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If each of two nonparallel transversals with nonminimal directions meets a given curve in finite points only, then the ratio of products of the distances from the two sets of ...

The pentanacci constant is the limiting ratio of adjacent pentanacci numbers. It is the algebraic number P = (x^5-x^4-x^3-x^2-x-1)_1 (1) = 1.96594823... (2) (OEIS A103814), ...

The lines joining the vertices of a tetrahedron to the centroids of the opposite faces are called medians. Commandino's theorem states that the four medians of a tetrahedron ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...

There are at least two results known as "the area principle." The geometric area principle states that (|A_1P|)/(|A_2P|)=(|A_1BC|)/(|A_2BC|). (1) This can also be written in ...

Given five equal disks placed symmetrically about a given center, what is the smallest radius r for which the radius of the circular area covered by the five disks is 1? The ...

As Lagrange showed, any irrational number alpha has an infinity of rational approximations p/q which satisfy |alpha-p/q|<1/(sqrt(5)q^2). (1) Furthermore, if there are no ...

Quantization is a nonlinear process which generates additional frequency components (Thompson et al. 1986). This means that the signal is no longer band-limited, so the ...

A tree which is not rooted, i.e., a normal tree with no node singled out for special treatment (Skiena 1990, p. 107). Free trees are sometimes known instead as unrooted trees ...

A special function mostly commonly denoted psi_n(z), psi^((n))(z), or F_n(z-1) which is given by the (n+1)st derivative of the logarithm of the gamma function Gamma(z) (or, ...