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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 ...

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 ...

The tetranacci constant is ratio to which adjacent tetranacci numbers tend, and is given by T = (x^4-x^3-x^2-x-1)_2 (1) = 1.92756... (2) (OEIS A086088), where (P(x))_n ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...

The golden angle is the angle that divides a full angle in a golden ratio (but measured in the opposite direction so that it measures less than 180 degrees), i.e., GA = ...

The elliptic lambda function lambda(tau) is a lambda-modular function defined on the upper half-plane by lambda(tau)=(theta_2^4(0,q))/(theta_3^4(0,q)), (1) where tau is the ...