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The illusion illustrated above in which the bounding rectangle and inner square both appear distorted.

Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.

A function which has infinitely many derivatives at a point. If a function is not polygenic, it is monogenic.

A primary ideal is an ideal I such that if ab in I, then either a in I or b^m in I for some m>0. Prime ideals are always primary. A primary decomposition expresses any ideal ...

S_n(z) = zj_n(z)=sqrt((piz)/2)J_(n+1/2)(z) (1) C_n(z) = -zn_n(z)=-sqrt((piz)/2)N_(n+1/2)(z), (2) where j_n(z) and n_n(z) are spherical Bessel functions of the first and ...

A space curve consisting of a spiral wound around a helix. It has parametric equations x = [R+acos(omegat)]cost (1) y = [R+acos(omegat)]sint (2) z = ht+asin(omegat). (3)

A condition which, if true, guarantees that a result is also true. (However, the result may also be true if the condition is not met.) If a condition is both necessary and ...

Let the speed sigma of a closed curve on the unit sphere S^2 never vanish. Then the tangent indicatrix, also called the tantrix, tau=(sigma^.)/(|sigma^.|) is another closed ...

An exchange of two elements of an ordered list with all others staying the same. A transposition is therefore a permutation of two elements. For example, the swapping of 2 ...

Let f be a family of meromorphic functions on the unit disk D which are not normal at 0. Then there exist sequences f_n in F, z_n, rho_n, and a nonconstant function f ...