Search Results for ""

Homogeneous coordinates (x_1,x_2,x_3) of a finite point (x,y) in the plane are any three numbers for which (x_1)/(x_3)=x (1) (x_2)/(x_3)=y. (2) Coordinates (x_1,x_2,0) for ...

A path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. A lattice path is therefore a sequence of points P_0, P_1, ...

Given a point P and a triangle DeltaABC, the Miquel triangle is the triangle DeltaP_AP_BP_C connecting the side points P_A, P_B, and P_C of DeltaABC with respect to which M ...

A pivotal isotomic cubic is a self-isotomic cubic that possesses a pivot point, i.e., in which points P lying on the conic and their isotomic conjugates are collinear with a ...

Let a line in three dimensions be specified by two points x_1=(x_1,y_1,z_1) and x_2=(x_2,y_2,z_2) lying on it, so a vector along the line is given by v=[x_1+(x_2-x_1)t; ...

The Riemann sphere, also called the extended complex plane, is a one-dimensional complex manifold C^* (C-star) which is the one-point compactification of the complex numbers ...

Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

If two curves phi and psi of multiplicities r_i!=0 and s_i!=0 have only ordinary points or ordinary singular points and cusps in common, then every curve which has at least ...

A topology on a set X whose open sets are the unions of open balls B(X_0,r)={x in x|g(x_0,x)<r}, where g is a pseudometric on X, x_0 is any point of X, and r>0. There is a ...

Given a succession of nonsingular points which are on a nonhyperelliptic curve of curve genus p, but are not a group of the canonical series, the number of groups of the ...