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A curious approximation to the Feigenbaum constant delta is given by pi+tan^(-1)(e^pi)=4.669201932..., (1) where e^pi is Gelfond's constant, which is good to 6 digits to the ...

The first practical algorithm for determining if there exist integers a_i for given real numbers x_i such that a_1x_1+a_2x_2+...+a_nx_n=0, or else establish bounds within ...

In one dimension, the Gaussian function is the probability density function of the normal distribution, f(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)), (1) sometimes also ...

Let theta(t) be the Riemann-Siegel function. The unique value g_n such that theta(g_n)=pin (1) where n=0, 1, ... is then known as a Gram point (Edwards 2001, pp. 125-126). An ...

Consider the sequence of partial sums defined by s_n=sum_(k=1)^n(-1)^kk^(1/k). (1) As can be seen in the plot above, the sequence has two limit points at -0.812140... and ...

There are two versions of the moat-crossing problem, one geometric and one algebraic. The geometric moat problems asks for the widest moat Rapunzel can cross to escape if she ...

Modular arithmetic is the arithmetic of congruences, sometimes known informally as "clock arithmetic." In modular arithmetic, numbers "wrap around" upon reaching a given ...

What is the sofa of greatest area S which can be moved around a right-angled hallway of unit width? Hammersley (Croft et al. 1994) showed that S>=pi/2+2/pi=2.2074... (1) ...

N. Nielsen (1909) and Ramanujan (Berndt 1985) considered the integrals a_k=int_1^2((lnx)^k)/(x-1)dx. (1) They found the values for k=1 and 2. The general constants for k>3 ...

The answer to the question "which fits better, a round peg in a square hole, or a square peg in a round hole?" can be interpreted as asking which is larger, the ratio of the ...