 About 18,800 results  books.google.com Michiel Hazewinkel  1994  Preview An affine coordinate system on a plane is defined by an ordered pair of non
collinear vectors C] and e2 (an affine ... In this geometry the affine (or, more
exactly, the equiaffine) curvature of a plane curve y=y(x) is calculated by the
formula ... 

 books.google.com In an equiaffine plane A2, any two vectors v1 ,v 2 have an invariant v1 × v2 (the
modulus of their cross product)—the surface area of the parallelogram
constructed on v1 and v2. Given a nonrectilinear curve γ = γ(t), its affine
parameter (or ... 

 books.google.com The affine plane R2 is referred to in terms of a coordinate system {x,>'. By an
allowable coordinate change, we mean (x,_y)>— » (x,y) such that (1.1) x = ax +
by where ,,.2, * Equiaffine geometry is concerned with geometric properties ... 

 books.google.com AFFINE GEOMETRY An ndimensional affine space over a field F is a set An (the
elements of which are called points of the ... In an equiaffine plane A2, any two
vectors v1 ,v 2 have an invariant v 1 × v 2  (the modulus of their cross product) ... 

 books.google.com Mario Pasquale Raffaele D'Angelo  1978  No preview 
 books.google.com Affine Invariants Properties of geometric objects which are invariant with respect
to the action of the affine transformation group are called ... In a projective plane
there is only one conic, which means that all conics are projectively equivalent. 

 books.google.com Here we shall refrain ourselves from listing the other properties of affine plane
curves. ... Further, the determinants of the form are clearly equiaffine invariants
rather than the invariants of the curve, because they depend upon a selection of ... 

 books.google.com Note that the affine plane is not Euclidean, since we have not reintroduced
Euclidean properties such as invariance of ... other triangle by means of an affine
transformation, that is, any two triangles in the affine plane are affine ly equivalent
. 

 books.google.com Hence prenormal affine planes and standard affine planes validate the same
formulas. These considerations prove that: Proposition 11. The following
conditions are equivalent: (i) φ is a theorem of ML(SAP); (ii) φ is valid in every
standard ... 

 books.google.com Let IT be an affine plane which admits a collineation r such that the cyclic group
generated by r leaves one point (say X) fixed, ... We now show that the study of
cyclic affine planes is equivalent to the study of "affine difference sets" of order n. 

 