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The Tucker circles are a generalization of the cosine circle and first Lemoine circle which can be viewed as a family of circles obtained by parallel displacing sides of the ...

x^(2n)+1=[x^2-2xcos(pi/(2n))+1] ×[x^2-2xcos((3pi)/(2n))+1]×...× ×[x^2-2xcos(((2n-1)pi)/(2n))+1].

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

The functions describing the horizontal and vertical positions of a point on a circle as a function of angle (cosine and sine) and those functions derived from them: cotx = ...

Trigonometry

The exponential function has two different natural q-extensions, denoted e_q(z) and E_q(z). They are defined by e_q(z) = sum_(n=0)^(infty)(z^n)/((q;q)_n) (1) = _1phi_0[0; ...

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular ...

A hyperbola (plural "hyperbolas"; Gray 1997, p. 45) is a conic section defined as the locus of all points P in the plane the difference of whose distances r_1=F_1P and ...

Convergents of the pi continued fractions are the simplest approximants to pi. The first few are given by 3, 22/7, 333/106, 355/113, 103993/33102, 104348/33215, ... (OEIS ...