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A knot K is an n-embeddable knot if it can be placed on a genus n standard embedded surface without crossings, but K cannot be placed on any standardly embedded surface of ...

The second-order ordinary differential equation (x^2y^')^'+x^2y^n=0.

Two nonsuperimposable objects which are mirror images of each other are called enantiomers. The term enantiomer is synonymous with enantiomorph. For example, the letters b ...

Given a set S of points in the plane, an enclosing circle is a circle for which all points S lie in its interior.

Given a module M over a unit ring R, the set End_R(M) of its module endomorphisms is a ring with respect to the addition of maps, (f+g)(x)=f(x)+g(x), for all x in M, and the ...

A finite-dimensional Lie algebra all of whose elements are ad-nilpotent is itself a nilpotent Lie algebra.

A modular form which is not allowed to have poles in the upper half-plane H or at iinfty.

Relates evolutes to single paths in the calculus of variations. Proved in the general case by Darboux and Zermelo in 1894 and Kneser in 1898. It states: "When a single ...

A 1-cusped epicycloid has b=a, so n=1. The radius measured from the center of the large circle for a 1-cusped epicycloid is given by epicycloid equation (◇) with n=1 so r^2 = ...

The evolute of the epicycloid x = (a+b)cost-bcos[((a+b)/b)t] (1) y = (a+b)sint-bsin[((a+b)/b)t] (2) is another epicycloid given by x = a/(a+2b){(a+b)cost+bcos[((a+b)/b)t]} ...