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Two circles and only a straightedge


Authors: Arseniy Akopyan and Roman Fedorov
Journal: Proc. Amer. Math. Soc. 147 (2019), 91-102
MSC (2010): Primary 14A25, 14H52, 51M09, 52C30
DOI: https://doi.org/10.1090/proc/14240
Published electronically: October 3, 2018
MathSciNet review: 3876733
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Abstract: We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely many families of pairs of circles for which such construction is possible.


References [Enhancements On Off] (What's this?)

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Additional Information

Arseniy Akopyan
Affiliation: Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria
Email: akopjan@gmail.com

Roman Fedorov
Affiliation: The Dietrich School of Arts and Sciences, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260
Email: rmfedorov@gmail.com

DOI: https://doi.org/10.1090/proc/14240
Received by editor(s): April 10, 2018
Published electronically: October 3, 2018
Additional Notes: The second author is partially supported by the NSF grant DMS-1764391
Communicated by: Alexander Braverman
Article copyright: © Copyright 2018 American Mathematical Society