- A Partial Solution to the Baragar-Kontorovich Conjecture
- Project Year:
2018
- REU Student (s):
Gabriel Eiseman | Rutgers University-New Brunswick NJ
- Student 1 Institution:
Rutgers University-New Brunswick
- Project Mentor:
Alex Kontorovich
- Project Mentor Area:
Mathematics
- Project Abstract:
I investigated the minimality of a construction for the fourth tangent circle to three tangent circles (aka the Apollonian circle). Baragar and Kontorovich (my mentor) discovered a general 7 step construction and I showed that under certain assumptions about arbitrary points it is indeed minimal. I also found a 5 step construction for when the circles' centers form a right triangle and showed it and known constructions for isosceles (5 steps) and equilateral (3 steps) triangles are minimal. I am pretty sure the assumption I made about arbitrary points, which is that only a certain subset of them actually need to be considered, is correct, but have not formalized the argument.
