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Journal for Geometry and Graphics 25 (2021), No. 2, 187--195 Copyright Heldermann Verlag 2021 Projective Line Revisited Nicholas Phat Nguyen Lynnwood, Washington 98037, U.S.A nicholas.pn@gmail.com This article provides a new perspective on the geometry of a projective line, which helps clarify and illuminate some classical results about projective plane. As part of the same train of ideas, the article also provides a proof of the nine-point circle theorem valid for any affine plane over a commutative field of characteristic different from 2. Keywords: Projective line, involution, eleven-point conic, nine-point circle. MSC: 51N15; 51A63, 51A05. [ Fulltext-pdf (292 KB)] for subscribers only. |