Jürgen Richter-Gebert/Publikationen

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  • J. Richter: “Kombinatorische Realisierbarkeitskriterien f ̈ur orientierte Matroide”. Mitteilungen aus dem Math. Sem. Gießen, 194 (1989) 113 p.
  • J. Bokowski & J. Richter: “On the finding of final polynomials”. Europ. J. Combinatorics, 11 (1990) 21–34.
  • J. Bokowski, J. Richter & B. Sturmfels: “Nonrealizability proofs in computational geometry”. Discrete Comput. Geometry, 5 (1990) 333–350.
  • J. Bokowski, A. Guedes de Oliveira & J. Richter-Gebert: “Algebraic Varieties Characterizing Matroids and Oriented Matroids”. Advances in Math., 87 (1991) 160–185.
  • J., Richter & B. Sturmfels: “On the topology and geometric construction of oriented matroids and convexpolytopes”. Trans. Amer. Math. Soc., 325 (1991) 389–412.
  • J. Bokowski & J. Richter-Gebert: “A new Sylvester-Gallai configuration representing the 13-point projectiveplane in R4”. J. Comb. Theory, B 54 (1992) 161–165.
  • J. Bokowski, J. Richter-Gebert & W. Schindler: “On the distribution of order types”. Computational Geometry: Theory and Applications, 1 (1992) 127–142.
  • J. Richter-Gebert: “Euclideaness and final polynomials in oriented matroid theory”. Combinatorica, 13 (1993)259–268.
  • N. Mn ̈ev & J. Richter-Gebert: “Two constructions of oriented matroids with disconnected extension space”. Discrete Comput. Geometry, (special issue: ”Oriented Matroids“ , eds. J. Richter-Gebert, G.M. Ziegler), 10 (1993) 271–285.
  • J. Richter-Gebert: “Oriented matroids with few mutations”. Discrete Comput. Geometry, (special issue: ”Oriented Matroids“ , eds. J. Richter-Gebert, G.M. Ziegler), 10 (1993) 251–269.
  • J. Richter-Gebert: “Combinatorial obstructions to the lifting of weaving diagrams”. Discrete Comput. Ge- ometry, (special issue: ”Oriented Matroids“ , eds. J. Richter-Gebert, G.M. Ziegler), 10 (1993) 287–312.
  • J. Richter-Gebert: “Line arrangements and zonotopal tilings: A little printer exercise”. Hyperspace, 2 (1993) 8–17.
  • J. Richter-Gebert & G.M. Ziegler: “Zonotopal tilings and the Bohne-Dress Theorem”. Contemporary Mathe- matics, 178 (1994) 211–232.
  • J. Richter-Gebert: “Mechanical theorem proving in projective geometry”. Annals of Mathematics and Artifi- cial Intelligence, 13 (1995) 139–172.
  • J. Richter-Gebert: “Mn ̈ev’s universality theorem revisited”. S ́eminaire Lotharingien de Combinatoire, 1995, 211–225.
  • J. Richter-Gebert & G.M. Ziegler: “Realization spaces of 4-polytopes are universal”. Bulletin of the AMS (research report), 32 (1995) 403–412.
  • H. Crapo & J. Richter-Gebert: “Automatic proving of geometric theorems”. in: “Invariant Methods in Discrete and Computational Geometry”, Neil White ed., Kluwer Academic Publishers (1995).
  • J. Richter-Gebert: “Two Interesting Oriented Matroids”. Doc. Math. J. DMV, 1 (1996) 149–197.
  • U.H. Kortenkamp, J. Richter-Gebert, A. Sarangarajan & G.M. Ziegler: “Extremal properties of 0/1-polytopes”. Discrete & Computational Geometry, 17 (1997) 439–448.
  • J. Richter-Gebert & G.M. Ziegler: “Oriented Matroids”. CRC Handbook on “Discrete and Computational Geometry” (J.E. Goodman, J. O’Rourke, eds.) pp. 111–132, CRC Press, Boca Raton, New York (1997).
  • M. Henk, J. Richter-Gebert & G.M. Ziegler: “Basic properties of convex polytopes”. CRC Handbook on “Discrete and Computational Geometry” (J.E. Goodman, J. O’Rourke, eds.) pp. 243–270, CRC Press, Boca Raton, New York (1997).
  • U.H. Kortenkamp & J. Richter-Gebert: “Geometry and Education in the Internet Age”. ED-MEDIA World Conference on Educational Multimedia, Hypermedia and Telecommunications, pp. 790-799., (1998).
