Titlebook: Geometry; Our Cultural Heritag Audun Holme Textbook 20021st edition Springer-Verlag Berlin Heidelberg 2002 Algebra.Apollonius.Fractal.Geome

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Geometry in the Hellenistic EraAlexandria was founded where the Nile meets the Mediterranean by Alexander the Great, in the year 331 B.C. The city became the capital of Egypt, and rapidly developed into one of the richest and most beautiful cities in the world. That is to say, in the world known to the antique.

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Axiomatic Projective GeometryThe axiomatic treatment of . has at its starting point three .. We are given one . ?, which we call ., and another set ℒ which we call .. Further, there is given a . between elements from ? and elements from ℒ which is denoted by ., and referred to as .. If . holds for . ∈ ? and . ∈ ℒ, then we say that ..

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Making Things PreciseIn Section 8.3 we saw how a model for the projective plane may be constructed by taking the northern hemisphere of a spherical surface, including the equator, and then . diametrically opposite points on the equator.

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Geometry in the Affine and the Projective PlaneIn this chapter we shall, among other things, prove the classical theorems of .. These theorems are valid in the projective plane ℙ. (ℝ), and we shall give simple algebraic proofs, which fully take advantage of the strength inherent in ..

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Higher Geometry in the Projective PlaneWe define curves in the . ℙ. (ℙ) analogously to curves in the affine plane ℙ.. The difference is that we can not use ordinary polynomials in two variables, but have to work with . instead. We have seen this in Section 12.8, for conics.

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