Points and lines in the plane

Marcel Berger ()
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Marcel Berger: IHÉS, Bures-sur-Yvette, Institut des Hautes Études Scientifiques

Chapter Chapter I in Geometry Revealed, 2010, pp 1-59 from Springer

Abstract: Abstract We first work in the coordinate plane, which is familiar to everyone, with its points and lines. As is usual in the “elementary” geometry of school instruction, this has to do with Euclidean geometry, where there are distances (lengths), angles, circles, etc. This will also be the setting of the next chapter, but even in this first chapter we will see that we can already do many subtle and difficult things − and even find open questions − with only the so-called “affine plane”. Affine geometry is a weaker structure than Euclidean geometry. Simply put: we won’t be working with anything but points and lines; the mathematical definition is given in Sect. I.XYZ at the end of the chapter. Here we need only recall: two distinct points uniquely determine a line that contains them, along with a segment that joins them; two distinct lines intersect in a single point, with the sole exception of parallel lines.

Keywords: Projective Space; Projective Plane; Projective Geometry; Projective Line; Projective Transformation (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-540-70997-8_1

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