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Let a, b, and k be integers with k>=1. For j=0, 1, 2, let S_j=sum_(i=j (mod 3))(-1)^i(k; i)a^(k-i)b^i. Then 2(a^2+ab+b^2)^(2k)=(S_0-S_1)^4+(S_1-S_2)^4+(S_2-S_0)^4.

The Galilean spiral is the curve with polar equation r=btheta^2-a for a>0 which describes the trajectory of a point uniformly accelerated along a line rotating about a point.

The solution to a game in game theory. When a game saddle point is present max_(i<=m)min_(j<=n)a_(ij)=min_(j<=n)max_(i<=m)a_(ij)=v, and v is the value for pure strategies.

The Garfield curve is the name sometimes given to the curve with polar equation r=thetacostheta when plotted from theta=-2pi to 2pi (Sisson and Szarvas 2016) because of its ...

When applied to a system possessing a length R at which solutions in a variable r change character (such as the gravitational field of a sphere as r runs from the interior to ...

Harmonic coordinates satisfy the condition Gamma^lambda=g^(munu)Gamma_(munu)^lambda=0, (1) or equivalently, partial/(partialx^kappa)(sqrt(g)g^(lambdakappa))=0. (2) It is ...

The study, first developed by Boole, of shift-invariant operators which are polynomials in the differential operator D^~. Heaviside calculus can be used to solve any ordinary ...

A function S_n(z) which satisfies the recurrence relation S_(n-1)(z)-S_(n+1)(z)=2S_n^'(z) together with S_1(z)=-S_0^'(z) is called a hemicylindrical function.

A 16-sided polygon, sometimes also called a hexakaidecagon. The regular hexadecagon is a constructible polygon, and the inradius r, circumradius R, and area A of the regular ...

The hippopede, also known as the horse fetter, is a curve given by the polar equation r^2=4b(a-bsin^2theta). Hippopedes are plotted above for values of a/b=0.2 to 2.0.