View:

- no detail
- some detail
- full detail

## Outlook

*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

View:

- no detail
- some detail
- full detail