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Desargues’s Theorem as a Case Study of Mathematical Explanation, Existence, and Natural Properties

Marc Lange

in Because Without Cause: Non-Causal Explanations in Science and Mathematics

Published in print:
2016
Published Online:
December 2016
ISBN:
9780190269487
eISBN:
9780190269500
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780190269487.003.0009
Subject:
Philosophy, Philosophy of Science, General

This chapter applies the account of explanatory proofs in mathematics from previous chapters to proofs of Desargues’s theorem. Mathematicians regard a nonmetrical proof exiting to the third dimension ... More


Representable Matroids

James Oxley

in Matroid Theory

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198566946
eISBN:
9780191774904
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566946.003.0007
Subject:
Mathematics, Educational Mathematics

This chapter provides an overview of the basic questions associated with matroid representability and indicates how one actually goes about constructing representations. The key ideas are presented ... More


A Very Short Course in Projective Geometry

Tony Robbin

in Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought

Published in print:
2006
Published Online:
October 2013
ISBN:
9780300110395
eISBN:
9780300129625
Item type:
chapter
Publisher:
Yale University Press
DOI:
10.12987/yale/9780300110395.003.0005
Subject:
Society and Culture, Technology and Society

This chapter serves as a brief lesson on projective geometry. It starts by discussing two basic theorems of projective geometry, which are concerned with perspectives from a point and perspectives ... More


Pictorial Perspective and the Indexical

Bas C. van Fraassen

in Scientific Representation: Paradoxes of Perspective

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199278220
eISBN:
9780191707926
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278220.003.0004
Subject:
Philosophy, Philosophy of Mind, Philosophy of Science

The connection between perspective and the indexical shows up in the sciences, for example, when talk of frames of reference is conducted in terms of observers (whose frames they are, so to speak). ... More


Conclusion: Art, Math, and Technical Drawing

Tony Robbin

in Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought

Published in print:
2006
Published Online:
October 2013
ISBN:
9780300110395
eISBN:
9780300129625
Item type:
chapter
Publisher:
Yale University Press
DOI:
10.12987/yale/9780300110395.003.0011
Subject:
Society and Culture, Technology and Society

This chapter reviews the key concepts related to projective geometry, which is the field that has helped develop thinking on physics and mathematics. It first looks at the fact that Felix Klein ... More


Matroid Theory

James Oxley

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198566946
eISBN:
9780191774904
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566946.001.0001
Subject:
Mathematics, Educational Mathematics

Seventy-five years of the study of matroids has seen the development of a rich theory with links to graphs, lattices, codes, transversals,0020and projective geometries. Matroids are of fundamental ... More


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