## 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

## 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

## 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

## Introduction

*M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko*

### in Advances in the Casimir Effect

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199238743
- eISBN:
- 9780191716461
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238743.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This introductory chapter discusses the general physical foundations of the Casimir effect as manifestation of the existence of zero-point vacuum oscillations. Connections between the Casimir force, ... 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

## 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

## Algebraic Art: Mathematical Formalism and Victorian Culture

*Andrea Henderson*

- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198809982
- eISBN:
- 9780191860140
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198809982.001.0001
- Subject:
- Literature, 19th-century Literature and Romanticism

Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth ... More

## A Mathematical Sculptor’s Perspective on Space

*George Hart*

### 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/9780199914104.003.0014
- Subject:
- Philosophy, Metaphysics/Epistemology, History of Philosophy

In this Reflection, a mathematician discusses four sculptures he created to express important aspects of various kinds of spaces, including ordinary Euclidean, hyperbolic space. The sculptures ... 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

## 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

## The Concepts of Generalized Fractality and Chaos

### in Theory of Identities

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780231168946
- eISBN:
- 9780231541459
- Item type:
- chapter

- Publisher:
- Columbia University Press
- DOI:
- 10.7312/columbia/9780231168946.003.0004
- Subject:
- Philosophy, Metaphysics/Epistemology

This chapter elaborates the notions of “fractality” and “chaos” in order to lead to a rigorous understanding of “identities”. It begins by explaining how philosophy would approach these scientific ... More

## Memo to Readers: Overview and Synopsis

*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/9780199328314.003.0001
- Subject:
- Philosophy, History of Philosophy

This introductory text signals what is new and noteworthy in the book and provides guidance for comprehending and evaluating it. It opens with some general remarks regarding the book’s relation to ... 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

## 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

## 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

## 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

##
“Writings of Paraboles”: Geometric Traditionalism and Corporeal Topography in the *Wake*’s “Night Lessons”

*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/9780813066288.003.0002
- Subject:
- Literature, 20th-century Literature and Modernism

This chapter explores how James Joyce interrogates the traditional procedures through which geometric symbols of "perfection and the divine”—including the concept of the infinitely straight line—are ... More

## Geometry on my Mind

*David D. Nolte*

### in Galileo Unbound: A Path Across Life, the Universe and Everything

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198805847
- eISBN:
- 9780191843808
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805847.003.0005
- Subject:
- Physics, History of Physics

This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who ... 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

## Non-Euclidean Extensions

*Geoffrey Hellman and Stewart Shapiro*

### in Varieties of Continua: From Regions to Points and Back

- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198712749
- eISBN:
- 9780191781087
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198712749.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter adapts the foregoing results to present two non-Euclidean theories, both in line with the (semi-)Aristotelian theme of rejecting points, as parts of regions (but working with actual ... More