On the Total Curvature of a
Nonplanar Knotted Curve by Istvan Fary. The translation from French is in pdf
format. (Last modified October 2001.)
Sur La Courbure Totale D'une Courbe Gauche Faisant un Noeud.
Bull. Soc. Math. France. Vol 77, 1949 (p. 128-138).
- Please note that I have just translated the text. There are some
pictures in the paper after equation (20) - see the original paper.
- Please email me any corrections or suggestions to improve the translation.
An Elementary Geometrical Property of Links and Knots by
Erika Pannwitz. The translation from the German (with Thomas Kuhnt) is in pdf
format. (Last modified 5th June 2004.)
Eine elementargeometrische Eigenshaft von Verschlingungen und Knoten.
Math. Annal. 108 (1933), p.629-672.
- Of interest is the way Pannwitz proves the existence of
quadrisecants. Note that G. Kuperberg (J. Knot Theory
Vol. 3 No. 1 (1994) p. 41-50) and C. Schmitz (Geom.
Dedicata 71 p. 83-90, 1998) both repeat arguments from
her paper. In particular, those arguments dealing with quadrisecants
arising from trisecants with common first and third points
(Kuperberg) and common first and second points (Schmitz).
- The paper is
long, so I have included the original page numbers in the
margins - this should aid those who wish to consult the original
- I have just translated the text. There are some
pictures in the paper not in this pdf document - see the original paper:
Fig. 1 on p. 639 consists of the usual Reidemeister
Fig. 2 on p. 644 consists of the trefoil knot linked with an
unknot. The unknot is placed about a crossing on the trefoil. It
crosses over two strands, then under two strands.
Fig. 3 on p. 644
consists of a trefoil knot together with a curve parallel to it.
Fig. 4. on
p. 645 consists of the Whitehead (or Antoine) Link.
- This translation was done quickly. Some sentences have paraphrased
the original, others have a distinct Germanic flavor to
them. Please email corrections or suggestions for a smoother translation!
Thanks to Gyo Taek Jin for corrections!
Thanks for Lee Rudolph for reminding us all that Math. Annalen is now online, freely accessible. (I'm still trying to find a link to this paper that works reliably.)