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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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