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The two-dimensional space consisting of the set of triples {(a,b,c):a,b,c in K, not all zero}, where triples which are scalar multiples of each other are identified.

The evolute of the prolate cycloid x = at-bsint (1) y = a-bcost (2) (with b>a) is given by x = a[t+((bcost-a)sint)/(acost-b)] (3) y = (a(a-bcost)^2)/(b(acost-b)). (4)

If proofreader A finds a mistakes and proofreader B finds b mistakes, c of which were also found by A, how many mistakes were missed by both A and B? Assume there are a total ...

The 4-polyhex illustrated above.

A proper factor of a positive integer n is a factor of n other than 1 or n (Derbyshire 2004, p. 32). For example, 2 and 3 are positive proper factors of 6, but 1 and 6 are ...

A proper fraction is a fraction p/q with p,q>0 such that p/q<1. A fraction p/q>1 is called an improper fraction.

A proper subset S^' of a set S, denoted S^' subset S, is a subset that is strictly contained in S and so necessarily excludes at least one member of S. The empty set is ...

A knot having the property that no surgery could possibly yield a counterexample to the Poincaré conjecture is said to satisfy Property P (Adams 1994, p. 262).

A proposition is a mathematical statement such as "3 is greater than 4," "an infinite set exists," or "7 is prime." An axiom is a proposition that is assumed to be true. With ...

For N=k·2^n+1 with k odd and 2^n>k, if there exists an integer a such that a^((N-1)/2)=-1 (mod N), then N is prime. A prime of this form is known as a Proth prime.