Die Sechseck-n-Waben in der Ebene, welche von n Kreisbüscheln erzeugt werden

Abstract

In this paper, the problem of determining the pencils of circles which form a hexagonal n-web in E2, is completely solved. It is well-known that n pencils of circles orthogonal to a fixed circle form a hexagonal n-web. Therefore, the main problem is the determination of all circle pencils which form a hexagonal n-web and which do not cut a fixed circle orthogonally. In this connection the following results have been obtained: The number of hexagonal 4-webs is six, whereas the number of hexagonal 5-webs is two. Finally, after having proved that the number of hexagonal 6-webs is one, it is shown that, for n⩾7, there exist no circle pencils forming a hexagonal n-web without being orthogonal to a fixed circle.