The Erdos Distance Problem

Β· Β·
· Student Mathematical Library Книга 56 · American Mathematical Soc.
Π•Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
150
Π‘Ρ‚Ρ€Π°Π½ΠΈΡ†ΠΈ

Всичко Π·Π° Ρ‚Π°Π·ΠΈ Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°

The Erd s problem asks, What is the smallest possible number of distinct distances between points of a large finite subset of the Euclidean space in dimensions two and higher? The main goal of this book is to introduce the reader to the techniques, ideas, and consequences related to the Erd s problem. The authors introduce these concepts in a concrete and elementary way that allows a wide audience--from motivated high school students interested in mathematics to graduate students specializing in combinatorics and geometry--to absorb the content and appreciate its far-reaching implications. In the process, the reader is familiarized with a wide range of techniques from several areas of mathematics and can appreciate the power of the resulting symbiosis. The book is heavily problem oriented, following the authors' firm belief that most of the learning in mathematics is done by working through the exercises. Many of these problems are recently published results by mathematicians working in the area. The order of the exercises is designed both to reinforce the material presented in the text and, equally importantly, to entice the reader to leave all worldly concerns behind and launch head first into the multifaceted and rewarding world of Erd s combinatorics.
The Erd s problem asks, What is the smallest possible number of distinct distances between points of a large finite subset of the Euclidean space in dimensions two and higher? The main goal of this book is to introduce the reader to the techniques, ideas, and consequences related to the Erd s pro...

ΠžΡ‚ΠΊΡ€ΠΈΠΉΡ‚Π΅ ΠΎΡ‰Π΅

ΠžΡ†Π΅Π½Π΅Ρ‚Π΅ Ρ‚Π°Π·ΠΈ Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°

ΠšΠ°ΠΆΠ΅Ρ‚Π΅ Π½ΠΈ ΠΊΠ°ΠΊΠ²ΠΎ мислитС.

Π˜Π½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΡ Π·Π° Ρ‡Π΅Ρ‚Π΅Π½Π΅Ρ‚ΠΎ

Π‘ΠΌΠ°Ρ€Ρ‚Ρ„ΠΎΠ½ΠΈ ΠΈ Ρ‚Π°Π±Π»Π΅Ρ‚ΠΈ
Π˜Π½ΡΡ‚Π°Π»ΠΈΡ€Π°ΠΉΡ‚Π΅ ΠΏΡ€ΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅Ρ‚ΠΎ Google Play Книги Π·Π° Android ΠΈ iPad/iPhone. Π’ΠΎ Π°Π²Ρ‚ΠΎΠΌΠ°Ρ‚ΠΈΡ‡Π½ΠΎ сС синхронизира с ΠΏΡ€ΠΎΡ„ΠΈΠ»Π° Π²ΠΈ ΠΈ Π²ΠΈ позволява Π΄Π° Ρ‡Π΅Ρ‚Π΅Ρ‚Π΅ ΠΎΠ½Π»Π°ΠΉΠ½ ΠΈΠ»ΠΈ ΠΎΡ„Π»Π°ΠΉΠ½, ΠΊΡŠΠ΄Π΅Ρ‚ΠΎ ΠΈ Π΄Π° стС.
Π›Π°ΠΏΡ‚ΠΎΠΏΠΈ ΠΈ ΠΊΠΎΠΌΠΏΡŽΡ‚Ρ€ΠΈ
ΠœΠΎΠΆΠ΅Ρ‚Π΅ Π΄Π° ΡΠ»ΡƒΡˆΠ°Ρ‚Π΅ Π·Π°ΠΊΡƒΠΏΠ΅Π½ΠΈΡ‚Π΅ ΠΎΡ‚ Google Play Π°ΡƒΠ΄ΠΈΠΎΠΊΠ½ΠΈΠ³ΠΈ посрСдством ΡƒΠ΅Π± Π±Ρ€Π°ΡƒΠ·ΡŠΡ€Π° Π½Π° ΠΊΠΎΠΌΠΏΡŽΡ‚ΡŠΡ€Π° си.
Π•Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½ΠΈ Ρ‡Π΅Ρ‚Ρ†ΠΈ ΠΈ Π΄Ρ€ΡƒΠ³ΠΈ устройства
Π—Π° Π΄Π° Ρ‡Π΅Ρ‚Π΅Ρ‚Π΅ Π½Π° устройства с Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½ΠΎ мастило, ΠΊΠ°Ρ‚ΠΎ Π½Π°ΠΏΡ€ΠΈΠΌΠ΅Ρ€ Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½ΠΈΡ‚Π΅ Ρ‡Π΅Ρ‚Ρ†ΠΈ ΠΎΡ‚ Kobo, трябва Π΄Π° ΠΈΠ·Ρ‚Π΅Π³Π»ΠΈΡ‚Π΅ Ρ„Π°ΠΉΠ» ΠΈ Π΄Π° Π³ΠΎ ΠΏΡ€Π΅Ρ…Π²ΡŠΡ€Π»ΠΈΡ‚Π΅ Π½Π° устройството си. Π˜Π·ΠΏΡŠΠ»Π½Π΅Ρ‚Π΅ ΠΏΠΎΠ΄Ρ€ΠΎΠ±Π½ΠΈΡ‚Π΅ инструкции Π² ΠŸΠΎΠΌΠΎΡ‰Π½ΠΈΡ Ρ†Π΅Π½Ρ‚ΡŠΡ€, Π·Π° Π΄Π° ΠΏΡ€Π΅Ρ…Π²ΡŠΡ€Π»ΠΈΡ‚Π΅ Ρ„Π°ΠΉΠ»ΠΎΠ²Π΅Ρ‚Π΅ Π² ΠΏΠΎΠ΄Π΄ΡŠΡ€ΠΆΠ°Π½ΠΈΡ‚Π΅ Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½ΠΈ Ρ‡Π΅Ρ‚Ρ†ΠΈ.

ΠŸΡ€ΠΎΠ΄ΡŠΠ»ΠΆΠ°Π²Π°Π½Π΅ Π½Π° ΠΏΠΎΡ€Π΅Π΄ΠΈΡ†Π°Ρ‚Π°

ΠžΡ‰Π΅ ΠΎΡ‚ Julia Garibaldi

Подобни Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½ΠΈ ΠΊΠ½ΠΈΠ³ΠΈ