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The sum of the values of an integral of the "first" or "second" sort int_(x_0,y_0)^(x_1,y_1)(Pdx)/Q+...+int_(x_0,y_0)^(x_N,y_N)(Pdx)/Q=F(z) and ...

Let P=p:q:r and U=u:v:w be distinct points, neither lying on a side line of the reference triangle DeltaABC. Then the P-cross conjugate of U is the point ...

Two similar figures with parallel homologous lines and connectors of homologous points concurrent at the homothetic center are said to be in homothetic position. If two ...

A nonuniform rational B-spline surface of degree (p,q) is defined by ...

The plane spanned by the three points x(t), x(t+h_1), and x(t+h_2) on a curve as h_1,h_2->0. Let z be a point on the osculating plane, then [(z-x),x^',x^('')]=0, where ...

The period for a quasiperiodic trajectory to pass through the same point in a surface of section. If the rotation number is irrational, the trajectory will densely fill out a ...

A tetractys, also called a tetraktys or decad, is an arrangement of 10 points in the form of a triangle with 1 point in the first row, two in the second, three in the third, ...

Define a = d(u,v)d(w,x) (1) b = d(u,w)d(v,x) (2) c = d(u,x)d(v,w), (3) where u, v, w, and x are vertices of a graph and d(i,j) is the graph distance between vertices i and j. ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

The dimension e(G), also called the Euclidean dimension (e.g., Buckley and Harary 1988) of a graph, is the smallest dimension n of Euclidean n-space in which G can be ...