Differential Geometry and Geometric Structures

Hellmuth Stachel

Full Professor

Institut für Diskrete Mathematik und Geometrie
Forschungsgruppe Differentialgeometrie und Geometrische Strukturen
Technische Universität Wien
Wiedner Hauptstraße 8-10/104
A-1040 Wien, Austria

Phone	(+43)-(0)1-58801/11320
Fax	(+43)-(0)1-58801/11399
Email	stachel@geometrie.tuwien.ac.at
Room	DA 08 L02 (8th floor)

Curriculum Vitae

Mag. rer. nat., Univ. Graz, 1965
Dr. phil. in Mathematics, Univ. Graz, 1969
Universitätsassistent, Institut für Geometrie, TU Graz, 1967-1976
Habilitation in Geometry, TU Graz, 1971
Associate Professor for Geometry, TU Graz, 1976-1978
Professor for Geometry, Mining University Leoben, 1979-1980
Professor for Geometry, TU Wien, since 10/1980
Corresponding member, Austrian Academy of Sciences, since 1991
Editor in Chief of the 'Journal for Geometry and Graphics', since 1997
Winner of the Steve M. Slaby Award 2004

Research Interests

Theory of Linear Mappings
Classical Geometry and its Applications
Descriptive Geometry
Computer Aided Design
Kinematics
Flexible Polyhedra
Geometry of Mechanisms
Elementary Geometry

Publications

List of publications

Teaching Activities

Courses for Students of Mechanical Engineering
- Geometric Kinematics
Courses for Students of Geometry and Mathematics
- Geometric Modelling and Visualisation
- Projective Geometry
- Linear Algebra
- Kinematics
- Geometric Mappings
- Non-Euclidean Geometry
- Algebraic Curves
- Geometry Seminar

Selected Recent Publications

Remarks on Miura-ori, a Japanese Folding Method. Acta Technica Napocensis, Ser. Applied Mathematics and Mechanics 52 (2009), Vol. Ia (ISSN
1221-5872), pp. 245-248
The Computational Fundamentals of Spatial Cycloidal Gearing (with G. Figliolini and J. Angeles). In A. Kecskemèthy, A. Müller (eds.): Computational Kinematics, Springer, Berlin Heidelberg 2009, (ISBN: 978-3-642-01946-3, e-ISBN: 978-3-642-01947-0), pp. 375-384
Mathematik (with T. Arens, F. Hettlich, Ch. Karpfinger, U. Kockelkorn, and K. Lichtenegger). 1. Aufl., Spektrum Akademischer Verlag, Heidelberg 2008, 1500 p. (ISBN 978-3-8274-1758-9)
Another cubic associated with the triangle (with S. Abu-Saymeh and M. Hajja). J. Geom. Graphics 11, 15-26 (2007)
A new look at the Ball-Disteli diagram and its relevance to spatial gearing (with G. Figliolini and J. Angeles). Mech. Mach. Theory 42/10, 1362-1375 (2007)
Descriptive Geometry Meets Computer Vision - The Geometry of Two Images. J. Geometry Graphics 10, 137-153 (2006)
Flexible Octahedra in the Hyperbolic Space. In A. Prekopa, E. Molnár (eds.): Non-euclidean geometries: János Bolyai memorial volume, Mathematics and its applications, vol. 581, Springer, New York 2006, (ISBN 978-0-387-29554-1) pp. 209-225
Descriptive Geometry in today's engineering curriculum. Transactions of FAMENA 29/2, 35-44 (2005)
Teaching Spatial Kinematics for Engineers. Proc. ICEE 2005, Gliwice/Poland, vol. 2, 845-851
Schraubtorsen als Zahnflanken. Informationsblätter der Geometrie 23, Heft 2, 46-50 (2004)
On Arne Dür's equation concerning central axonometries. J. Geometry Graphics 8, 215-224 (2004)
Ivory's theorem in hyperbolic spaces (with J. Wallner). [Preprint: Technical Report No. 107, September 2003] Sib. Math. J. 45, no. 4, 785-794 (2004). russ: Sib. Mat. Zh.45, no. 4, 946-959
On Jack Phillips' Spatial Involute Gearing. Proc. 11th ICGG,Guangzhou/China, August 1-5, 2004 (ISBN 5-8037-0184), 43-48
On Spatial Involute Gearing. [Geometry Preprints no. 119, March 2004] Proc. 6th ICAI, Eger/Hungary, January 27-31, 2004 (to appear)
What is Descriptive Geometry for? Proc. DSG-CK Dresden Symposium Geometrie: konstruktiv & kinematisch, TU Dresden 2003 (ISBN 3-86005-394-9), 327-336 (2003)
Remarks on A. Hirsch's Paper concerning Villarceau Sections. J. Geometry Graphics 6, 133-139 (2002)
Configuration Theorems on Bipartite Frameworks. Rend. Circ. Mat. Palermo, II. Ser., 70, 335-351 (2002)
Napoleon's Theorem and Generalizations Through Linear Maps. Beitr. Algebra Geom.43, 433-444 (2002) [Preprint ]
Remarks on Bricard's Flexible Octahedra of Type 3. Proc. 10th ICGG, Kiev (Ukraine), July 28 - Aug. 3, 2002: Vol. 1, 8-12
Ivory's theorem in the Minkowski Plane. Math. Pannon. 13, 11-22 (2002) [Preprint Technical Report No. 85, Oct. 2001]
A way to geometry through descriptive geometry. Applied Geometry and Engineering Graphics, Kyiv, 70, 14-19 (2002)
Flexible Cross-Polytopes in the Euclidean 4-Space. J. Geometry Graphics 4, 159-167 (2000)
Das Gleichlauf-Kugelgelenk - ein Beispiel zum anwendungsorientierten Unterricht aus Darstellender Geometrie. Proceedings SDG Symposium Darstellende Geometrie, Dresden 2000, 151-156
Instantaneous spatial kinematics and the invariants of the axodes. Proceedings Ball 2000 Symposium, Cambridge 2000, no. 23, 14 p.

