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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 ...

A spherical segment is the solid defined by cutting a sphere with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it ...

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 ...

Let O and I be the circumcenter and incenter of a triangle with circumradius R and inradius r. Let d be the distance between O and I. Then d^2=R(R-2r) (Mackay 1886-1887; ...

A hypotrochoid is a roulette traced by a point P attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where P is a distance h from the ...

The mittenpunkt (also called the middlespoint) of a triangle DeltaABC is the symmedian point of the excentral triangle, i.e., the point of concurrence M of the lines from the ...

Parallel curves, frequently called "offset curves" in computer graphics applications, are curves which are displaced from a base curve by a constant offset, either positive ...

Let a Cevian PC be drawn on a triangle DeltaABC, and denote the lengths m=PA^_ and n=PB^_, with c=m+n. Then Stewart's theorem, also called Apollonius' theorem, states that ...

The Moser spindle is the 7-node unit-distance graph illustrated above (Read and Wilson 1998, p. 187). It is sometimes called the Hajós graph (e.g., Bondy and Murty 2008. p. ...

For an ellipse with parametric equations x = acost (1) y = bsint, (2) the negative pedal curve with respect to the origin has parametric equations x_n = ...