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Friday, July 17, 2020 | History

1 edition of The Erdös distance problem found in the catalog.

The Erdös distance problem

Julia Garibaldi

# The Erdös distance problem

## by Julia Garibaldi

• 181 Want to read
• 1 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

Subjects:
• Geometry,
• Combinatorics,
• Harmonic analysis on Euclidean spaces,
• Harmonic analysis,
• Combinatorial analysis,
• Number theory

• Edition Notes

Includes bibliographical references and index.

Classifications The Physical Object Statement Julia Garibaldi, Alex Iosevich, Steven Senger Series Student mathematical library -- v. 56 Contributions Iosevich, Alex, 1967-, Senger, Steven, 1982- LC Classifications QA164 .G37 2010 Pagination p. cm. Open Library OL24816385M ISBN 10 9780821852811 LC Control Number 2010033266

By this term I mean, loosely, the study of the geometry of certain subsets of Euclidean space $\mathbb{E}^n$ from a point of view which is either the "classical" one (i.e. axiomatic), or one that involves more modern tools, but the problem in question has not to be "clearly" a problem within some other branch of maths such as differential or.   The mathematician Terence Tao, of the University of California, Los Angeles, has presented a solution to an year-old number theory problem posed by the legendary Hungarian mathematician Paul Erdős. Erdős was famous for the thousands of puzzles he came up with, many of which have led to surprisingly deep mathematical discoveries. This particular problem, which came to .

I. Palásti, A distance problem of P. Erdös with some further restrictionsDiscrete Math. 76() – MathSciNet zbMATH CrossRef Google Scholar I. Palásti, Lattice point examples for Cited by: 1. Remembering Uncle Paul: a memorial to Paul Erdös written by Fan Chung Graham, which appeared in the Preface to her book "Erdös on Graphs." N is a Number: A Portrait of Paul Erdös - an hour-long documentary from on the mathematical life of Paul Erdös, directed by George Paul Csicsery. Collected papers of Paul Erdös.

Zbl • Erdös, Paul, Problems and results in combinatorial analysis and combinatorial number theory., Alavi, Yousef (ed.) et al., Graph theory, combinatorics, and applications, Vol. 1. Proceedings of the sixth quadrennial international conference on the theory and applications of graphs held at Western Michigan University, Kalamazoo, Michigan, May June 3, JOURNAL OF COMBINATORIAL THEORY 5, () On a Problem of P. ErdSs PAUL C. KA[NEN Department of Mathematics, Cornell University, Ithaca, New York Communicated by P. Erdds ABSTRACT In this paper it is shown that 1 lim n-4c(Kn) -- n~r~o 64 where c(Kn) denotes the minimum number of crossings with which the complete graph Kn can be drawn in the by:

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### The Erdös distance problem by Julia Garibaldi Download PDF EPUB FB2

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 conjecture. In what follows let g(n) denote the minimal number of distinct distances between n points in the plane, or equivalently the smallest possible cardinality of their distance his paper, Erdős proved the estimates − / − / ≤ ≤ / ⁡ for some lower bound was given by an easy argument.

ISBN: OCLC Number: Description: xii, pages: illustrations ; 22 cm. Contents: 1. The [square root of n] theory The [n to the 2/3 power] theory The Cauchy-Schwarz inequality Graph theory and incidences The [n to the 4/5 power] theory The [n to the 6/7 power] theory Beyond [n The Erdös distance problem book the 6/7 power] Paul Erdős (Hungarian: Erdős Pál [ˈɛrdøːʃ ˈpaːl]; 26 March – 20 September ) was a renowned Hungarian was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century.

He was known both for his social practice of mathematics (he engaged more than collaborators) and for his eccentric lifestyle (Time magazine Born: 26 MarchBudapest, Austria-Hungary. Pages from Volume (), Issue 1 by Larry Guth, Nets Hawk KatzCited by: Genre/Form: Electronic books: Additional Physical Format: Print version: Garibaldi, Julia, Erdös distance problem.

