Johannes Kepler Symposium für Mathematik

Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird Prof. Dr. Adolf Karger Dr. Sc., Department of Mathematics Education, Mathematical Institute of Charles University, am Wed, May 18, 2005 um 17:00 Uhr im HS 9 einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "Computer proofs of geometric theorems" halten, zu dem die Veranstalter des Symposiums,

O.Univ.-Prof. Dr. Ulrich Langer,
Univ.-Prof. Dr. Gerhard Larcher
A.Univ.-Prof. Dr. Jürgen Maaß, und
die ÖMG (Österreichische Mathematische Gesellschaft)

hiermit herzlich einladen.

Series A - General Colloquium:

The intention is to present general information not only to experts, but also to students and guests from outside the mathematical institutes.

Computer proofs of geometric theorems

We shall discuss problems motivated by the geometry of parallel manipulators. We describe the concept of a singular position of such a manipulator. Singular positions of parallel manipulators have very simple geometric characterization and they are projectively invariant.

The general equation for singular positions is too large to be of any use (about 10^6 terms), but using computer algebra we can prove some purely geometric theorems for some special cases of parallel manipulators.