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Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the third fundamental form is given by III(v_(p),w_(p))=S(v_(p))·S(w_(p)), where S is ...

The Trott curve is a simple example of a quartic curve having 28 real bitangents-the maximum possible for a quartic-given by the equation ...

Except for triangles, every simple polygon has at least two nonoverlapping ears.

The right conoid surface given by the parametric equations x(u,v) = vcosu (1) y(u,v) = vsinu (2) z(u,v) = csqrt(a^2-b^2cos^2u). (3)

An oriented surface for which every point belongs to a Wiedersehen pair. Proof of the Blaschke conjecture established that the only Wiedersehen surfaces are the standard ...

The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point X_(179) called the first Ajima-Malfatti point ...

Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

The curve formed by the intersection of a cylinder and a sphere is known as Viviani's curve. The problem of finding the lateral surface area of a cylinder of radius r ...

The Gergonne point Ge is the perspector of a triangle DeltaABC and its contact triangle DeltaT_AT_BT_C. It has equivalent triangle center functions alpha = [a(b+c-a)]^(-1) ...

One of the three standard tori given by the parametric equations x = a(1+cosv)cosu (1) y = a(1+cosv)sinu (2) z = asinv, (3) corresponding to the torus with a=c. It has ...