Providence, R.I.: American Mathematical. People in other sciences or even social sciences may also have small Erdös numbers. My brother (a physician with only one publication) has an Erdös number of at most 9. An author in the MathSciNet database, Mutt, is a computer with an Erdös number of 2.

We’ve even heard about a horse who claimed to have an Erdös number of 3. We study the Erdös–Falconer distance problem in vector spaces over finite fields with respect to the cubic metric.

Estimates for discrete Airy sums and Adolphson–Sperber estimates for exponential sums in terms of Newton polyhedra play a crucial by: Paul Erdös has been described as a "prince of problem solvers and the absolute monarch of problem posers." This is a testament to both his legacy of over publications and his numerous proposed problems, many of which are still open today.

Throughout his career, work on his proposed problems in a variety of areas of mathematics. Erdös was famous for having many collaborators ( at last count). This has given rise to the notion of an "Erdös number". All those mathematicians who co-authored a paper or book with Erdös are said to have Erdös number 1; those who have co-authored with someone of Erdös number 1 (but not with Erdös himself) have Erdös number 2; and so on.

Abstract. The Erdös unit distance conjecture in the plane says that the number of pairs of points from a point set of size n separated by a fixed (Euclidean) distance is $$\le C_{\varepsilon } n^{1+\varepsilon }$$ for any $$\varepsilon >0$$.The best known bound is $$Cn^{\frac{4}{3}}$$.We show that if the set under consideration is homogeneous, or, more generally, s-adaptable in the sense of Author: Alex Iosevich.

Paul Erdös Erdös the man Erdös focused on problem-solving, particu- Erdös and ‘the Book’ Erdös liked to imagine that God had a book in tary a problem is, the better.

Erdös was the consum-mate problem solver; his hallmark was the succinct and clever argument, often. The incidence estimate for lines in R 3 in [12] was motivated by the Erdős distinct distance problem in the plane.

The problem asks for the minimal number of distinct distances determined by N. The Erdös Number Project. This is the website for the Erdös Number Project, which studies research collaboration among mathematicians.

The site is maintained by Jerry Grossman at Oakland University. Patrick Ion, a retired editor at Mathematical Reviews, and Rodrigo De Castro at the Universidad Nacional de Colombia, Bogota provided assistance in the past.

We study the Erdos distance problem over finite Euclidean and non-Euclidean spaces. Our main tools are graphs associated to finite Euclidean and non-Euclidean spaces that are considered in Bannai Author: Le Anh Vinh.

To my count, the difference between the publication dates of the Sylvester () and Erdös () questions is closer to 50 than to 40, so perhaps the reason for the confusion is that Grünwald found and reported his solution to Erdös 10 years before the later decided to go out public with the problem.

If you have a disability and are having trouble accessing information on this website or need materials in an alternate format, contact [email protected] for [email protected] for.

There's a nice book by Garibaldi, Iosevich, and Senger, The Erdős Distance Problem, in the Student Mathematical Library series of the American Mathematical Society. Mostly it's about the problem in the plane, but there is some discussion of, and references to, work on higher dimensions.

Erdös-Mordell Inequality. Inthe following problem proposal appeared in the "Advanced Problems" section of the American Mathematical Monthly.

Proposed by Paul Erdös, The University of Manchester, England. A new entropy inequality for the Erdös distance problem.

In Towards a theory of Geometric Graphs, volume of Contemporary Mathematics. American Mathematical Society. On a problem of Erdös, Straus and Schinzel - Volume 17 Issue 2 - R.

C. Vaughan Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our by:   Actually, I can say that this book made me like to read biographies in general.

It is written in very lively tone. Very entertaining story about the legendary Paul Erdos, his 19 hours of working/day, his movement among conferences (He actually didn't have a home), and his continuous quest for proving theorems "from the book"/5.Title: Erdos/Falconer distance problems in vector spaces over finite fields JanuaryPure Mathematics Seminar, University of Bristol Title: Erdos/Falconer distance problem in vector spaces over finite fields.

() DecemberAnnual Meeting of the Canadian Mathematical Society.