 About 16,900 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 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 An ndimensional affine space over a field F is a set An (the elements of which
are called points of the affine space) to ... In an equiaffine plane A2, any two
vectors v1 ;v2 have an invariant jv1 v2 j (the modulus of their cross product)—the
... 

 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 They are warped products of twodimensional affine spheres (Z3) or positive
definite quadrics (SO(2)) or indefinite quadrics ... In the equiaffine theory of
surfaces in R4 the assumption that the ∇geodesics are plane curves is very
restrictive. 

 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 Area, as defined in (18.1), is thus an equiaffine invariant. ... there is no affine
meaning in the statement that two triangles with equal base and altitude have the
same area, since length and perpendicularity are undefined in the affine plane. 

 books.google.com In Section4we classify all the solutions to the Hessian one equation (1.2) that are
globally defined on the plane, and have a ... Here, an equiaffine transformation is
an affine transformation of R3 of a certain type; these transformations preserve ... 

 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 The maximally symmetric curves for the equi affine group arc those whose equi
affine curvature (8.26) is constant. ... equation for conic sections, meaning an
ordinary differential equation whose solutions are all conic sections in the plane. 

 