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Adventures of the Diagonal: Non-Euclidean Mathematics and Narrative

Arkady Plotnitsky

Apostolos Doxiadis and Barry Mazur (eds)

in Circles Disturbed: The Interplay of Mathematics and Narrative

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691149042
eISBN:
9781400842681
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149042.003.0012
Subject:
Mathematics, History of Mathematics

This chapter explores the relationship between narrative and non-Euclidean mathematics. It considers how non-Euclidean mathematics and the narratives accompanying it are linked: first, to the ... More


Ancient Greek Mathematics: A Role for Diagrams

José Ferreirós

in Mathematical Knowledge and the Interplay of Practices

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167510
eISBN:
9781400874002
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167510.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the ancient Greek tradition of geometrical proof in light of recent studies by Kenneth Manders and others. It advances the view that the borderline of elementary mathematics ... More


Space and Geometry

Ian Hinckfuss

in The Existence of Space and Time

Published in print:
1975
Published Online:
October 2011
ISBN:
9780198245193
eISBN:
9780191680854
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198245193.003.0004
Subject:
Philosophy, Metaphysics/Epistemology

This chapter first reports the geometrical properties of space. One of the assumptions of Newtonian dynamics is that space is Euclidean; that is, space satisfies the axioms, and hence the theorems, ... More


Time, space and mass

JESPER LÜTZEN

in Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics'

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567370
eISBN:
9780191717925
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567370.003.0011
Subject:
Physics, History of Physics

Heinrich Hertz introduced the three fundamental concepts of his mechanics — time, space, and mass — at the beginning of his book Principles of Mechanics. This chapter analyses Hertz's concepts of ... More


The Longest Journey: Bertrand Russell

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/9780199278220.003.00010
Subject:
Philosophy, Philosophy of Mind, Philosophy of Science

The first sustained, rigorous development of a structuralist view of science appeared in the writings of Bertrand Russell, where the philosophical motivation precedes a precise formulation drawing on ... More


Kant’s Theory of Geometry and Transcendental Idealism II

Thomas C. Vinci

in Space, Geometry, and Kant's Transcendental Deduction of the Categories

Published in print:
2014
Published Online:
October 2014
ISBN:
9780199381166
eISBN:
9780199381234
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199381166.003.0005
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

Chapter 4 has three main parts. The first develops an account of Kant’s mathematical method, based partly on work by Philip Kitcher, called the KV account. This account allows for epistemically ... More


Introduction

Ciaran McMorran

in Joyce and Geometry

Published in print:
2020
Published Online:
September 2020
ISBN:
9780813066288
eISBN:
9780813065267
Item type:
chapter
Publisher:
University Press of Florida
DOI:
10.5744/florida/9780813066288.003.0001
Subject:
Literature, 20th-century Literature and Modernism

This chapter explores how James Joyce evokes an overarching concern with the linear in his works, both formally (in terms of the Euclidean ideal of rectilinearity) and conceptually (in terms of ... More


Metric description of a curved space

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Einstein's new theory of gravitation is formulated in a geometric framework of curved spacetime. Here the subject of non-Euclidean geometry is introduced by way of Gauss's theory of curved surfaces. ... More


Geometry: Math for Math’s Sake: Non-Euclidean Geometry and Aestheticism

Andrea Henderson

in Algebraic Art: Mathematical Formalism and Victorian Culture

Published in print:
2018
Published Online:
May 2018
ISBN:
9780198809982
eISBN:
9780191860140
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198809982.003.0002
Subject:
Literature, 19th-century Literature and Romanticism

Edwin Abbott’s Flatland dramatizes the implications of dethroning what Victorians regarded as the preeminent representational system: Euclidean geometry. The displacement of the singular Euclidean ... More


Geometry

Olivier Darrigol

in Physics and Necessity: Rationalist Pursuits from the Cartesian Past to the Quantum Present

