By Leopold Flatto
Poncelet's theorem is a recognized lead to algebraic geometry, relationship to the early a part of the 19th century. It issues closed polygons inscribed in a single conic and circumscribed approximately one other. the concept is of serious intensity in that it pertains to a wide and numerous physique of arithmetic. There are numerous proofs of the concept, none of that's effortless. a very beautiful function of the concept, that's simply understood yet tricky to turn out, is that it serves as a prism wherein possible research and savour loads of appealing arithmetic. The author's unique study in queuing thought and dynamical structures figures prominently within the e-book. This booklet stresses the fashionable method of the topic and includes a lot fabric no longer formerly to be had in ebook shape. It additionally discusses the relation among Poncelet's theorem and a few features of queueing thought and mathematical billiards. The facts of Poncelet's theorem awarded during this ebook relates it to the idea of elliptic curves and exploits the truth that such curves are endowed with a gaggle constitution. The booklet additionally treats the true and degenerate situations of Poncelet's theorem. those instances are attention-grabbing in themselves, and their proofs require another issues. the genuine case is dealt with via making use of notions from dynamical platforms. the cloth during this e-book can be comprehensible to a person who has taken the traditional classes in undergraduate arithmetic. to accomplish this, the writer has incorporated within the e-book initial chapters facing projective geometry, Riemann surfaces, elliptic features, and elliptic curves. The e-book additionally includes quite a few figures illustrating a variety of geometric techniques.
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