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Visual Thinking in Mathematics

Marcus Giaquinto

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Visual thinking — visual imagination or perception of diagrams and symbol arrays, and mental operations on them — is omnipresent in mathematics. Is this visual thinking merely a psychological aid, ... More


Truth-operations

Michael Potter

in Wittgenstein's Notes on Logic

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199215836
eISBN:
9780191721243
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215836.003.0018
Subject:
Philosophy, Logic/Philosophy of Mathematics

From a single proposition p we form its negation not-p. From two propositions p and q we form various further propositions, e.g., p or q, p and q, etc.; similarly (though less often) with three or ... More


Crystallization theory

Naomi E. Chayen, John R. Helliwell, and Edward H. Snell

in Macromolecular Crystallization and Crystal Perfection

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199213252
eISBN:
9780191707575
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213252.003.0002
Subject:
Physics, Crystallography

A basic understanding of crystallization theory exists through the phase‐diagram description. More detailed theories are available but no one theory can currently predict crystallization behaviour. ... More


The Physics of Lyotropic Liquid Crystals: Phase Transitions and Structural Properties

Antônio M. Figueiredo Neto and Silvio R. A. Salinas

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198525509
eISBN:
9780191711756
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525509.001.0001
Subject:
Physics, Crystallography

Mixtures of surfactant or amphiphilic molecules and solvents are known to display a large number of lyotropic mesophases. Although the physics of thermotropic liquid crystals has been vastly ... More


Schematic Comparison

Dov-Ber Kerler

in The Origins of Modern Literary Yiddish

Published in print:
1993
Published Online:
October 2011
ISBN:
9780198151661
eISBN:
9780191672798
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198151661.003.0023
Subject:
Literature, European Literature

This chapter uses a schematic diagram to illustrate the scope of Linguistic Easternization. The parameters used are morphology and syntax; these are deemed to be representationally sufficient for the ... More


The Distribution of Ministries

Ian Budge and Hans Keman

in Parties and Democracy: Coalition Formation and Government Functioning in Twenty States

Published in print:
1993
Published Online:
November 2003
ISBN:
9780198279259
eISBN:
9780191598883
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198279256.003.0005
Subject:
Political Science, Comparative Politics

The policy goals sought by parties in the various ideological ‘families’ are specified and flow diagrams created of how relevant ministries should be distributed among parties in government under ... More


Conclusions

A. Townsend Peterson, Jorge Soberón, Richard G. Pearson, Robert P. Anderson, Enrique Martínez-Meyer, Miguel Nakamura, and Miguel Bastos Araújo

in Ecological Niches and Geographic Distributions (MPB-49)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691136868
eISBN:
9781400840670
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691136868.003.0016
Subject:
Biology, Ecology

This book has described a comprehensive framework for thinking about the geography and ecology of species distributions, arguing that such a framework is critical to further progress in the field of ... More


British Management and Organization up to the 1940s

John F. Wilson and Andrew Thomson

in The Making of Modern Management: British Management in Historical Perspective

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199261581
eISBN:
9780191718588
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199261581.003.0003
Subject:
Business and Management, Business History

This chapter describes a period when in spite of the scale and nature of British business activities and the emergence of big business (mostly through intense merger activity), there was a ... More


Superconducting Alloys

Nikolai B. Kopnin

in Theory of Nonequilibrium Superconductivity

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198507888
eISBN:
9780191709722
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507888.003.04
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explains how to incorporate scattering by random impurity atoms into the general Green function formalism of the theory of superconductivity. The cross-diagram technique based on the ... More


Geometrical Discovery by Visualizing

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/9780199285945.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter shows how, using basic beliefs, one can go on to make a geometrical discovery by visual means in a non-empirical manner. It focuses on a simple example in order to illustrate the general ... More


Diagrams in Geometric Proofs

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/9780199285945.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

Presentations of geometric proofs are often accompanied by diagrams for quick and easy comprehension. But to many people, it seems clear that diagrammatic reasoning cannot be a part of the argument ... More


The Euclidean Diagram (1995)

Kenneth Manders

in The Philosophy of Mathematical Practice

Published in print:
2008
Published Online:
February 2010
ISBN:
9780199296453
eISBN:
9780191711961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296453.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is ... More


HISTORY AND BEYOND

A. A. Ivanov

in The Fourth Janko Group

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198527596
eISBN:
9780191713163
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527596.003.0009
Subject:
Mathematics, Pure Mathematics

This chapter surveys the history of discovery, construction, and characterization of J4. It shows when and how the crucial ingredients of the proof of the Main Theorem emerged. Topics covered include ... More


CATEGORIES OF DIAGRAMS

Steve Awodey

in Category Theory

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568612
eISBN:
9780191717567
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568612.003.0008
Subject:
Mathematics, Algebra

This chapter presents the proof for the Yoneda Lemma, which is probably the single most used result in category theory. It is interesting how often it comes up, especially in view of the fact that it ... More


Hailfinder: Tools for and Experiences with Bayesian Normative Modeling

Jie W Weiss and David J Weiss

in A Science of Decision Making: The Legacy of Ward Edwards

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195322989
eISBN:
9780199869206
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195322989.003.0010
Subject:
Psychology, Cognitive Psychology

Bayes Nets (BNs) and Influence Diagrams (IDs), new tools that use graphic user interfaces to facilitate representation of complex inference and decision structures, it are the core elements of new ... More


Finite Elements on Tetrahedra

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0005
Subject:
Mathematics, Numerical Analysis

The finite element method is based on a geometric decomposition of the domain of Maxwell’s equations into simple elements. This chapter is devoted to tetrahedral elements, which are very common in ... More


Finite Elements on Hexahedra

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0006
Subject:
Mathematics, Numerical Analysis

An alternative to the tetrahedral elements discussed in the previous chapter is to use finite elements based on cubes, or more generally, hexahedra. Hexahedral elements have been used in several ... More


Bonding in Coordination Compounds

Wai-Kee Li, Gong-Du Zhou, and Thomas Chung Wai Mak

in Advanced Structural Inorganic Chemistry

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199216949
eISBN:
9780191711992
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199216949.003.0008
Subject:
Physics, Crystallography

This chapter covers the electronic structure of coordination complexes, using the language of group theory throughout. The bonding of these complexes ranges from ionic (crystal field theory, or CFT) ... More


Imagining Jerusalem in the Medieval West

Lucy Donkin and Hanna Vorholt (eds)

Published in print:
2012
Published Online:
January 2013
ISBN:
9780197265048
eISBN:
9780191754159
Item type:
book
Publisher:
British Academy
DOI:
10.5871/bacad/9780197265048.001.0001
Subject:
History, European Medieval History

Jerusalem was the object of intense study and devotion throughout the Middle Ages. This book illuminates ways in which the city was represented by Christians in Western Europe, from the 600s the ... More


Niches and Geographic Distributions

A. Townsend Peterson, Jorge Soberón, Richard G. Pearson, Robert P. Anderson, Enrique Martínez-Meyer, Miguel Nakamura, and Miguel Bastos Araújo

in Ecological Niches and Geographic Distributions (MPB-49)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691136868
eISBN:
9781400840670
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691136868.003.0003
Subject:
Biology, Ecology

This chapter considers a concept of niche that emphasizes multidimensional spaces of scenopoetic variables and provides a natural connection to the study of geographic distributions of species. It ... More


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