Last semester we were very fortunate to have Dr. Tatiana Shubin join us and present on Geometric Combinatorics. Following are some of the problems she presented:
1. Prove that if each three of n points in a plane can be enclosed in a circle of radius 1, then all n points can be enclosed in such a circle.
2. Given 7 lines in a plane, if no two of them are parallel to one another prove that there exists a pair of lines with the angle between them less than 26 degrees
3. How many acute inner angles can a convex n-gon have?
If you would care to answer them in the comments please do. These are just a sampling of the interesting problems and topics to be found at Metroplex Math Circle.