantheon of great mathematics books.

Aucune description trouvée dans une bibliothèque

Description du livre
Résumé sous forme de haïku

Discussion en cours

Aucun

Couvertures populaires

Vos raccourcis

Évaluation

Moyenne: (4.13)
0.5
1
1.5
2
2.5
3 2
3.5
4 3
4.5
5 3

Est-ce vous ?

Devenez un(e) auteur LibraryThing.

 

À propos | Contact | LibraryThing.com | Respect de la vie privée et règles d'utilisation | Aide/FAQ | Blog | Boutique | APIs | TinyCat | Bibliothèques historiques | Critiques en avant-première | Partage des connaissances | 207,147,527 livres! | Barre supérieure: Toujours visible