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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


Combinatorics: Ancient and Modern

Robin Wilson and John J. Watkins (eds)

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199656592
eISBN:
9780191748059
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199656592.001.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to ... 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


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


Partitions

GEORGE E. ANDREWS

in Combinatorics: Ancient and Modern

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199656592
eISBN:
9780191748059
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199656592.003.0010
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

While Leibniz appears to have been the earliest to consider the partitioning of integers into sums, Euler was the first person to make truly deep discoveries. J. J. Sylvester was the next researcher ... More


Early graph theory

ROBIN WILSON

in Combinatorics: Ancient and Modern

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199656592
eISBN:
9780191748059
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199656592.003.0009
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

The origins of graph theory are humble, even frivolous. Whereas many branches of mathematics were motivated by fundamental problems of calculation, motion, and measurement, the problems which led to ... More


e: A very special number

Marcel Danesi

in Pythagoras' Legacy: Mathematics in Ten Great Ideas

Published in print:
2020
Published Online:
January 2020
ISBN:
9780198852247
eISBN:
9780191886959
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198852247.003.0006
Subject:
Mathematics, History of Mathematics, Educational Mathematics

The number e, which is equal to 2.71828…, might seem like something trivial—a play on numbers by mathematicians. Nothing could be further from the truth. It is defined as the limit of the expression ... More


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