________For pictures of more workshops please go to Gallery page under Workshops 

Lecture and workshop in Lowicz, Poland. Feb. 04. 

XIII National Conference of the Polish Association of Teachers of Mathematics

An ongoing workshop was open 24 hours a day for three days, where people could share and explore many types of hands-on math games, puzzles, geometric model making of all kinds, paper cutting, and folding circles.

The pictures below were taken during a lecture/workshop session. Notice the four balls of yarn demonstrating the arrangement they are trying to figure out with the spheres they have made.


Participants in groups of four folded and joined four circles into a spherical vector equilibrium. Here the groups are trying to figure out how to arrange four spheres to form a tetrahedron pattern.


Below: the arrangement shows the two-frequency tetrahedron revealed in the relationship of the center points of the four tangent spheres. The octahedron is the space between the spheres defined by the six points of connection, making a total of 10 points defining the full tetrahedron arrangement. They observed that all four spheres have to be consistantly in the same orientation. They found much to think about in this arrangement of the closest packing of spheres.   


                                                            Photos by Margaret Fryska