Geometry and the interplay of thought with the measurable, the abstract with the concrete.

Compact seminar together with Peter Bexte,
Gabriele Gramelsberger, and Karin Lingnau,
December 2013 in lab3.

Geometry is almost as old as mankind. It is literally about the survey of the earth itself. Therefore, there is a long pictorial tradition in operating geometry on the floor. But geometry is not just registering the given conditions we find at our feet, but constructing the world and world as an abstract.

David Hilbert’s work on the foundations of geometry in 1899, begins with the sentence: „Wir denken drei verschiedene Systeme von Dingen: die Dinge des ersten Systems nennen wir Punkte und bezeichnen sie mit A, B, C, …; die Dinge des zweiten Systems nennen wir Geraden und bezeichnen sie mit a, b, c, …; “ Key is: points, lines and planes exist nowhere in the world, we think of these things and only by thinking them will they become existent. Once they are but thought we can look for them in the world by measuring and constructing.

This interplay of thought with the measurable, the abstract with the concrete, is the basic form of geometry. We find them in mechanics, architecture, astronomy and surveying, but also in perspective drawing or music. Coordinate systems are just one example for applications on analog and digital levels, such as in computer games, GPS navigation systems and animation programs.

The seminar provides an overview of the evolution of geometry, beginning with the elements by Euklid (approx. 300 BC). Relevant geometric constructions will be experienced hands-on and with the necessary equipment like ruler, compass and other tools.