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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 ...

A root-finding algorithm also known as the tangent hyperbolas method or Halley's rational formula. As in Halley's irrational formula, take the second-order Taylor series ...

A device consisting of two coupled pendula, usually oscillating at right angles to each other, which are attached to a pen. The resulting motion can produce beautiful, ...

Let M be a Riemannian manifold, and let the topological metric on M be defined by letting the distance between two points be the infimum of the lengths of curves joining the ...

The notion of height is defined for proper ideals in a commutative Noetherian unit ring R. The height of a proper prime ideal P of R is the maximum of the lengths n of the ...

The radical of an ideal a in a ring R is the ideal which is the intersection of all prime ideals containing a. Note that any ideal is contained in a maximal ideal, which is ...

A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...