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By the definition of the functions of trigonometry, the sine of pi is equal to the y-coordinate of the point with polar coordinates (r,theta)=(1,pi), giving sinpi=0. ...

Construction of the angle pi/4=45 degrees produces an isosceles right triangle. Since the sides are equal, sin^2theta+cos^2theta=2sin^2theta=1, (1) so solving for ...

The right conoid surface given by the parametric equations x(u,v) = vcosu (1) y(u,v) = vsinu (2) z(u,v) = csqrt(a^2-b^2cos^2u). (3)

The q-analog of the derivative, defined by (d/(dx))_qf(x)=(f(x)-f(qx))/(x-qx). (1) For example, (d/(dx))_qsinx = (sinx-sin(qx))/(x-qx) (2) (d/(dx))_qlnx = ...

An algorithm for making tables of primes. Sequentially write down the integers from 2 to the highest number n you wish to include in the table. Cross out all numbers >2 which ...

The vertex cover number is the size of a minimum vertex cover in a graph G is known as the vertex cover number of G, denoted tau(G). The König-Egeváry theorem states that the ...

A two-dimensional binary (k=2) totalistic cellular automaton with a von Neumann neighborhood of range r=1. It has a birth rule that at least 2 of its 4 neighbors are alive, ...

Let z be defined as a function of w in terms of a parameter alpha by z=w+alphaphi(z). (1) Then Lagrange's inversion theorem, also called a Lagrange expansion, states that any ...

A sum is the result of an addition. For example, adding 1, 2, 3, and 4 gives the sum 10, written 1+2+3+4=10. (1) The numbers being summed are called addends, or sometimes ...

A unit in a ring is an element u such that there exists u^(-1) where u·u^(-1)=1.