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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

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.

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