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A derived polygon with side ratios chosen as r=1/2 so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle P, the ...

A minor arc (left figure) is an arc of a circle having measure less than or equal to 180 degrees (pi radians).

The mixtilinear circle is the circumcircle of the mixtilinear triangle, i.e., the triangle formed by the centers of the mixtilinear incircles. Neither its center not circle ...

The radical circle of the mixtilinear incircles has a center with trilinear center function alpha_(999)=cosA-2, (1) which is Kimberling center X_(999). It has radius (2) ...

The mixtilinear triangle is the triangle connecting the centers of the mixtilinear incircles. It has trilinear vertex matrix (1) In has area (2) where Delta is the area of ...

A curve consisting of two mirror-reversed intersecting crescents (lunes). This curve can be traced unicursally. The region common to both crescents is a lens.

Morley's circle is the circumcircle of the first Morley triangle. Its center is the first Morley center, which has center function alpha_(356)=cos(1/3A)+2cos(1/3B)cos(1/3C), ...

An oval whose construction is illustrated in the above diagram.

A principal vertex x_i of a simple polygon P is called a mouth if the diagonal [x_(i-1),x_(i+1)] is an extremal diagonal (i.e., the interior of [x_(i-1),x_(i+1)] lies in the ...

Multisection of a mathematical quantity or figure is division of it into a number of (usually) equal parts. Division of a quantity into two equal parts is known as bisection, ...