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References in periodicals archive ?
Kneebone, Algebraic projective geometry, Clarendon Press, Oxford, UK, 1952.
Casse, Projective Geometry: an Introduction, Oxford university press, New York, NY, USA, 2006.
To infer euclidean properties of space we present a collection of autocalibration methods based on the projective geometry formalism.
Recent results in different fields of pure mathematical geometry of Banach spaces [2, 3], partial differential equations [9], topology [19] and number theory [22] were proven with the help of the fundamental theorems of Projective Geometry. Projective Geometry is used in applied science to prove results in mechanics [20], in composition analysis of building structure [21] and in coding theory and cryptography [4, 14].
If [xi]: [GAMMA] [right arrow] P(V) and [xi]: [GAMMA]' [right arrow] P(V') are embeddings of [GAMMA] and [GAMMA]' over division rings D and D', then D = D' and there is a D-semilinear map V [right arrow] V' inducing [phi] this is the Fundamental Theorem of Projective Geometry).
Modernism in geometry is associated with changing views on the nature of and developments within geometry (non-Euclidean geometry, projective geometry, Hilbert's axiomatization of elementary geometry, Italian axiomatic geometry) as well as on geometry's relation to science and everyday experience.
Projective geometry, Lie geometry and incidence theorems are also discussed.
In [18] coordinates were introduced, algebraic extension to ordered projective geometry was given, and collineations were investigated.
As an example, Chapter 7 is a good aid for teaching projective geometry, an interesting aspect of the progression from cartesian to polar coordinates in trigonometry (usually taught in Year 9 in Australia); see Anno's anamorphic art section of Picture books.
According to Evans, projective geometry originated in the creative impulse of the Early Renaissance that sought to resolve the polarity between science and art, between the rational and the intuitive.
He thinks of it as something like a cross between the midpoint map and the so-called pentagram map, and calls it the projective heat map because he imagines that the construction models how heat might flow in a world governed by projective geometry. He admits that he might have scant justification for such imagination, but the midpoint map, when written in coordinates, is a linear transformation that is closely related to the heat equation.