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.
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Literaturhinweise
BLASCHKE, W.: Einführung in die Geometrie der Waben. Basel 1955
ERDOGAN, H.İ.: Triples of circle-pencils forming a hexagonal three-web in E2. J.of Geometry35 (1989), 39–65
KRAMES, J. L.: Vorlesungen über darstellende Geometrie, Band II. (die Zyklographie). Leipzig und Wien 1929
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Erdoğan, H.İ. Die Sechseck-n-Waben in der Ebene, welche von n Kreisbüscheln erzeugt werden. J Geom 40, 47–59 (1991). https://doi.org/10.1007/BF01225871
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DOI: https://doi.org/10.1007/BF01225871