# The centre symmetry set

Banach Center Publications (1999)

- Volume: 50, Issue: 1, page 91-105
- ISSN: 0137-6934

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topGiblin, Peter, and Holtom, Paul. "The centre symmetry set." Banach Center Publications 50.1 (1999): 91-105. <http://eudml.org/doc/209020>.

@article{Giblin1999,

abstract = {A centrally symmetric plane curve has a point called it’s centre of symmetry. We define (following Janeczko) a set which measures the central symmetry of an arbitrary strictly convex plane curve, or surface in $R^3$. We investigate some of it’s properties, and begin the study of non-convex cases.},

author = {Giblin, Peter, Holtom, Paul},

journal = {Banach Center Publications},

keywords = {generalized central symmetry; oval; envelope of lines; central symmetry set},

language = {eng},

number = {1},

pages = {91-105},

title = {The centre symmetry set},

url = {http://eudml.org/doc/209020},

volume = {50},

year = {1999},

}

TY - JOUR

AU - Giblin, Peter

AU - Holtom, Paul

TI - The centre symmetry set

JO - Banach Center Publications

PY - 1999

VL - 50

IS - 1

SP - 91

EP - 105

AB - A centrally symmetric plane curve has a point called it’s centre of symmetry. We define (following Janeczko) a set which measures the central symmetry of an arbitrary strictly convex plane curve, or surface in $R^3$. We investigate some of it’s properties, and begin the study of non-convex cases.

LA - eng

KW - generalized central symmetry; oval; envelope of lines; central symmetry set

UR - http://eudml.org/doc/209020

ER -

## References

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- [3] J. W. Bruce and P. J. Giblin, Growth, motion and 1-parameter families of symmetry sets, Proc. Roy. Soc. Edinburgh Sect. A 104 (1986), 179-204. Zbl0656.58022
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- [2] J. W. Bruce, P. J. Giblin and C. G. Gibson, Symmetry sets, Proc. Roy. Soc. Edinburgh Sect. A 101 (1985), 163-186. Zbl0593.58012
- [6] P. J. Giblin and S. A. Brassett, Local symmetry of plane curves, Amer. Math. Monthly 92 (1985), 689-707. Zbl0604.53001
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- [8] V. V. Goryunov, Projections of generic surfaces with boundary, in: Theory of Singularities and its Applications, V. I. Arnol'd (ed.), Adv. Soviet Math. 1, Amer. Math. Soc., Providence, 1990, 157-200.
- [9] P. Holtom, Local Central Symmetry for Euclidean Plane Curves, M.Sc. Dissertation, University of Liverpool, Sept. 1997.
- [10] S. Janeczko, Bifurcations of the center of symmetry, Geom. Dedicata 60 (1996), 9-16. Zbl0868.58015
- [11] Liverpool Surface Modelling Package, written by Richard Morris for Silicon Graphics and X Windows. See R. J. Morris, The use of computer graphics for solving problems in singularity theory, in: Visualization in Mathematics, H.-C. Hege and K. Polthier (eds.), Springer, Heidelberg, 1997, 53-66.
- [5] Buchin Su, Affine Differential Geometry, Science Press, Beijing; Gordon and Breach, New York, 1983. Zbl0539.53002
- [12] V. M. Zakalyukin, Envelopes of families of wave fronts and control theory, Proc. Steklov Inst. Math. 209 (1995), 114-123. Zbl0883.93008

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