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General Theorems From Specific Images

Marcus Giaquinto

in Visual Thinking in Mathematics

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter shows that some general arithmetical theorems almost certainly can be discovered by visualizing. First, it describes two examples of what look like acceptable routes to general theorems ... More


The arithmetical triangle

A. W. F. EDWARDS

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/9780199656592.003.0008
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

The arithmetical triangle is the most famous of all number patterns. Apparently a simple listing of the binomial coefficients, it contains the triangular and pyramidal numbers of ancient Greece, the ... More


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