Search Results for ""

If equilateral triangles DeltaABE_(AB), DeltaBCE_(BC), and DeltaACE_(AC) are erected externally on the sides of any triangle DeltaABC, then their centers N_(AB), N_(BC), and ...

The value nearest to but still inside an inner fence.

Araya and Wiener (2011) found the two cubic planar hypohamiltonian graphs on 70 and 88 vertices, respectively, illustrated above.

The orthogonal polynomials on the interval [-1,1] associated with the weighting functions w(x) = (1-x^2)^(-1/2) (1) w(x) = (1-x^2)^(1/2) (2) w(x) = sqrt((1-x)/(1+x)), (3) ...

A function is in big-theta of f if it is not much worse but also not much better than f, Theta(f(n))=O(f(n)) intersection Omega(f(n)).

Let beta=detB=x^2-ty^2, (1) where B is the Brahmagupta matrix, then det[B(x_1,y_1) B(x_2,y_2)] = det[B(x_1,y_1)]det[B(x_2,y_2)] (2) = beta_1beta_2]. (3)

B(x,y)=[x y; +/-ty +/-x]. (1) It satisfies B(x_1,y_1)B(x_2,y_2)=B(x_1x_2+/-ty_1y_2,x_1y_2+/-y_1x_2). (2) Powers of the matrix are defined by B^n = [x y; ty x]^n (3) = [x_n ...

For R[mu+nu]>1, int_(-pi/2)^(pi/2)cos^(mu+nu-2)thetae^(itheta(mu-nu+2xi))dtheta=(piGamma(mu+nu-1))/(2^(mu+nu-2)Gamma(mu+xi)Gamma(nu-xi)), where Gamma(z) is the gamma function.

The three planes determined by the edges of a trihedron and the internal bisectors of the respectively opposite faces are coaxal, and the common line of these planes is ...

A flat disk that acts as a two-sided die.