ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

18. Teaching and Popularization of Mathematics

1991 MS Classification: 51M04 Fritsch, Rudolf, Universität München, Deutschland Remarks on quadrangles A classification scheme for the most common convex quadrangles, a so-called house of quadrangles is discussed. There appears a gap in the systematic treatment which has to be filled with an “exquadrangle”, ie, a quadrangle having an excircle; that is a circle touching the supporting lines of all four sides of the quadrangle whose center is outside the quadrangle (not a new notion, but rather unknown). A characterization by diagonal segments and the diagonal angle leads to interesting results concerning quadrangles having an incircle and/or an excircle. Theorem: In every class of convex quadrangles with given diagonal segments there is up to congruence exactly one circumscribed quadrangle and at most one exquadrangle.