Differential Geometry and Geometric Structures

Hellmuth Stachel

Professor emeritus

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)1-58801/10434
Email	stachel@dmg.tuwien.ac.at
Room	DA 08 L08 (8th floor)

Emeritation 2011

Curriculum Vitae

Mag. rer. nat., University of Graz, 1965
Dr. phil. in Mathematics, University of Graz, 1969
Universitätsassistent, Institut für Geometrie, Graz Univ. of Tech., 1967-1976
Habilitation in Geometry, Graz University of Technology, 1971
Associate Professor for Geometry, Graz Univ. of Technology, 1976-1978
Professor for Geometry, Mining University Leoben, 1979-1980
Professor for Geometry, Vienna University of Technology, 10/1980 - 9/2011
Corresponding member, Austrian Academy of Sciences, since 1991
Editor in Chief of the 'Journal for Geometry and Graphics', 1997-2020
Winner of the Steve M. Slaby Award 2004
Dr.rer.nat. h.c., Technische Universität Dresden, Nov. 2010
Emeritation from Vienna Univ. of Technology, Sept. 30, 2011
Honorary President of the International Society for Geometry and Graphics, Aug. 2018
Golden Doctor, University of Graz, May 2019

Research Interests

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

Publications

List of publications

2007

Former 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

Ivory's Theorem

Ivory

Thread construction

Selected Recent Publications

G. Glaeser, H. Stachel, and B. Odehnal. The Universe of Conics, 2nd ed., Springer Spektrum, Heidelberg 2024, 580 p., 422 illus. (ISBN 978-3-662-70305-2, 978-3-662-70306-9 (eBook))
H. Stachel. The design of skew gears from the geometric point of view. In I. Bajšanski, M. Jovanović (eds.): Geometry, Graphics and Design in the Digital Age. Proceedings MoNGeometrija2023, Faculty of Technical Sciences, University of Novi Sad (ISBN 978-86-6022-575-9), pp. 217-228.
T. Arens, F. Hettlich, Ch. Karpfinger, U. Kockelkorn, K. Lichtenegger und H. Stachel. Mathematik, 5. Aufl., Springer Spektrum, Heidelberg 2022, 1666 p. (ISBN 978-3-662-64388-4, 978-3-662-64389-1 (eBook))
H. Stachel. On the Motion of Billiards in Ellipses. Europ. J. Math. 8/4 (Special Issue: New Developments in Integrable Systems) 1602-1622 (2022), DOI 10.1007/s40879-021-00524-2
T. Arens, R. Busam, F. Hettlich, Ch. Karpfinger and H. Stachel. Grundwissen Mathematikstudium - Analysis und Lineare Algebra mit Querverbindungen, 2nd edition, Springer Spektrum, Berlin 2021, 1182 p., 684 illus. (ISBN 978-3-662-63312-0, 978-3-662-63313-7 (eBook))
H. Stachel. The Geometry of Billiards in Ellipses and their Poncelet Grids. J. Geom. 112:40 (2021), DOI 10.1007/s00022-021-00606-2
H. Stachel. Isometric Billiards in Ellipses and Focal Billiards in Ellipsoids. J. Geom. Graphics 25/1, 97-118 (2021).
H. Stachel. Recalling Thread Constructions of Quadrics. J. Geom. Graphics 24/2, 143-157 (2020).
Ch. Karpfinger und H. Stachel. Lineare Algebra, Springer Spektrum, Berlin 2020, 431 p. (ISBN 978-3-662-61339-9, 978-3-662-61340-5 (eBook))
B. Odehnal, H. Stachel, and G. Glaeser. The Universe of Quadrics, Springer-Verlag GmbH Germany, Berlin Heidelberg 2020, 606 p., 365 illus. (ISBN 978-3-662-61052-7, 978-3-662-61053-4 (eBook))
H. Stachel. The Evolution of Descriptive Geometry in Austria. In É. Barbin, M. Menghini, K. Volkert (eds): The Spread of a Polytechnic Art (The Legacy of Gaspard Monge), Springer 2019, pp. 181-195.
G. Figliolini, H. Stachel, and J. Angeles. Kinematic Properties of Planar and Spherical Logarithmic Spirals: Applications to the Synthesis of Involute Tooth Profiles. Mech. Mach. Theory 136, 14-26 (2019).

Senj 2024

Bologna 2018

Recent Talks

357 Canal surfaces containing four straight lines.
Sept. 2, 2024: 24th Scientific-Professional Colloquium on Geometry and Graphics, Sept. 1-5, 2024, Senj/Croatia
351 On the Diagonals of Billiards.
Aug. 15, 2022: 20th International Conference on Geometry and Graphics (online), Aug. 15-19, 2022, São Paulo/Brazil
349 Billiards in ellipses and ellipsoids.
Sept. 8, 2021: 22nd Scientific-Professional Colloquium on Geometry and Graphics, Sept. 5-9, 2021, \v Ciovo/Croatia
348 String constructions of quadrics.
Jan. 18, 2021: 19th International Conference on Geometry and Graphics (online), Jan. 18-22, 2021, São Paulo/Brazil
346 Plücker's conoid, hyperboloids of revolution and orthogonal hyperbolic paraboloids.
Sept. 21, 2020: 7th International Conference - moNGeometrija2020, Sept. 18-21, 2020, Belgrade/Serbia
345 Movement of conics on quadrics.
September 11, 2019: 5th Slovak-Czech Conference on Geometry and Graphics, Sept. 9-12, 2019, Trenčianske Teplice/Slovakia
340 On the Interdisciplinarity of Geometry.
October 29, 2018: 14th Miklós Iványi International PhD & DLA Symposium, University of Pécs/Hungary, Faculty of Engineering and Information Technology
339 Between Rigidity and Flexibility.
September 24, 2018: Workshop on Rigidity and Flexibility, ESI Vienna/Austria
337 Two Remarkable Spherical Arrangements of Circles.
August 4, 2018: 18th International Conference on Geometry and Graphics, 40th Anniversary, Aug. 3-7, Politecnico di Milano/Italy
335 Die Geschichte der Darstellenden Geometrie in Österreich.
11. Jänner, 2018: Oberseminar, AG Didaktik und Geschichte der Mathematik, Bergische Universität Wuppertal/Germany
334 Die Rolle der Geometrie bei Navigationssystemen.
9. November, 2017: 38. Fortbildungstagung für Geometrie, Strobl am Wolfgangsee
327 Mathematisches zur Sonnenreflexionsuhr.
February 24, 2017: Präsentation des Buches von F. Mayrhofer, G. Liechtenstein (Hrsg.): Die Sonnenreflexionsuhr im Stift Heiligenkreuz, Be&Be-Verlag 2017, Stift Heiligenkreuz
285 Wozu Geometrie?
Nov. 1, 2010: Feierliche Ehrenpromotion, TU Dresden/Germany