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The geometry history and epistemology


Jean-Pierre Friedelmeyer – Irem Strasbourg
Slideshow commented.

Summary – In 79 slides commented, this document traces the history of geometry from its origins Mesopotamian, Egyptian and Greek to non-Euclidean theories developed in the nineteenth century. The first part deals with the development of mathematical science as geometry, a second part deals with non-Euclidean geometry and introduces a new concept of geometry.
More than just history, it is an epistemological reflection on the relationship between mathematics and reality, which will interest both philosophers that mathematicians.
 * Text comments
 * Slides: introduction
 * Slides: Part I
 * Slides: Part II

Using class – This slide show was prepared in Terminale scientist at the joint request of Elizabeth ARBOGAST, professor of mathematics and Nafissa HAIDAR, professor of philosophy, both in high school Ribeaupierre of Ribeauvillé (Haut-Rhin). Initially, Mrs. Haidar had wanted a briefing on non-Euclidean geometry and from there, address issues of epistemology program class Terminale Scientifique. Very quickly, we have agreed on the following objective: to put in motion a dynamic of thinking that breaks with the disciplinary segregation, which brings students to say when mathematics: What is the meaning of what I do in math? Why is it an exact science? How was it built? What relationship with what I do in philosophy? And when they are being philosophy: What examples can I draw from my other learning, mathematics, physics, SVT, and so on. to embody the philosophical concepts to illustrate topics such as intuition, clear truth, accuracy, imagination, reality?

External Resources
Geometry in the twentieth century, 1930-2000: 49 videos recorded at the international symposium in Paris in 2001.
Inventing space, 15 videos recorded during an interdisciplinary symposium (MSH, Paris, 2006) on "The role of space in these various disciplines" and "borrowing mutual structure designs space in various disciplines."
Stories geometries I (videos, 2002)
Stories geometries II (videos, 2003)
Stories geometries III (videos, 2004)
Stories geometries IV (videos, 2005)
Stories geometries V (videos, 2006)
Henri Poincaré and the World Non-Euclidean, slide shows Etienne Ghys