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Given a polygon with an even number of sides, the derived polygon is obtained by joining the points which are a fractional distance r along each side. If r=1/2, then the ...

Two sextuples of skew lines on the general cubic surface such that each line of one is skew to one line in the other set. In all, there are 30 points, with two lines through ...

The normal to an ellipse at a point P intersects the ellipse at another point Q. The angle corresponding to Q can be found by solving the equation (P-Q)·(dP)/(dt)=0 (1) for ...

An equichordal point is a point p for which all the chords of a curve C passing through p are of the same length. In other words, p is an equichordal point if, for every ...

Is there a planar convex set having two distinct equichordal points? The problem was first proposed by Fujiwara (1916) and Blaschke et al. (1917), but long defied solution. ...

p is an equireciprocal point if, for every chord [x,y] of a curve C, p satisfies |x-p|^(-1)+|y-p|^(-1)=c for some constant c. The foci of an ellipse are equichordal points.

The trilinear coordinates alpha:beta:gamma of a point P relative to a reference triangle are proportional to the directed distances a^':b^':c^' from P to the side lines of ...

A circumconic hyperbola, which therefore passes through the orthocenter, is a rectangular hyperbola, and has center on the nine-point circle. Its circumconic parameters are ...

A general space based on the line element ds=F(x^1,...,x^n;dx^1,...,dx^n), with F(x,y)>0 for y!=0 a function on the tangent bundle T(M), and homogeneous of degree 1 in y. ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the first fundamental form is the inner product of tangent vectors, ...