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The incentral circle is the circumcircle of the incentral triangle. It has radius R_I=(sqrt(abcf(a,b,c)f(b,c,a)f(c,a,b)))/(8Delta(a+b)(a+c)(b+c)), (1) where Delta is the area ...

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 third mid-arc point is the triangle center with triangle center function alpha_(2089)=[-cos(1/2A)+cos(1/2B)+cos(1/2C)]sec(1/2A). It is Kimberling center X_(2089).

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

Proportionally cutting circles are circles that intersect the sidelines of a reference triangle DeltaABC such that length of the chords that are cut off have lengths mua, ...

Given a chord PQ of a circle, draw any other two chords AB and CD passing through its midpoint. Call the points where AD and BC meet PQ X and Y. Then M is also the midpoint ...

A point process N is called self-correcting if cov(N(s,t),N(t,u))<0 for s<t<u where here, cov denotes the covariance of the two quantities. Intuitively, a process is ...

A point process N is called self-exciting if cov(N(s,t),N(t,u))>0 for s<t<u where here, cov denotes the covariance of the two quantities. Intuitively, a process is ...

The general curve of a system which is linearly dependent on a certain number of given irreducible curves will not have a singular point which is not fixed for all the curves ...

Alexandrov's theorem addresses conditions under which a polygon will fold into a convex polyhedron (Malkevitch).