On an 8x8 field big chessboard eight Ladies have to be positioned, so two ladies can not beat each other.

A Dodekaeder is a platonic body, which surface consists out of twelve congruent pentagons. In this exhibit all vertices have to be connected. Where each edge can be visited just one time and the threads do not cross each other. The detected way is the classical „Hamilton-Weg”. That is a way round, which includes every intersection one time.

Squares or rectangular forms are fitting perfectly on each other and are able to cover complete areas. This is not possible with circles- you can only pack them as close as possible. Mathematicians are interested how to place a number of even panes, so they do not overlap each other but also have minimal spaces between them.