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The first definition of the logarithm was constructed by Napier and popularized through his posthumous pamphlet (Napier 1619). It this pamphlet, Napier sought to reduce the ...

The decimal expansion of the natural logarithm of 2 is given by ln2=0.69314718055994530941... (OEIS A002162). It was computed to 10^(11) decimal digits by S. Kondo on May 14, ...

The negative binomial distribution, also known as the Pascal distribution or Pólya distribution, gives the probability of r-1 successes and x failures in x+r-1 trials, and ...

Given a curve C and O=(x_0,y_0) a fixed point called the pedal point, then for a point P on C, draw a line perpendicular to OP. The envelope of these lines as P describes the ...

Newton's iteration is an algorithm for computing the square root sqrt(n) of a number n via the recurrence equation x_(k+1)=1/2(x_k+n/(x_k)), (1) where x_0=1. This recurrence ...

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 doubly noncentral F-distribution describes the distribution (X/n_1)/(Y/n_2) for two independently distributed noncentral chi-squared variables X:chi_(n_1)^2(lambda_1) and ...

A surface such as the Möbius strip or Klein bottle (Gray 1997, pp. 322-323) on which there exists a closed path such that the directrix is reversed when moved around this ...

By asking a small number of innocent-sounding questions about an unknown number, it is possible to reconstruct the number with absolute certainty (assuming that the questions ...

A nut graph is a graph on n>=2 vertices with adjacency matrix A such that A has matrix rank 1 and contains no 0 element (Sciriha 1998, 2008; Sciriha and Gutman, 1998; and ...