Jacob Steiner's construction of conics revisited

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12410%2F19%3A43900271" target="_blank" >RIV/60076658:12410/19:43900271 - isvavai.cz</a>
Result on the web
<a href="http://www.heldermann.de/JGG/JGG23/JGG232/jgg23018.htm" target="_blank" >http://www.heldermann.de/JGG/JGG23/JGG232/jgg23018.htm</a>
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Jacob Steiner's construction of conics revisited
Original language description
We aim at presenting material on conics, which can be used to formulate, e.g., GeoGebra problems for high-school and freshmen maths courses at universities. In a (real) projective plane two pencils of lines, which are projectively related, generate, in general, a conic. This fact due to Jakob Steiner [4] allows to construct points of a cocnic given by, e.g., 5 points. Hereby the problem of transfering a given cross-ratio of four lines of the first pencil to the corresponding and uniform way we propose a method, which uses the well-known fact that a projective mapping from one line (or pencil) to another always can be decomposed into a product of perspectivities. By extending the presented graphical methods, we also construct tangents and osculating circles at points of a conic. The calculation following the graphic treatment delivers a parametrisation of conic arcs applicable also for so-called 2nd order biarcs. Even so the topic and its theoretical background is a matter of the 19th century, it is not at all well-known nowadays, as also is stated in [3]. Some of the presented constructions might also be new.
Czech name
—
Czech description
—

Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)