**No Thresholds, no Ceilings in
GEOMLAND **

*Bojidar Sendov
Faculty of Mathematics and Informatics
Sofia University, Bulgaria
5 James Bourchier blvd.,
Sofia 1164, Bulgaria
tel/fax (+359-2) 68 71 80*

The goals of the workshop will be to provide the participants with tools for exploring geometric constructions in GEOMLAND - a Logo-based environment of a laboratory type. The emphasis will be on the recursion in the context of Eucledean Geometry. The following topics will be considered:

Breef introduction in GEOMLAND:

- Constructing points,lines, segments, rays, circles etc.;
- Defining procedures.

Definition of "new" mathematical notions: angle bisector, altitude, medicenter, etc.

Exploring properties of sequence of triangles and inscribed circles

What are the trees in GEOMLAND?

Definition of inversion and problems using inversion ("trains of circles")

Demonstration of some interesting models: pendulum, billiard, Galton board.

The importance of the programming language for discussing different approaches in problem solving will be illustrated.