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The maximum and minimum of the normal curvature kappa_1 and kappa_2 at a given point on a surface are called the principal curvatures. The principal curvatures measure the ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

A principal ideal domain is an integral domain in which every proper ideal can be generated by a single element. The term "principal ideal domain" is often abbreviated P.I.D. ...

At each point on a given a two-dimensional surface, there are two "principal" radii of curvature. The larger is denoted R_1, and the smaller R_2. The "principal directions" ...

A principal nth root omega of unity is a root satisfying the equations omega^n=1 and sum_(i=0)^(n-1)omega^(ij)=0 for j=1, 2, ..., n. Therefore, every primitive root of unity ...

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...

The Cauchy principal value of a finite integral of a function f about a point c with a<=c<=b is given by ...

The vectors +/-a_1, ..., +/-a_n in a three-space form a normalized eutactic star iff Tx=x for all x in the three-space.

A general quintic equation a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 (1) can be reduced to one of the form y^5+b_2y^2+b_1y+b_0=0, (2) called the principal quintic form. Vieta's ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...