تحت إشراف قسم الرياضيات والإحصاء أقيم يوم الاثنين 16/8/1442هـ سيمنار بعنوان:
Poncelet's Theorem and Some Related Formulae in Euclidean and Hyperbolic Geometry
قدمته د.أمل العبداللطيف وذلك في تمام الساعة 2:00 مساءً عبر برنامج الزووم
ملخص البحث:
Abstract:
In 1813, J. Poncelet proved his theorem in projective geometry, Poncelet's Closure Theorem, which states that: if C and D are two smooth conics in general position, and there is an n-gon inscribed in C and circumscribed around D, then for any point of C, there exists an n-gon, also inscribed in C and circumscribed around D, which has this point for one of its vertices.
There are some formulae related to Poncelet's Theorem, in which introduce relations between two circles' data (their radii and the distance between their centers), when there is a bicentric n-gon between them. In Euclidean geometry, for example, we have Chapple's and Fuss's Formulae.
We introduce a proof that Poncelet's Theorem holds in hyperbolic geometry. Also, we present hyperbolic Chapple's and Fuss's Formulae, and more general, we prove a Euclidean general formula, and two version of hyperbolic general formulae, which connect two circles' data, when there is an embedded bicentric n-gon between them.
