[{"oa_version":"Preprint","abstract":[{"lang":"eng","text":"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. "}],"month":"01","intvolume":" 147","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1709.02562"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":147,"_id":"6050","status":"public","type":"journal_article","date_updated":"2023-08-24T14:48:59Z","department":[{"_id":"HeEd"}],"publisher":"AMS","quality_controlled":"1","oa":1,"day":"01","publication":"Proceedings of the American Mathematical Society","isi":1,"year":"2019","date_published":"2019-01-01T00:00:00Z","doi":"10.1090/proc/14240","date_created":"2019-02-24T22:59:19Z","page":"91-102","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society, vol. 147, AMS, 2019, pp. 91–102, doi:10.1090/proc/14240.","apa":"Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240","ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102.","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.","chicago":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240.","ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102."},"title":"Two circles and only a straightedge","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"first_name":"Roman","full_name":"Fedorov, Roman","last_name":"Fedorov"}],"external_id":{"arxiv":["1709.02562"],"isi":["000450363900008"]},"article_processing_charge":"No"}]