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A number r is an nth root of unity if r^n=1 and a primitive nth root of unity if, in addition, n is the smallest integer of k=1, ..., n for which r^k=1.

The semimajor axis (also called the major semi-axis, major semiaxis, or major radius) of an ellipse (or related figure) is half its extent along the longer of the two ...

The semiminor axis (also called the minor semi-axis, minor semiaxis, or minor radius) of an ellipse (or related figure) is half its extent along the shorter of the two ...

On an algebraic curve, the sum of the number of coincidences at a noncuspidal point C is the sum of the orders of the infinitesimal distances from a nearby point P to the ...

Differential Geometry

Given a number z, the cube root of z, denoted RadicalBox[z, 3] or z^(1/3) (z to the 1/3 power), is a number a such that a^3=z. The cube root is therefore an nth root with ...

Take K a number field and m a divisor of K. A congruence subgroup H is defined as a subgroup of the group of all fractional ideals relative prime to m (I_K^m) that contains ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

The triangle bounded by the polars of the vertices of a triangle DeltaABC with respect to a conic is called its polar triangle. The following table summarizes polar triangles ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...