Abstract
We prove a generalization of both Pascal's Theorem and its converse, the Braikenridge–Maclaurin Theorem: If two sets of k lines meet in k2 distinct points, and if dk of those points lie on an irreducible curve C of degree d, then the remaining k(k − d) points lie on a unique curve S of degree k − d. If S is a curve of degree k − d produced in this manner using a curve C of degree d, we say that S is d-constructible. For fixed degree d, we show that almost every curve of high degree is not d-constructible. In contrast, almost all curves of degree 3 or less are d-constructible. The proof of this last result uses the group structure on an elliptic curve and is inspired by a construction due to Möbius. The exposition is embellished with several exercises designed to amuse the reader.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
