Search Results for ""

The points of tangency t_1 and t_2 for the four lines tangent to two circles with centers x_1 and x_2 and radii r_1 and r_2 are given by solving the simultaneous equations ...

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

The circle map is a one-dimensional map which maps a circle onto itself theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n), (1) where theta_(n+1) is computed mod 1 and K is a ...

An n×n matrix whose rows are composed of cyclically shifted versions of a length-n list l. For example, the 4×4 circulant matrix on the list l={1,2,3,4} is given by C=[4 1 2 ...

A prime number p is called circular if it remains prime after any cyclic permutation of its digits. An example in base-10 is 1,193 because 1,931, 9,311, and 3,119 are all ...

The circumcenter of mass is a concept that can be defined by analogy with one of the the constructions for the geometric centroid for the case of polygons. The geometric ...

A circumhyperbola is a circumconic that is a hyperbola. A rectangular circumhyperbola always passes through the orthocenter H and has center on the nine-point circle ...

Take K a number field and m a divisor of K. A congruence subgroup H is defined as a subgroup of the group of all fractional ideals relative prime to m (I_K^m) that contains ...

Define S_n(x) = sum_(k=1)^(infty)(sin(kx))/(k^n) (1) C_n(x) = sum_(k=1)^(infty)(cos(kx))/(k^n), (2) then the Clausen functions are defined by ...