Search Results for ""

The probability that two elements P_1 and P_2 of a symmetric group generate the entire group tends to 3/4 as n->infty (Netto 1964, p. 90). The conjecture was proven by Dixon ...

A graph or directed graph together with a function which assigns a positive real number to each edge (Harary 1994, p. 52).

A geometric construction, also called a verging construction, which allows the classical geometric construction rules to be bent in order to permit sliding of a marked ruler. ...

A paradox in decision theory. Given two boxes, B1 which contains $1000 and B2 which contains either nothing or a million dollars, you may pick either B2 or both. However, at ...

Samuel Pepys wrote Isaac Newton a long letter asking him to determine the probabilities for a set of dice rolls related to a wager he planned to make. Pepys asked which was ...

Curves with Cartesian equation ay^2=x(x^2-2bx+c) with a>0. The above equation represents the third class of Newton's classification of cubic curves, which Newton divided into ...

The next prime function NP(n) gives the smallest prime larger than n. The function can be given explicitly as NP(n)=p_(1+pi(n)), where p_i is the ith prime and pi(n) is the ...

A nialpdrome is a number whose hexadecimal digits are in nonincreasing order. The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 32, 33, 34, 48, 49, ...

Nielsen's spiral, also called the sici spiral (von Seggern 1993) is the spiral with parametric equations x(t) = aci(t) (1) y(t) = asi(t), (2) where ci(t) is the cosine ...

A Lie algebra is nilpotent when its Lie algebra lower central series g_k vanishes for some k. Any nilpotent Lie algebra is also solvable. The basic example of a nilpotent Lie ...