Recent Talks

275 Flexible Kokotsakis Meshes
Sept. 21, 2009: ÖMG-DMV Congress, Sept. 20-25, 2009, Graz/Austria
270 The Computational Fundamentals of Spatial Cycloidal Gearing
May 8, 2009: Computational Kinematics 2009, May 6-9, Duisburg/Germany
267 Falten und Verebnen polyedrischer Figuren
[Folding and unfolding polyhedra] Nov. 4, 2008: 29. Fortbildungstagung für Geometrie, Nov. 3-6, 2008, Strobl/Austria
264 Gears and belt drives for non-uniform transmission
Sept. 18, 2008: EUCOMES08 - Second European Conference on Mechanism Science, Sept. 17-20, 2008, Cassino/Italy
262 Comments on helical developables
Aug. 4, 2008: 13th ICGG - Internat. Conference on Geometry and Graphics, Aug. 4-8, 2008, Dresden/Germany
257 A proposal for a proper definition of higher-order rigidity
July 13, 2007: Tensegrity Workshop 2007, July 9-13, 2007, La Vacquerie/France
256 The geometry behind the numerical reconstruction of two photos
June 8, 2007: ICEGD 2007, 2nd International Conference on Engineering Graphics and Design, June 7-10, Galati/Romania
255 From Rytz to the covariance ellipsoid
June 5, 2007: Conference on Geometry: Theory and Applications, June 3-8, Vorau/Austria
254 The Status of Todays Descriptive Geometry Related Education (CAD/CG/DG) in Europe
May 12, 2007: 40th anniversary of the Japan Society for Graphics Science, May 12-13, The University of Tokyo
247 On Martin Disteli's Main Achievements in Spatial Gearing: Disteli's Diagram
Feb. 22, 2006: EuCoMeS - 1st European Conference on Mechanism Science, Obergurgl/Austria