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Trigonometric identities which prove useful in the construction of map projections include (1) where A^' = A-C (2) B^' = 2B-4D (3) C^' = 4C (4) D^' = 8D. (5) ...

A nonsingular linear map A:R^n->R^n is orientation-reversing if det(A)<0.

A map projection in which the parallels are represented by concentric circular arcs and the meridians by concurrent curves.

Let z=x+iy and f(z)=u(x,y)+iv(x,y) on some region G containing the point z_0. If f(z) satisfies the Cauchy-Riemann equations and has continuous first partial derivatives in ...

A map projection in which the distances between one or two points and every other point on the map differ from the corresponding distances on the sphere by only a constant ...

The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...

Let f:R×R->R be a one-parameter family of C^2 map satisfying f(0,0)=0 [(partialf)/(partialx)]_(mu=0,x=0)=0 [(partial^2f)/(partialx^2)]_(mu=0,x=0)>0 ...

Given a map f from a space X to a space Y and another map g from a space Z to a space Y, a lift is a map h from X to Z such that gh=f. In other words, a lift of f is a map h ...

The invariance of domain theorem states that if f:M->N is a one-to-one and continuous map between n-manifolds without boundary, then f is an open map.

If K is a finite complex and h:|K|->|K| is a continuous map, then Lambda(h)=sum(-1)^pTr(h_*,H_p(K)/T_p(K)) is the Lefschetz number of the map h.