Search Results for ""

A function f is Fréchet differentiable at a if lim_(x->a)(f(x)-f(a))/(x-a) exists. This is equivalent to the statement that phi has a removable discontinuity at a, where ...

Fubini's theorem, sometimes called Tonelli's theorem, establishes a connection between a multiple integral and a repeated one. If f(x,y) is continuous on the rectangular ...

Let X and Y be Banach spaces and let f:X->Y be a function between them. f is said to be Gâteaux differentiable if there exists an operator T_x:X->Y such that, for all v in X, ...

The generalized diameter is the greatest distance between any two points on the boundary of a closed figure. The diameter of a subset E of a Euclidean space R^n is therefore ...

A topologically invariant property of a surface defined as the largest number of nonintersecting simple closed curves that can be drawn on the surface without separating it. ...

In antiquity, geometric constructions of figures and lengths were restricted to the use of only a straightedge and compass (or in Plato's case, a compass only; a technique ...

The Gosper island (Mandelbrot 1977), also known as a flowsnake (Gardner 1989, p. 41), is a fractal that is a modification of the Koch snowflake. The term "Gosper island" was ...

A graceful permutation sigma on n letters is a permutation such that {|sigma(i)-sigma(i+1)|:i=1,2,...,n-1}={1,2,...,n-1}. For example, there are four graceful permutations on ...

With three cuts, dissect an equilateral triangle into a square. The problem was first proposed by Dudeney in 1902, and subsequently discussed in Dudeney (1958), and Gardner ...

A root-finding algorithm which makes use of a third-order Taylor series f(x)=f(x_n)+f^'(x_n)(x-x_n)+1/2f^('')(x_n)(x-x_n)^2+.... (1) A root of f(x) satisfies f(x)=0, so 0 ...