# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics
**Prof. Dr. Adolf
Karger Dr. Sc.**, Department of Mathematics Education, Mathematical Institute of Charles University,
will give a public talk (followed by a discussion) on **Wed, May 18, 2005**
at **15:00 o'clock** at **HS 9**
on the topic of
"Computer proofs of geometric theorems"
. The organziers of the symposium,

Univ.-Prof. Dr. Gerhard Larcher

A.Univ.-Prof. Dr. Jürgen Maaß, and

die ÖMG (Österreichische Mathematische Gesellschaft),

hereby cordially invite you.

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.