Search Results for ""

A number which is simultaneously square and triangular. Let T_n denote the nth triangular number and S_m the mth square number, then a number which is both triangular and ...

Pre-Algebra

A plot of the map winding number W resulting from mode locking as a function of Omega for the circle map theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n) (1) with K=1. (Since ...

The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...

Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It ...

A homework problem proposed in Steffi's math class in January 2003 asked students to prove that no ratio of two unequal numbers obtained by permuting all the digits 1, 2, ...

The number one (1), also called "unity," is the first positive integer. It is an odd number. Although the number 1 used to be considered a prime number, it requires special ...

The law appearing in the definition of Boolean algebras and lattice which states that a ^ (a v b)=a v (a ^ b)=a for binary operators v and ^ (which most commonly are logical ...

A golden rhombohedron is a trigonal trapezohedron (and therefore rhombohedron with congruent rhombic faces) whose faces consist of six equal golden rhombi. There are two ...