Department of Mathematics
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Ever since Wiles' proof of FLT, the group law on cubic curves has become very popular. But it is not that well-known that there is a simple and natural geometric procedure to construct a group law on conics as well. Here we use such groups to represent several \( C(n_4) \)-configurations both algebraically and geometrically over the real plane. This gives a partial solution to the geometric realization problem recently raised by Branko Grünbaum. This is part of an ongoing research done in collaboration with Jeffrey Lanyon.

References:

1. B. Grünbaum, Which \( (n_4) \) Configurations Exist?, Geombinatorics 9 (2000), no. 4, 164-169.
2. B. Grünbaum, Configurations of Points and Lines, AMS Graduate Studies in Mathematics vol. 103, 2009.
3. F. Lemmermeyer, Conics - a poor man's Elliptic Curves, arXiv:math/0311306v1
4. Jeffrey Lanyon, Group realizations of configurations, M.Sc Thesis, University of Manitoba, 2018.