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The pentagonal orthobicupola is a convex equilateral orthobicupola having regular pentagonal upper and lower faces. It is Johnson solid J_(30). The unit pentagonal ...

The pentagonal orthobirotunda is a convex equilateral orthobirotunda having regular pentagonal upper and lower faces arranged symmetrically about the midplane. It is Johnson ...

The pentagonal orthocupolarotunda is a convex equilateral solid that is Johnson solid J_(32). The unit pentagonal orthocupolarotunda has volume V=1/3(5+4sqrt(5)) (1) and Dehn ...

Let u and v be any functions of a set of variables (q_1,...,q_n,p_1,...,p_n). Then the expression ...

The differential equation describing exponential growth is (dN)/(dt)=rN. (1) This can be integrated directly int_(N_0)^N(dN)/N=int_0^trdt (2) to give ln(N/(N_0))=rt, (3) ...

Typesetting "errors" in which exponents or multiplication signs are omitted but the resulting expression is equivalent to the original one. Examples include 2^59^2=2592 (1) ...

A surface of constant Gaussian curvature that can be given parametrically by x = a(Ucosu-U^'sinu) (1) y = -a(Usinu+U^'cosu) (2) z = v-aV^', (3) where U = ...

A generalization of the binomial coefficient whose notation was suggested by Knuth, |_n; k]=(|_n]!)/(|_k]!|_n-k]!), (1) where |_n] is a Roman factorial. The above expression ...

A row-convex polyomino is a self-avoiding convex polyomino such that the intersection of any horizontal line with the polyomino has at most two connected components. A ...

When computing the sample variance s numerically, the mean must be computed before s^2 can be determined. This requires storing the set of sample values. However, it is ...