  • J. Richter-Gebert: “Universality Theorems for Oriented Matroids and Polytopes”. Contemporary Mathematics, 223 (1999) 269–292.
  • U.H. Kortenkamp & J. Richter-Gebert: “Cinderella”. in: Erfahrungen mit Java, Silvano Maffeis, Fridtjof Toenniessen, Christian Zeidler (eds), dpunkt.verlag, pp 383-407, (1999).
  • J. Richter-Gebert: “Orientability of matroids is NP-complete”. Advances in Applied Mathematics (special issue: “in the honor of Henry Crapo” , ed. J. Kung), 23 (1999) 78–90.
  • U. Kortenkamp & J. Richter-Gebert: “Dynamic geometry I: The problem of continuity”. In Abstracts 15th Europ. Workshop Comput. Geom. Herve Br ̈onniman (ed.), INRIA Sophia-Antipolis, 1999, 51–53.
  • U. Kortenkamp & J. Richter-Gebert: “Dynamic geometry II: Applications”. In Abstracts 15th Europ. Work- shop Comput. Geom. Herve Br ̈onniman (ed.), INRIA Sophia-Antipolis, 1999, 109–111.
  • A. Below, J. De Loera & J. Richter-Gebert: “Finding minimal triangulations of convex 3-polytopes in NP-hard (Extended Abstract)”. Proceedings of the eleventh annual ACM-SIAM symposium on discrete algorithms (SODA 2000), 2000, 65–66.
  • A. Below, U. Brehm, J. Richter-Gebert, J. De Loera: “Minimal simplicial dissections and triangulations of convex 3-polytopes”. Discrete & Computational Geometry, 24 (2000) 35–48.
  • J. Richter-Gebert & U. Kortenkamp: “Cinderella — Nachmittagssoftware im Unterricht”. Rundgang, Ausgabe f ̈ur Lehrerinnen und Lehrer aller Stufen, Klett und Balmer Verlag, Zug, 25 (2000) 6–7.
  • J. Richter-Gebert: “Finding small triangulations of polytope boundaries is hard”. Discrete & Computational Geometry, 24 (2000) 502–518.
  • U.H. Kortenkamp & J. Richter-Gebert: “Euklidische und Nicht-Euklidische Geometrie in Cinderella”. Journal f ̈ur Mathematik-Didaktik, B.G. Teubner,, 21 (2000) 303–324.
  • J. Richter-Gebert & U.H. Kortenkamp: “Dynamic Aspects in Computational Geometry (Extended Abstract)”. Proceedings of the EACA 2000, Barcelona, 2000, 51–61.
  • J. Richter-Gebert: “Dynamische Geometrie Grundlagen und M ̈oglichkeiten”. SATW Fachtagung 2000 – Neue Medien im Unterricht, Polygon Verlag, St. Gallen, 2001, 34–43.
  • U.H. Kortenkamp & J. Richter-Gebert: “Decision Complexity in Dynamic Geometry”. In: Automated Deduc- tion in Geometry, J. Richter-Gebert, D. Wang (eds), Springer Lecture Notes in Artificial Intelligence 2061, Springer Heidelberg, pp 216-220, (2001).
  • U. Kortenkamp & J. Richter-Gebert: “Grundlagen Dynamischer Geometrie”. In Zeichnung — Figur — Zug- figur Mathematische und didaktische Aspekte Dynamischer Geometrie-Software H.-J. Elschenbroich, Th. Gawlick, H.-W. Henn (eds.) , Verlag Franzbecker, pp 123–145, (2001).
  • U.H. Kortenkamp & J. Richter-Gebert: “A dynamic setup for elementary geometry”. In Proceedings of MTCM 2000, Multimedia Tools in Comunicating Mathematics, J. Borwein, M.H. Morales, K. Polthier, (eds.), Springer Heidelberg, pp 203–221, (2002).
  • U. Kortenkamp & J. Richter-Gebert: “Complexity issues in dynamic geometry”. In Festschrift in the honor of Stephen Smale’s 70th birthday, M. Rojas, F. Cucker (eds.), World Scientific, pp 355–404, (2002).
  • U. Kortenkamp & J. Richter-Gebert: “Making the move: The next version of Cinderella”. Proceedings of the First International Congress of Mathematical Software In Arjeh M. Cohen, Xiao-Shan Gao, and Nobuki Takayama, (eds), World Scientific. , pp 208–216 (2002).
  • A. Below, V. Krummeck & J. Richter-Gebert: “Matroids with complex coefficients – phirotopes and their realizations in rank 2”. In Discrete and Computational Geometry – The Goodman-Pollack Festschrift” B. Aronov, S. Basu, J. Pach, M. Sharir (eds), Algorithms and Combinatorics 25, Springer Verlag, Berlin, pp. 205-235., (2003).
