@conference {RicKor-CIDG-2002,
	title = {Complexity issues in Dynamic Geometry},
	booktitle = {Foundations of Computational Mathematics (Proceedings of the Smale Fest 2000)},
	year = {2002},
	note = {Also available as technical report TRB-2000/22, Freie Universit{\"a}t Berlin},
	publisher = {World Scientific},
	organization = {World Scientific},
	abstract = {<p>
	This article deals with the intrinsic complexity of tracing and reachability questions in the context of elementary geometric constructions. We consider constructions from elementary geometry as dynamic entities: while the free points of a construction perform a continuous motion the dependent points should move consistently and continuously. We focus on constructions that are entirely built up from join, meet and angular bisector operations. In particular the last operation introduces an intrinsic ambiguity: Two intersecting lines have two different angular bisectors. Under the requirement of continuity it is a fundamental algorithmic problem to resolve this ambiguity properly during motions of the free elements. After formalizing this intuitive setup we prove the following main results of this article: It is NP-hard to trace the dependent elements in such a construction. It is NP-hard to decide whether two instances of the same construction lie in the same component of the configuration space. The last problem becomes PSPACE-hard if we allow one additional sidedness test which has to be satisfied during the entire motion. On the one hand the results have practical relevance for the implementations of Dynamic Geometry Systems. On the other hand the results can be interpreted as statements concerning the intrinsic complexity of analytic continuation.</p>
},
	keywords = {refereed},
	author = {Richter-Gebert, J{\"u}rgen and Kortenkamp, Ulrich H.},
	editor = {Cucker, Felipe and Rojas, J. Maurice}
}
@inbook {KorRic-C-1999,
	title = {Das {C}inderella-{P}rojekt},
	booktitle = {Erfahrungen mit Java},
	year = {1999},
	pages = {381{\textendash}401},
	publisher = {dpunkt.verlag},
	organization = {dpunkt.verlag},
	chapter = {17},
	address = {Heidelberg},
	keywords = {refereed},
	url = {http://www.amazon.de/exec/obidos/ASIN/3932588339/theinteractive07},
	author = {Kortenkamp, Ulrich H. and Richter-Gebert, J{\"u}rgen},
	editor = {Maffeis, Silvano and Toenniessen, Fridtjof and Zeidler, Christian}
}
@conference {RicKor-DGPC-1999,
	title = {Dynamic Geometry {I}: The Problem of Continuity},
	booktitle = {Abstracts 15th European Workshop Comput. Geom.},
	year = {1999},
	pages = {51{\textendash}53},
	publisher = {INRIA Sophia-Antipolis},
	organization = {INRIA Sophia-Antipolis},
	keywords = {refereed},
	url = {http://www.cinderella.de/papers/antibes-1.pdf},
	author = {Richter-Gebert, J{\"u}rgen and Kortenkamp, Ulrich H.}
}
@conference {KorRic-DGA-1999,
	title = {Dynamic Geometry {II}: Applications},
	booktitle = {Abstracts 15th European Workshop Comput. Geom.},
	year = {1999},
	pages = {109{\textendash}111},
	publisher = {INRIA Sophia-Antipolis},
	organization = {INRIA Sophia-Antipolis},
	keywords = {refereed},
	url = {http://cinderella.de/papers/antibes-2.pdf},
	author = {Kortenkamp, Ulrich H. and Richter-Gebert, J{\"u}rgen}
}
@conference {KorRic-GEI-1998,
	title = {Geometry and education in the {I}nternet age},
	booktitle = {Ed-Media \& Ed-Telecom 98. Proceedings of the Tenth World Conference on Educational Multimedia and Hypermedia \& World Conference on Educational Telecommunications, Freiburg, Germany, June 20-25, 1998},
	year = {1998},
	publisher = {AACE},
	organization = {AACE},
	address = {Charlottesville},
	abstract = {<p>
	Interactive Geometry is a major tool in modern geometry education and various software tools are available. We discuss the requirements of such tools and how they can be fulfilled. We also explain how a geometry tool can benefit from the Internet and present Cinderella{\textquoteright}s Caf{\'e}, which is an internet-aware geometry tool with a high mathematical background.</p>
},
	keywords = {refereed},
	url = {http://www.cinderella.de/papers/geo-i.pdf.gz},
	author = {Kortenkamp, Ulrich H. and Richter-Gebert, J{\"u}rgen},
	editor = {Ottmann, Thomas and Tomek, Ivan}
}
