2. Mathematik
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Esther Ramharter
Abstract
Chapter 2, Mathematics, deals with the kinds and aspects of mathematical objects that in non-terminological parlance can be called lines - e.g., curves or the boundaries of surfaces -, the limits of the concept line, linearity as a generalisation of lines, and the foundational status of lines in geometry. The introductory part of this chapter discusses, among other things, the relations between lines and one-dimensionality, measuring, boundary, and drawing (i.e., of lines). The chapter then presents a choice of texts ranging from antiquity to the present, with a special focus on the 19th and the beginning of the 20th century - a period that saw a significant rise of interest in geometry and its foundational issues. Examples from the following authors are included: Aristotle, Euclid, René Descartes, Johann Benedict Listing, Richard Dedekind, Charles S. Peirce, David Hilbert, Gottlob Frege, Felix Klein, Hugo Dingler, Benoît Mandelbrot, Gilles Deleuze/Félix Guattari. The final text, by Harro Heuser, is not about lines, but about linearity.
Abstract
Chapter 2, Mathematics, deals with the kinds and aspects of mathematical objects that in non-terminological parlance can be called lines - e.g., curves or the boundaries of surfaces -, the limits of the concept line, linearity as a generalisation of lines, and the foundational status of lines in geometry. The introductory part of this chapter discusses, among other things, the relations between lines and one-dimensionality, measuring, boundary, and drawing (i.e., of lines). The chapter then presents a choice of texts ranging from antiquity to the present, with a special focus on the 19th and the beginning of the 20th century - a period that saw a significant rise of interest in geometry and its foundational issues. Examples from the following authors are included: Aristotle, Euclid, René Descartes, Johann Benedict Listing, Richard Dedekind, Charles S. Peirce, David Hilbert, Gottlob Frege, Felix Klein, Hugo Dingler, Benoît Mandelbrot, Gilles Deleuze/Félix Guattari. The final text, by Harro Heuser, is not about lines, but about linearity.
Kapitel in diesem Buch
- Frontmatter I
- Vorwort V
- Inhaltsverzeichnis VII
- Abkürzungsverzeichnis XIII
- 0. Linienwissen und Liniendenken. Einleitung in ein Forschungsfeld 1
- 1. Philosophie 19
- 2. Mathematik 79
- 3. Ethnologie und Anthropologie 141
- 4. Geographie und Kartographie 202
- 5. Kunsttheorie und -geschichte 282
- Literaturverzeichnis 425
- Namenregister 467
- Sachregister 470
Kapitel in diesem Buch
- Frontmatter I
- Vorwort V
- Inhaltsverzeichnis VII
- Abkürzungsverzeichnis XIII
- 0. Linienwissen und Liniendenken. Einleitung in ein Forschungsfeld 1
- 1. Philosophie 19
- 2. Mathematik 79
- 3. Ethnologie und Anthropologie 141
- 4. Geographie und Kartographie 202
- 5. Kunsttheorie und -geschichte 282
- Literaturverzeichnis 425
- Namenregister 467
- Sachregister 470
