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The distance between two skew lines with equations x = x_1+(x_2-x_1)s (1) x = x_3+(x_4-x_3)t (2) is given by D=(|(x_3-x_1)·[(x_2-x_1)x(x_4-x_3)]|)/(|(x_2-x_1)x(x_4-x_3)|) (3) ...

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 ...

Mark a point P on a side of a triangle and draw the perpendiculars from the point to the two other sides. The line between the feet of these two perpendiculars is called the ...

The line on which the orthocenter H, triangle centroid G, circumcenter O, de Longchamps point L, nine-point center N, and a number of other important triangle centers lie. ...

A point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point.

A straight line is tangent to a given curve f(x) at a point x_0 on the curve if the line passes through the point (x_0,f(x_0)) on the curve and has slope f^'(x_0), where ...

If P is a point on the circumcircle of a reference triangle, then the line PP^(-1), where P^(-1) is the isogonal conjugate of P, is called the antipedal line of P. It is a ...

The Nagel line is the term proposed for the first time in this work for the line on which the incenter I, triangle centroid G, Spieker center Sp, and Nagel point Na lie. ...

The Gergonne line is Oldknow's (1996) term for the perspectrix of a contact triangle DeltaDEF and its reference triangle DeltaABC. It is determined by the Nobbs points D^', ...

A point which does not lie on at least one ordinary line.