Antiparallelogram
An antiparallelogram is a self-intersecting rectangle whose opposite, i.e. non-adjacent sides are of the same length and in which (in contrast to a normal parallelogram ) two sides intersect and are not parallel . In particular, it is not convex . Sometimes an antiparallelogram is also required to have a pair of opposite sides parallel.
If the lengths of the neighboring sides of an antiparallelogram are in relation and one of the two longer sides is held, then the center of the opposite side describes a Bernoulli lemniscate .
If you set up an antiparallelogram as a coupling gear with rigid sides and joints at the corner points, you can use it to convert straight movements into circular ones, i.e. create a replacement for a connecting rod . (See also Inversor von Hart )
literature
- Harold Scott MacDonald Coxeter, Michael S. Longuet-Higgins, JCP Miller: Uniform polyhedra . In: Philosophical Transactions of the Royal Society of London (= A. Mathematical and Physical Sciences ). tape 246 , 1954, pp. 401-450 , doi : 10.1098 / rsta.1954.0003 .
- Norbert Treitz: The antiparallelogram (I) . In: Spectrum of Science . April 2006, p. 114–116 ( Spektrum.de [accessed June 4, 2013]).
- John Briant, Christopher J. Sangwin: How round is your circle? Where Engineering and Mathematics Meet . Princeton University Pres, 2008, ISBN 978-0-691-13118-4 , pp. 54–56 ( online on google-books [accessed June 4, 2013]).
- EA Dijksman: Motion Geometry of Mechanisms . Cambridge University Press, 1976, ISBN 978-0-521-20841-3 , pp. 203 f . ( online on google-books [accessed June 4, 2013]).
Web links
- The online lexicon Academic dictionaries and encyclopedias defines an antiparallelogram as “a square in which one pair of opposite sides is parallel but unequal, the other is the same but not parallel.” This article is based on the definition given in the next above literature is used.
- The spectrum of science shows: