{"publication":"Proceedings of the American Mathematical Society","doi":"10.1090/proc/14240","intvolume":"       147","main_file_link":[{"url":"https://arxiv.org/abs/1709.02562","open_access":"1"}],"year":"2019","language":[{"iso":"eng"}],"date_updated":"2023-08-24T14:48:59Z","day":"01","oa":1,"external_id":{"arxiv":["1709.02562"],"isi":["000450363900008"]},"abstract":[{"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. ","lang":"eng"}],"publisher":"AMS","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"page":"91-102","oa_version":"Preprint","article_processing_charge":"No","type":"journal_article","department":[{"_id":"HeEd"}],"quality_controlled":"1","publication_status":"published","volume":147,"_id":"6050","status":"public","citation":{"ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. <i>Proceedings of the American Mathematical Society</i>. 2019;147:91-102. doi:<a href=\"https://doi.org/10.1090/proc/14240\">10.1090/proc/14240</a>","chicago":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” <i>Proceedings of the American Mathematical Society</i>. AMS, 2019. <a href=\"https://doi.org/10.1090/proc/14240\">https://doi.org/10.1090/proc/14240</a>.","apa":"Akopyan, A., &#38; Fedorov, R. (2019). Two circles and only a straightedge. <i>Proceedings of the American Mathematical Society</i>. AMS. <a href=\"https://doi.org/10.1090/proc/14240\">https://doi.org/10.1090/proc/14240</a>","mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” <i>Proceedings of the American Mathematical Society</i>, vol. 147, AMS, 2019, pp. 91–102, doi:<a href=\"https://doi.org/10.1090/proc/14240\">10.1090/proc/14240</a>.","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” <i>Proceedings of the American Mathematical Society</i>, vol. 147. AMS, pp. 91–102, 2019.","ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102."},"month":"01","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"last_name":"Fedorov","first_name":"Roman","full_name":"Fedorov, Roman"}],"scopus_import":"1","date_created":"2019-02-24T22:59:19Z","date_published":"2019-01-01T00:00:00Z","title":"Two circles and only a straightedge"}