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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 ...

A number of the form +/-sqrt(a), where a is a positive rational number which is not the square of another rational number is called a pure quadratic surd. A number of the ...

The radius of curvature is given by R=1/(|kappa|), (1) where kappa is the curvature. At a given point on a curve, R is the radius of the osculating circle. The symbol rho is ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

Let a closed interval [a,b] be partitioned by points a<x_1<x_2<...<x_(n-1)<b, where the lengths of the resulting intervals between the points are denoted Deltax_1, Deltax_2, ...

The second Brocard circle is the circle having center at the circumcenter O of the reference triangle and radius R_B = sqrt(1-4sin^2omega)R (1) = (2) where R is the ...

The Sendov conjecture, proposed by Blagovest Sendov circa 1958, that for a polynomial f(z)=(z-r_1)(z-r_2)...(z-r_n) with n>=2 and each root r_k located inside the closed unit ...

Draw an initial circle, and arrange six circles tangent to it such that they touch both the original circle and their two neighbors. Then the three lines joining opposite ...

The negative derivative S(v)=-D_(v)N (1) of the unit normal N vector field of a surface is called the shape operator (or Weingarten map or second fundamental tensor). The ...

The slant height of an object (such as a frustum, or pyramid) is the distance measured along a lateral face from the base to the apex along the "center" of the face. In other ...