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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 ...

Begin with the Yff central triangle and then parallel-displace the isoscelizers in such a way as to reduce the central triangle to a point while keeping the other three ...

The directrix of a conic section is the line which, together with the point known as the focus, serves to define a conic section as the locus of points whose distance from ...

The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is ...

The subset B of the Euclidean plane formed by the union of the interval [0,1] of the x-axis and all line segments of unit length passing through the origin which form an ...

The circumcircle of the Fuhrmann triangle. It has the line HNa, where H is the orthocenter and Na is the Nagel point, as its diameter. In fact, these points (Kimberling ...

If perpendiculars A^', B^', and C^' are dropped on any line L from the vertices of a triangle DeltaABC, then the perpendiculars to the opposite sides from their perpendicular ...

If a plane cuts the sides AB, BC, CD, and DA of a skew quadrilateral ABCD in points P, Q, R, and S, then (AP)/(PB)·(BQ)/(QC)·(CR)/(RD)·(DS)/(SA)=1 both in magnitude and sign ...

A basis vector in an n-dimensional vector space is one of any chosen set of n vectors in the space forming a vector basis, i.e., having the property that every vector in the ...

Given a unit line segment [0,1], pick two points at random on it. Call the first point x_1 and the second point x_2. Find the distribution of distances d between points. The ...