Geometry of Plane Curves

Special Session at the 23rd International Conference on
Applications of Computer Algebra (ACA'2017),
July 17 - 21, 2017, Jerusalem, Israel

Aim and scope

   Of all the objects considered in modern geometry, the plane is the most interesting, and the most prolific in producing theorems. Furthermore, of all the objects of the plane, the curves seem to stand out as perfect objects to study, in the framework of both differential geometry and analytic geometry.

   Many people think that the theory of curves is already finished, but there are still many open problems whose solutions are extremely difficult to find. New results and new proofs of old results in this field have been published during the recent period. Moreover, the usage of various kinds of modern technology (Computer Algebra Systems, Dynamical Geometry Packages, etc.) has transformed this theoretical field into an experimental one.

   The purpose of this section is to present a series of results in the local and global theory of curves, which show vitality and attractiveness of these topics. Among the topics which will be addressed, we mention ovals (which attained mathematical immortality by possessing many interesting properties and giving rise to many problems and generalizations), isoptic curves of plane curves, envelopes of families of curves (a domain with numerous applied occurrences), etc.

   Anyone is invited to participate in the session who has original, provocative or inspiring assertions.



   If you are interested in proposing a talk, please send an abstract by email to Witold Mozgawa (1-2 pages, with references). Each presentation including Q&A is 30 minutes. Please use this LaTeX template for your abstract and send both the LaTeX source and a compiled PDF version. If you do not work with LaTeX, the submission may be sent in Word format (.doc or .docx file) and later, once accepted, we will try to adapt the proposal to the LaTeX template.

Tentative abstract submission deadline is May 25, 2017; early submissions are appreciated. More than one abstract may be submitted.


  1. Inflection points of bisoptic curves of conics (Abstract),
    Inflection points of bisoptic curves of conics (Presentation)
    (Thierry Dana-Picard, Jerusalem College of Technology)
  2. On the closest distance between a point and a convex body (Abstract)
    On the closest distance between a point and a convex body (Presentation)
    (Witold Mozgawa, Maria Curie-Skłodowska University)
  3. Isoptic curves of Fermat curves (Abstract)
    Isoptic curves of Fermat curves (Presentation)
    (Thierry Dana-Picard and Aharon Naiman, Jerusalem College of Technology)
  4. Constructing Linkages for Drawing Plane Curves (Abstract)
    Constructing Linkages for Drawing Plane Curves (Presentation)
    (Christoph Koutschan, RICAM, Linz, Austria)

Detailed information about the session is posted at the ACA2017 conference web page