  • A. Below, J. de Loeara & J. Richter-Gebert: “The complexity of finding small triangulations of convex 3- polytopes”. Journal of Algorithms, 50 (2004) 134–167.
  • J. Richter-Gebert: “Aschenputtel und die Perlen”. DMV Mitteilungen, 12-1 (2004) 21–29.
  • U. Kortenkamp & J. Richter-Gebert: “Mathematik in der Architektur Formgebung, Formfindung, Formver- wirklichung”. aviso - Zeitschrift f ̈ur Wissenschaft und Kunst in Bayern, (2004) 26–33 — also apeared in Pi and Co. Hrsg. Behrends, Gritzmann and Ziegler, pp 342–349, Springer (2008).
  • U. Kortenkamp & J. Richter-Gebert: “Using automatic theorem proving to improve the usability of geometry software”. Proceedings of MathUI, 2004, (online publication).
  • J. Richter-Gebert, B. Sturmfels, & T. Theobald: “First steps in tropical geometry”. Contemporary Math, 377 (2005) 289–318.
  • J. Richter-Gebert: “Mathematik spielend lernen”. In: Eva Hammes-Di Bernardo, Sabine Hebenstreit-M ̈uller (Hrsg.): (Innovationsprojekt Fr ̈uhpdagogik. Professionalit ̈at im Verbund von Praxis, Forschung, Aus- und Weiterbildung. pfv-Jahrbuch 10.) Baltmannsweiler: Schneider Verlag Hohengehren, 2005, 12p.
  • J. Richter-Gebert: “Cinderella.2 – an ǫ before release”. Oberwolfach Report, 17 (2005) 968–971.
  • V. Krummeck & J. Richter-Gebert: “Mathematik begreifen”. Welt des Kindes, 04 (2005) Sonderbeilage 1–8.
  • P. Lebmeir & J. Richter-Gebert: “Recognition of computationally constructed loci”. Proceedings of the ADG 2006 conference, 2006, 12p.
  • J. Richter-Gebert: “Meditations on Ceva’s Theorem”. In The Coxeter Legacy: Reflections and Projections (Eds. Chandler Davis & Eric Ellers, American Mathematical Society, Fields Institute), 227–254, 2006.
  • J. Richter-Gebert : “Ein Drunter und Dr ̈uber - Mathematik von statischen Konstruktionen spielerisch erfahren”. Wissen & Wachsen, Schwerpunktthema Mathematik & mathematische Fo ̈rderung, Praxis. Verf ̈ugbar ̈uber: http://www.wissen-und-wachsen.de, (2006).
  • J. Richter-Gebert : “Blicke in die Unendlichkeit”. In Alles Mathematik (Eds. Martin Aigner & Ehrhard Behrends, Vieweg & Teubner), 125–149, (2008).
  • U. Kortenkamp & J. Richter-Gebert: “Cinderella.2 – Geometrie und Physik im Dialog”. In: Computeralgebra- Rundbrief, Sonderheft zum Jahr der Mathematik , 12 – 14, (2008).
  • P. Lebmeir & J. Richter-Gebert: “Rotations, Translations and Symmetry Detection for Complexified Curves”. Computer Aided Geometric Design (special issue Classical Techniques for Applied Geometry), 25 (2008) 707–719.
  • J. Richter-Gebert: “Realization spaces of Polytopes”. Lecture Notes in Mathematics 1643, Springer Verlag,Heidelberg; 187 pages, (1997).
  • J. Richter-Gebert & U.H. Kortenkamp: “Cinderella – The interactive geometry software”. Springer, Heidelberg, 143 pages + CD-Rom, (1999); also: German (2000), Portuguese (2001), Italian (2001), Greek (2002), and Japanese (2003) translations.
  • J. Richter-Gebert & U.H. Kortenkamp: “Cinderella – Die Interaktive Geometriesoftware (Sch ̈ulerversion)”. (Software + Manual 80 pages) Heureka-KLETT, Stuttgart, (2000).
  • J. Richter-Gebert & Dongming Wang (eds): “Automated Deduction in Geometry”. Proceedings of the ADG 2000 workshop, Springer Lecture Notes in Artificial Intelligence 2061, Springer Heidelberg, 323 pages, (2001).
  • J. Richter-Gebert & U.H. Kortenkamp: “Cinderella.2”. Online download at www.cinderella.de, documen- tation at docs.cinderella.de, (2006).