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The circumcircle, Brocard circle, Lemoine axis, and isodynamic points belong to a coaxal system orthogonal to the Apollonius circles, called the Schoute coaxal system. In ...

The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v ...

A bitwin chain of length one consists of two pairs of twin primes with the property that they are related by being of the form: (n-1,n+1) and (2n-1,2n+1). (1) The first few ...

If the three straight lines joining the corresponding vertices of two triangles ABC and A^'B^'C^' all meet in a point (the perspector), then the three intersections of pairs ...

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method ...

There are two different definitions of generalized Fermat numbers, one of which is more general than the other. Ribenboim (1996, pp. 89 and 359-360) defines a generalized ...

A polyhedron is rigid if it cannot be continuously deformed into another configuration. A rigid polyhedron may have two or more stable forms which cannot be continuously ...

A special type of binary tree obtained by starting with the fractions 0/1 and 1/0 and iteratively inserting (m+m^')/(n+n^') between each two adjacent fractions m/n and ...

erf(z) is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function defined by ...

A linear transformation of period two. Since a linear transformation has the form, lambda^'=(alphalambda+beta)/(gammalambda+delta), (1) applying the transformation a second ...