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Sergey N. Dorogovtsev

in Lectures on Complex Networks

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199548927
eISBN:
9780191720574
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199548927.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this concluding section of the text, the three major milestones marking the history of the exploration of networks are indicated. These are: Leonhard Euler's work (1735), the introduction of ... More


The Fortunes of a Mechanical Model for Natural Philosophy

Stephen Gaukroger

in The Collapse of Mechanism and the Rise of Sensibility: Science and the Shaping of Modernity, 1680-1760

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199594931
eISBN:
9780191595745
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199594931.003.0009
Subject:
Philosophy, Philosophy of Science, General

The basic assumption of ‘rational mechanics’ was that all natural philosophy was mechanics, and that, as mechanics was pursued with greater and greater detail and sophistication, the rest of natural ... More


Tic-tac-toe on Affine Planes

Maureen T. Carroll and Steven T. Dougherty

in The Mathematics of Various Entertaining Subjects: Research in Recreational Math

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164038
eISBN:
9781400881338
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164038.003.0013
Subject:
Mathematics, History of Mathematics

This chapter introduces a new game of tic-tac-toe that fits squarely within the body of work inspired by mathematician Leonhard Euler's findings on the so-called “Graeco-Latin squares” and the ... More


Euler: The Mathematics of Musical Sadness

Peter Pesic

in Music and the Making of Modern Science

Published in print:
2014
Published Online:
May 2017
ISBN:
9780262027274
eISBN:
9780262324380
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262027274.003.0010
Subject:
Music, History, Western

Throughout his life, the great mathematician Leonhard Euler spent most of his free time on music, to which he devoted his first book. This chapter discusses how he reformulated the ordering of ... More


Euler: From Sound to Light

Peter Pesic

in Music and the Making of Modern Science

Published in print:
2014
Published Online:
May 2017
ISBN:
9780262027274
eISBN:
9780262324380
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262027274.003.0011
Subject:
Music, History, Western

Beside his enormous achievements in mathematics, Leonhard Euler was deeply involved in many areas of physics. His early work on music had a direct bearing on his contemporary study of sound, which in ... More


Traversing Graphs

Arthur Benjamin, Gary Chartrand, and Ping Zhang

in The Fascinating World of Graph Theory

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175638
eISBN:
9781400852000
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175638.003.0005
Subject:
Mathematics, Applied Mathematics

This chapter considers Eulerian graphs, a class of graphs named for the Swiss mathematician Leonhard Euler. It begins with a discussion of the the Königsberg Bridge Problem and its connection to ... More


Graph Theory: A Look Back—The Road Ahead

Arthur Benjamin, Gary Chartrand, and Ping Zhang

in The Fascinating World of Graph Theory

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175638
eISBN:
9781400852000
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175638.003.0013
Subject:
Mathematics, Applied Mathematics

This book concludes with an epilogue, which traces the evolution of graph theory, from the conceptualization of the Königsberg Bridge Problem and its generalization by Leonhard Euler, whose solution ... More


Prologue

Cristopher Moore and Stephan Mertens

in The Nature of Computation

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199233212
eISBN:
9780191775079
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233212.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This prologue begins by considering three examples to demonstrate that in order to solve different problems, fundamentally different kinds of search and different types of proof are required. The ... More


Areas, Angles, and Polyhedra

Glen Van Brummelen

in Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175997
eISBN:
9781400844807
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175997.003.0007
Subject:
Mathematics, History of Mathematics

This chapter explains how to find the area of an angle or polyhedron. It begins with a discussion of how to determine the area of a spherical triangle or polygon. The formula for the area of a ... More


The Principle of Least Action: From Teleology to Causality

Yemima Ben-Menahem

in Causation in Science

Published in print:
2018
Published Online:
January 2019
ISBN:
9780691174938
eISBN:
9781400889297
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174938.003.0006
Subject:
History, History of Science, Technology, and Medicine

This chapter examines the place of the “least action” principle in the causal family and its role in in modern science's transition from teleology to causality. It first provides an overview of the ... More


Making Walks Count: From Silent Circles to Hamiltonian Cycles

Max A. Alekseyev and Gérard P. Michon

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0010
Subject:
Mathematics, History of Mathematics

Leonhard Euler (1707–1783) invented graph theory in 1735, by solving a puzzle of interest to the inhabitants of Königsberg. The city comprised three distinct land masses, connected by seven bridges. ... More


Coloring Graphs

Arthur Benjamin, Gary Chartrand, and Ping Zhang

in The Fascinating World of Graph Theory

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175638
eISBN:
9781400852000
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175638.003.0011
Subject:
Mathematics, Applied Mathematics

This chapter considers the concept of coloring the vertices of a graph by focusing on the Four Color Problem. It begins with a discussion of three mathematics problems that involve conjecture, ... More


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