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The inverse curve of a lemniscate in a circle centered at the origin and touching the lemniscate where it crosses the x-axis produces a rectangular hyperbola (Wells 1991).

Also known as the first fundamental form, ds^2=g_(ab)dx^adx^b. In the principal axis frame for three dimensions, ds^2=g_(11)(dx^1)^2+g_(22)(dx^2)^2+g_(33)(dx^3)^2. At ...

A logarithmic singularity is a singularity of an analytic function whose main z-dependent term is of order O(lnz). An example is the singularity of the Bessel function of the ...

The unit lower half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]<0}.

The MacBeath circle, a term coined here for the first time, is the circumcircle of the MacBeath triangle. It has a fairly complicated radius, center function, and circle ...

The eigenvalues of a matrix A are called its spectrum, and are denoted lambda(A). If lambda(A)={lambda_1,...,lambda_n}, then the determinant of A is given by ...

Let f be a nonnegative and continuous function on the closed interval [a,b], then the solid of revolution obtained by rotating the curve f(x) about the x-axis from x=a to x=b ...

Let f and g be nonnegative and continuous functions on the closed interval [a,b], then the solid of revolution obtained by rotating the curves f(x) and g(x) about the x-axis ...

Calculus of variations can be used to find the curve from a point (x_1,y_1) to a point (x_2,y_2) which, when revolved around the x-axis, yields a surface of smallest surface ...

The involute of the nephroid given by x = 1/2[3cost-cos(3t)] (1) y = 1/2[3sint-sin(3t)] (2) beginning at the point where the nephroid cuts the y-axis is given by x = 4cos^3t ...