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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, ...

A curve also known as swan-like curve or streamline. It is given by the polar equation r=atheta+b, where a>0.

The center of a Neuberg circle.

The radical circle of the Neuberg circles has circle function l=(a^2b^4-b^4c^2+a^2c^4-b^2c^4)/(bc(a^2b^2+a^2c^2+b^2c^2)), (1) which does not correspond to any Kimberling ...

Let a triangle have side lengths a, b, and c with opposite angles A, B, and C. Then (b+c)/a = (cos[1/2(B-C)])/(sin(1/2A)) (1) (c+a)/b = (cos[1/2(C-A)])/(sin(1/2B)) (2) ...

The nonagon, also known as an enneagon, is a 9-sided polygon. Although the term "enneagon" is perhaps preferable (since it uses the Greek prefix and suffix instead of the ...