Nobuko Takeuchi
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Nobuko Takeuchi has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Shyuichi Izumiya
Department of Mathematics, Hokkaido University, Sapporo, Japan
6 shared publications - Kentaro Saji
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
1 shared publication - Kentaro Saji
Department of Mathematics Graduate School of Science Hiroshima University Higashi-Hiroshima 739-8526, Japan
1 shared publication - Kentaro Saji
Kobe University, Kobe, Japan
1 shared publication - Kiyoomi Kataoka
Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan
1 shared publication
Latest Publications
- Open Access
Pedals and inversions of quadratic curves
The pedal of a curve in the Euclidean plane is a classical subject which has a singular point at the inflection point of the original curve or the pedal point. The primitive of a curve is a curve given by the inverse construction for making the pedal. In this paper we consider the pedal of a quadratic curve. On of the main results gives a characterization of such curves, which is one of the generalizations of limacons of Pascal.
Open AccessPedals and inversions of quadratic curves
The pedal of a curve in the Euclidean plane is a classical subject which has a singular point at the inflection point of the original curve or the pedal point. The primitive of a curve is a curve given by the inverse construction for making the pedal. In this paper we consider the pedal of a quadratic curve. On of the main results gives a characterization of such curves, which is one of the generalizations of limacons of Pascal.
- 1 January 2017
- Published by Journal of Singularities in Journal of Singularities
Flat surfaces along cuspidal edges
- 1 January 2017
- Published by Journal of Singularities in Journal of Singularities
Flat surfaces along cuspidal edges
- 1 April 2013
- Published by Elsevier in Bulletin des Sciences Mathématiques
- Vol. 137 (3) , 325-360
A system of fifth-order partial differential equations describing a surface which contains many circles
- 1 April 2013
- Published by Elsevier in Bulletin des Sciences Mathématiques
- Vol. 137 (3) , 325-360
A system of fifth-order partial differential equations describing a surface which contains many circles
- 1 January 2008
- Published by Institute of Mathematics, Polish Academy of Sciences
- Vol. 82, 201-207
Surfaces which contain many circles
- 1 January 2008
- Published by Institute of Mathematics, Polish Academy of Sciences
- Vol. 82, 201-207
Surfaces which contain many circles
- 19 April 2007
- Published by Walter de Gruyter GmbH in Advances in Geometry
- Vol. 7 (2) , 295-313
Circular surfaces
A circular surface is a one-parameter family of standard circles in ℝ3. In this paper some correspondences between the properties of circular surfaces and those of classical ruled surfaces are investigated. Singularities of circular surfaces are also studied.
- 19 April 2007
- Published by Walter de Gruyter GmbH in Advances in Geometry
- Vol. 7 (2) , 295-313
Circular surfaces
A circular surface is a one-parameter family of standard circles in ℝ3. In this paper some correspondences between the properties of circular surfaces and those of classical ruled surfaces are investigated. Singularities of circular surfaces are also studied.
- 1 February 2003
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 133 (6) , 1341-1359
Singularities of line congruences
A line congruence is a two-parameter family of lines in R3. In this paper we study singularities of line congruences. We show that generic singularities of general line congruences are the same as those of stable mappings between three-dimensional manifolds. Moreover, we also study singularities of normal congruences and equiaffine normal congruences from the viewpoint of the theory of Lagrangian singularities.
- 1 February 2003
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 133 (6) , 1341-1359
Singularities of line congruences
A line congruence is a two-parameter family of lines in R3. In this paper we study singularities of line congruences. We show that generic singularities of general line congruences are the same as those of stable mappings between three-dimensional manifolds. Moreover, we also study singularities of normal congruences and equiaffine normal congruences from the viewpoint of the theory of Lagrangian singularities.
- 1 October 2002
- Published by Springer Nature in Journal of Geometry
- Vol. 74 (1-2) , 97-109
Generic properties of helices and Bertrand curves
- 1 October 2002
- Published by Springer Nature in Journal of Geometry
- Vol. 74 (1-2) , 97-109
Generic properties of helices and Bertrand curves
- 1 January 2001
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 130 (1) , 1-11
Singularities of ruled surfaces in ℝ3
We study singularities of ruled surfaces in ℝ3. The main result asserts that only cross-caps appear as singularities for generic ruled surfaces.
- 1 January 2001
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 130 (1) , 1-11
Singularities of ruled surfaces in ℝ3
We study singularities of ruled surfaces in ℝ3. The main result asserts that only cross-caps appear as singularities for generic ruled surfaces.