Title of the course: Scissors Congruence
Instructor: Prof. Murad Özaydın
Institution: University of Oklahoma
Dates: 15-21 July 2019
Prerequisites: Calculus, abstract math, linear algebra
Level: Graduate, advanced undergraduate, beginning Undergraduate
Abstract: Hilbert’s 3rd problem (1900) asked if two polyhedra with the same volume can be subdivided into a finite number of smaller polyhedra so that each piece of the first polyhedron is congruent to one of the second. Two such polyhedra are said to be Scissors Congruent. The corresponding statement for polygons in the plane was probably known in antiquity, but the first known proof is Wallace (1807). Dehn (1901) proved that a cube and a regular tetrahedron of the same volume are not Scissors Congruent and the invariant he defined for this purpose along with volume was shown by Sydler (1965) to be a complete set of invariants of Scissors Congruence in 3-space. A similar result in 4 dimensions was proven by Jessen (1972). In higher dimensions analogous questions are still open.
I plan to cover the theorems of Wallace (Scissors Congruence = Area in the plane) and Dehn (solution to Hilbert’s 3rd problem) and hope to mention some more recent developments.
Language: EN, TR