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Let E_n(f) be the error of the best uniform approximation to a real function f(x) on the interval [-1,1] by real polynomials of degree at most n. If alpha(x)=|x|, (1) then ...

Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

The most common form of cosine integral is Ci(x) = -int_x^infty(costdt)/t (1) = gamma+lnx+int_0^x(cost-1)/tdt (2) = 1/2[Ei(ix)+Ei(-ix)] (3) = -1/2[E_1(ix)+E_1(-ix)], (4) ...

A covariant tensor, denoted with a lowered index (e.g., a_mu) is a tensor having specific transformation properties. In general, these transformation properties differ from ...

Adding a damping force proportional to x^. to the equation of simple harmonic motion, the first derivative of x with respect to time, the equation of motion for damped simple ...

A simple way to describe a knot projection. The advantage of this notation is that it enables a knot diagram to be drawn quickly. For an oriented alternating knot with n ...

Einstein summation is a notational convention for simplifying expressions including summations of vectors, matrices, and general tensors. There are essentially three rules of ...

Through a point K in the plane of a triangle DeltaABC, draw parallelians through a point as illustrated above. Then there exist four points K for which ...

In 1757, V. Riccati first recorded the generalizations of the hyperbolic functions defined by F_(n,r)^alpha(x)=sum_(k=0)^infty(alpha^k)/((nk+r)!)x^(nk+r), (1) for r=0, ..., ...

The golden triangle, sometimes also called the sublime triangle, is an isosceles triangle such that the ratio of the hypotenuse a to base b is equal to the golden ratio, ...