Математика
Статья
  • формат pdf
  • размер 404.34 КБ
  • добавлен 22 декабря 2011 г.
Imagination and Layered Ontology in Greek Mathematics Reviel Netz
Configurations.
Volume 17, Numbers 1-2, Winter 2009.
pp. 19-50.

Subject Headings:
Mathematics, Greek - Philosophy.
Imagination (Philosophy).

Abstract:
This essay is a study in the routine use of imagination in Greek mathematical writings. By "routine" is meant both that this use is indeed very common, and that it is ultimately mundane. No flights of fancy, no poetical-like imaginative licenses are at stake. The issue rather is the systematic use made of the ability to imagine a virtual presence, and to refer to this virtual presence as if it were on equal footing with the real. This process is not merely routine in Greek mathematics: it may well be considered one of its chief characteristics. In this essay, I describe some features of this practice in detail, and then briefly offer some interpretative comments on the history and philosophy of this practice. The emphasis, however, is on the description, and I concentrate mainly on one key element—the use of the Greek verb noein. Thus the structure of the essay is as follows: part 1 is an analysis of noein in Greek mathematical writings; part 2 is a less-detailed description of other practices of Greek mathematics that involve "imagination" or, in general, a "layered" reality; and part 3 is a tentative interpretation.
Похожие разделы
  1. Академическая и специальная литература
  2. Военные дисциплины
  3. Баллистика и динамика выстрела
  1. Академическая и специальная литература
  2. Исторические дисциплины
  3. История науки и техники
  1. Академическая и специальная литература
  2. Концепции современного естествознания (КСЕ)
  1. Академическая и специальная литература
  2. Математика
  3. Периодика по математике
  4. Историко-математические исследования
  1. Академическая и специальная литература
  2. Математика
  3. Философия математики
  1. Академическая и специальная литература
  2. Транспорт
  3. Судостроение
  4. Теория корабля, ТУС, устройство и живучесть судов
  1. Академическая и специальная литература
  2. Физика
  3. Астрономия и астрофизика
  1. Академическая и специальная литература
  2. Физика
  3. Механика
  1. Академическая и специальная литература
  2. Философские дисциплины
  3. История философии
  1. Академическая и специальная литература
  2. Философские дисциплины
  3. Философия науки и техники
  1. Документальная литература
  2. Жизнь выдающихся людей
  3. Ученые, изобретатели, деятели науки
Смотрите также

Bernhard Riemann's Conceptual Mathematics and the Idea of Space - Arkady Plotnitsky

Статья
  • формат pdf
  • размер 307.8 КБ
  • добавлен 22 декабря 2011 г.
Configurations. Volume 17, Numbers 1-2, Winter 2009. pp. 105-130. Subject Headings: Riemann, Bernhard, 1826-1866. Mathematics. Abstract: This essay explores the power and fertility of mathematical imagination, as they are manifest in the thought of a nineteenth-century German mathematician Bernhard Riemann (1826–1866), one of the greatest and most imaginative mathematicians who ever lived. Riemann introduced radically new ideas in every main...

Hirsch C.R., Fey J.T., Hart E.W. et al. Core-Plus Mathematics

  • формат pdf
  • размер 24.05 МБ
  • добавлен 07 января 2011 г.
Glencoe, 2008. - 622 pages. Core-Plus Mathematics, is a standards-based, four-year integrated series covering the same mathematics concepts students learn in the Algebra 1-Geometry-Algebra 2-Precalculus sequence. Concepts from algebra, geometry, probability, and statistics are integrated, and the mathematics is developed using context-centered investigations. Developed by the CORE-Plus Math Project at Western Michigan University with funding...

Hirsch Ch.R., Fey J.T., Hart E.W., Schoen H.L., Watkins A.E. (Eds.) Core-Plus Mathematics: Contemporary Mathematics In Context

  • формат pdf
  • размер 35.77 МБ
  • добавлен 01 января 2012 г.
Course 2, 2 Edition, Glencoe/McGraw-Hill, 2008, 625 pages Core-Plus Mathematics, is a standards-based, four-year integrated series covering the same mathematics concepts students learn in the Algebra 1-Geometry-Algebra 2-Precalculus sequence. Concepts from algebra, geometry, probability, and statistics are integrated, and the mathematics is developed using context-centered investigations. Developed by the CORE-Plus Math Project at Western Mi...

Lautman A. Mathematics, Ideas and the Physical Real

  • формат pdf
  • размер 1.25 МБ
  • добавлен 18 октября 2011 г.
Continuum, 2011. - 352 pages. Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first...

Malloy C.E., Molix-Bailey R.J., Price J. Pre-Algebra

  • формат pdf
  • размер 62.38 МБ
  • добавлен 15 мая 2011 г.
Glencoe/McGraw-Hill, 2007. - 792 pages. Glencoe Pre-Algebra is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today’s high-stakes assessments. As you gear up to study mathematics, you are probably wondering, What will I learn this year? There are three focal points this year: Use basic principles of alge...

Mathematics and the Imagination: A Brief Introduction, by Arielle Saiber Henry S. Turner

  • формат pdf
  • размер 296.97 КБ
  • добавлен 22 декабря 2011 г.
Configurations, 2009, 17:1–18 © 2010 by The Johns Hopkins University Press and the Society for Literature and Science. Subject Headings: Mathematics - Philosophy. Imagination (Philosophy) In lieu of an abstract, here is a preview of the article. "[I]f mathematics is the study of purely imaginary states of things, poets must be great mathematicians." —Charles Sanders Peirce 1 I prove a theorem and the house expands: the windows jerk free to hov...

McKeague C.P. Basic College Mathematics: A Text/Workbook

  • формат pdf
  • размер 32.16 МБ
  • добавлен 08 октября 2011 г.
Brooks Cole, 2010. - 538 pages. 3 edition Learning basic mathematics is easy and engaging with this combined text/workbook! "Basic College Mathematics" is infused with Pat McKeague's passion for teaching mathematics. With years of classroom experience, he knows how to write in a way that you will understand and appreciate. McKeague's proven "EPAS" approach (Example, Practice Problem, Answer, and Solution) moves you through each new concept with...

Resnik M.D. Mathematics As a Science of Patterns

  • формат pdf
  • размер 29.45 МБ
  • добавлен 07 мая 2011 г.
Oxford University Press, 1997. - 304 pages. This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He...

Schleicher D., Lackmann M. (editors) An Invitation to Mathematics: From Competitions to Research

  • формат pdf
  • размер 4.37 МБ
  • добавлен 26 мая 2011 г.
Springer, 2011. - 244 pages. This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transitio...

Sriraman B., English L. Theories of Mathematics Education: Seeking New Frontiers

  • формат pdf
  • размер 3.02 МБ
  • добавлен 12 января 2011 г.
Springer, 2009. - 668 pages. This inaugural book in the new series Advances in Mathematics Education is the most up to date, comprehensive and avant garde treatment of Theories of Mathematics Education which use two highly acclaimed ZDM special issues on theories of mathematics education (issue 6/2005 and issue 1/2006), as a point of departure. Historically grounded in the Theories of Mathematics Education (TME group) revived by the book editors...