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Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...

If S is any nonempty partially ordered set in which every chain has an upper bound, then S has a maximal element. This statement is equivalent to the axiom of choice. Renteln ...

The probability of getting at least one "6" in four rolls of a single 6-sided die is 1-(5/6)^4 approx 0.5177, (1) which is slightly higher than the probability of at least ...

de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...

The q-analog of pi pi_q can be defined by setting a=0 in the q-factorial [a]_q!=1(1+q)(1+q+q^2)...(1+q+...+q^(a-1)) (1) to obtain ...

A q-analog of the Saalschütz theorem due to Jackson is given by where _3phi_2 is the q-hypergeometric function (Koepf 1998, p. 40; Schilling and Warnaar 1999).

Divide a triangle by its three medians into six smaller triangles. Surprisingly, the circumcenters O_(AB), O_(BA), etc. of the six circumcircles of these smaller triangles ...

Van der Corput sequences are a means of generating sequences of points that are maximally self-avoiding (a.k.a. quasirandom sequences). In the one-dimensional case, the ...

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. Its Schläfli symbol is {infty}. The apeirogon can produce a ...

For a bivariate normal distribution, the distribution of correlation coefficients is given by P(r) = (1) = (2) = (3) where rho is the population correlation coefficient, ...