Published in print:
2014
Published Online:
June 2014
ISBN:
9780198712886
eISBN:
9780191781360
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198712886.003.0004
Subject:
Physics, History of Physics

This chapter deals with the foundations of geometry, with emphasis on Helmholtz’s approach to this problem in the late 1860s. It is first recalled how the ancient belief in the apodictic truth of the ... More


Mathematics and the Unity of Sensibility

Waxman Wayne

in Kant's Anatomy of the Intelligent Mind

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199328314
eISBN:
9780199369348
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199328314.003.0007
Subject:
Philosophy, History of Philosophy

This chapter focuses on Kant’s account of the possibility of mathematics in relation to the transcendental expositions of space and time in the Transcendental Aesthetic, that is, the role of ... More


The Perils of Parallels!

Nicholas Mee

in Celestial Tapestry: The Warp and Weft of Art and Mathematics

Published in print:
2020
Published Online:
September 2020
ISBN:
9780198851950
eISBN:
9780191886690
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198851950.003.0016
Subject:
Physics, History of Physics

In the nineteenth century, three mathematicians—Bolyai, Gauss, and Lobachevsky—almost simultaneously discovered the possibility of non-Euclidean or hyperbolic geometries. These geometries rest on ... More


Non-Euclidean Geometry

Jeremy Gray

in Space: A History

Published in print:
2020
Published Online:
April 2020
ISBN:
9780199914104
eISBN:
9780190090579
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199914104.003.0013
Subject:
Philosophy, Metaphysics/Epistemology, History of Philosophy

Non-Euclidean geometry began as an inquiry into a possible weakness in Euclid’s Elements and became the source of the ideas that there are geometries of spaces other than the one imagined in ... More


Mathematical Knowledge and the Interplay of Practices

José Ferreirós

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167510
eISBN:
9781400874002
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167510.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction ... More


Embrace change, considering non-Euclidean geometry

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0016
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Embrace change, considering non-Euclidean geometry” offers a basic introduction to the geometry of curved surfaces in which the sum of the degrees of a triangle may equal more or less than 180°. The ... More


Rigor and Rigorization

John P. Burgess

in Rigor and Structure

Published in print:
2015
Published Online:
May 2015
ISBN:
9780198722229
eISBN:
9780191789076
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198722229.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter explains what heuristic methods, ubiquitous and indispensable in the context of discovery in mathematics, are prohibited in the context of justification by the requirement of rigor as ... 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


Joyce and Geometry

Ciaran McMorran

Published in print:
2020
Published Online:
September 2020
ISBN:
9780813066288
eISBN:
9780813065267
Item type:
book
Publisher:
University Press of Florida
DOI:
10.5744/florida/9780813066288.001.0001
Subject:
Literature, 20th-century Literature and Modernism

Following the development of non-Euclidean geometries from the mid-nineteenth century onwards, Euclid’s system came to be re-conceived as a language for describing reality rather than a set of ... More


Semantics and the Notion of Consequence

Jody Azzouni

in Tracking Reason: Proof, Consequence, and Truth

Published in print:
2006
Published Online:
October 2011
ISBN:
9780195187137
eISBN:
9780199850570
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195187137.003.0015
Subject:
Philosophy, Logic/Philosophy of Mathematics

Contemporary mathematics is the study of algorithmic systems of all sorts. There are two alternatives to the first-order thesis as a descriptive thesis of the logic of mature mathematics. The first ... More


Ezra Pound and the Materiality of the Fourth Dimension

Ian F. A. Bell

in Science in Modern Poetry: New Directions

Published in print:
2012
Published Online:
June 2013
ISBN:
9781846318092
eISBN:
9781846317743
Item type:
chapter
Publisher:
Liverpool University Press
DOI:
10.5949/UPO9781846317743.009
Subject:
Literature, Poetry

This chapter describes how Ezra Pound discovered the aesthetic potential of the concept of Vorticism and fourth-dimensional thought and integrated this into his writings. In his ‘Vorticism’ essay, ... More


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