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The method of d'Alembert provides a solution to the one-dimensional wave equation (partial^2y)/(partialx^2)=1/(c^2)(partial^2y)/(partialt^2) (1) that models vibrations of a ...

A theorem giving a criterion for an origami construction to be flat. Kawasaki's theorem states that a given crease pattern can be folded to a flat origami iff all the ...

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

Bowling, known as "ten pins" throughout most of the world, is a game played by rolling a heavy ball down a long narrow track and attempting to knock down ten pins arranged in ...

A Turing machine which, by appropriate programming using a finite length of input tape, can act as any Turing machine whatsoever. In his seminal paper, Turing himself gave ...

In spherical coordinates, the scale factors are h_r=1, h_theta=rsinphi, h_phi=r, and the separation functions are f_1(r)=r^2, f_2(theta)=1, f_3(phi)=sinphi, giving a Stäckel ...

For vectors u=(u_x,u_y,u_z) and v=(v_x,v_y,v_z) in R^3, the cross product in is defined by uxv = x^^(u_yv_z-u_zv_y)-y^^(u_xv_z-u_zv_x)+z^^(u_xv_y-u_yv_x) (1) = ...

The one-dimensional wave equation is given by (partial^2psi)/(partialx^2)=1/(v^2)(partial^2psi)/(partialt^2). (1) In order to specify a wave, the equation is subject to ...