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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 ...

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

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 ...

The inverse curve of the epispiral r=asec(ntheta) with inversion center at the origin and inversion radius k is the rose curve r=(kcos(ntheta))/a.

Parallel lines are everywhere equidistant. This postulate is equivalent to the parallel postulate.

The paradox "This statement is false," stated in the fourth century BC. It is a sharper version of the Epimenides paradox, "All Cretans are liars...One of their own poets has ...

A more common way to describe a Euclidean ring.

A weighted graph in which the weights are equal to the Euclidean lengths of the edges in a specified embedding (Skiena 1990, pp. 201 and 252).

An array of "trees" of unit height located at integer-coordinate points in a point lattice. When viewed from a corner along the line y=x in normal perspective, a quadrant of ...

An even perfect number is perfect number that is even, i.e., an even number n whose sum of divisors (including n itself) equals n. All known perfect numbers are even, and ...