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The mean line segment length l^_ is the average length of a line segment in line segment picking within some given shape. As summarized in the following table (where Delta(3) ...

External (or positive) and internal (or negative) similarity points of two circles with centers C and C^' and radii r and r^' are the points E and I on the lines CC^' such ...

The sequence of six 9s which begins at the 762nd decimal place of pi, pi=3.14159...134999999_()_(six 9s)837... (Wells 1986, p. 51). The positions of the first occurrences of ...

Let a in C and |a|<1, then phi_a(z)=(z-a)/(1-a^_z) is a Möbius transformation, where a^_ is the complex conjugate of a. phi_a is a conformal mapping self-map of the unit disk ...

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. ...

A conic section on which the midpoints of the sides of any complete quadrangle lie. The three diagonal points P, Q, and R also lie on this conic.

The circular points at infinity, also called the isotropic points, are the pair of (complex) points on the line at infinity through which all circles pass. The circular ...

The set of points of X fixed by a group action are called the group's set of fixed points, defined by {x:gx=x for all g in G}. In some cases, there may not be a group action, ...

There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal ...

A handlebody of type (n,k) is an n-dimensional manifold that is attained from the standard n-disk by attaching only k-D handles.