Search Results for ""

The trigonometric formulas for pi/5 can be derived using the multiple-angle formula sin(5theta)=5sintheta-20sin^3theta+16sin^5theta. (1) Letting theta=pi/5 and x=sintheta ...

A vector Laplacian can be defined for a vector A by del ^2A=del (del ·A)-del x(del xA), (1) where the notation ✡ is sometimes used to distinguish the vector Laplacian from ...

A surface which can be interpreted as a self-intersecting rectangle in three dimensions. The Whitney umbrella is the only stable singularity of mappings from R^2 to R^3. It ...

The surface area of a spherical segment. Call the radius of the sphere R, the upper and lower radii b and a, respectively, and the height of the spherical segment h. The zone ...

The parabolic cylinder functions are a class of functions sometimes called Weber functions. There are a number of slightly different definitions in use by various authors. ...

F_mF_(n+1)-F_nF_(m+1)=(-1)^nF_(m-n), where F_n is a Fibonacci number.

The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the ...

To define a recurring digital invariant of order k, compute the sum of the kth powers of the digits of a number n. If this number n^' is equal to the original number n, then ...

The number of ways of folding a strip of stamps has several possible variants. Considering only positions of the hinges for unlabeled stamps without regard to orientation of ...

The Dirac matrices are a class of 4×4 matrices which arise in quantum electrodynamics. There are a variety of different symbols used, and Dirac matrices are also known as ...