Poncelet's closure theorem and three levels of its understanding

Seminar

Speaker

George Shabat (Russian State University for the Humanities and Independent University of Moscow)

Date

24/12/2023 - 11:30 - 10:00Add to Calendar 2023-12-24 10:00:00 2023-12-24 11:30:00 Poncelet's closure theorem and three levels of its understanding Poncelet's 1814 theorem states that whenever a triangle is inscribed in one circle and circumscribed another one, the triangle belongs to the continuous family of triangles that are all inscribed in and circumscribe the same two circles. This theorem will be presented as (1) an "obvious" fact of elementary geometry; (2) as a rather difficult high-school theorem; (3) as a quite natural result of adult mathematics. The level (3) needs some understanding of complex algebraic geometry. However, no preliminary knowledge of it is assumed and all the necessary concepts will be explained. Building 216 Room 201 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public

Place

Building 216 Room 201

Abstract

Poncelet's 1814 theorem

states that whenever a triangle is inscribed in one circle and circumscribed another one, the triangle belongs to the continuous

family of triangles that are all inscribed in and circumscribe the same two circles.

This theorem will be presented as

(1) an "obvious" fact of elementary geometry;

(2) as a rather difficult high-school theorem;

(3) as a quite natural result of adult mathematics.

The level (3) needs some understanding of complex algebraic geometry. However, no preliminary knowledge of it is assumed and all

the necessary concepts will be explained.