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Starr roses are attractive geometric figures such as those illustrated above.

In the triangle DeltaABC illustrated above, side c subtends angle ∠C. More generally, given a geometric object O in the plane and a point P, let A be the angle from one edge ...

A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...

The triquetra is a geometric figure consisting of three mutually intersecting vesica piscis lens shapes, as illustrated above. The central region common to all three lenses ...

To each epsilon>0, there corresponds a delta such that ||f-g||<epsilon whenever ||f||=||g||=1 and ||(f+g)/2||>1-delta. This is a geometric property of the unit sphere of ...

The figure formed when the midpoints of adjacent sides of a quadrilateral are joined. Varignon's theorem demonstrated that this figure is a parallelogram. The center of the ...

If K is a simplicial complex, let V be the vertex set of K. Furthermore, let K be the collection of all subsets {a_0,...,a_n} of V such that the vertices a_0, ..., a_n span a ...

If each of two curves meets the line at infinity in distinct, nonsingular points, and if all their intersections are finite, then if to each common point there is attached a ...

There are a few plane curves known as "bean curves." The bean curve identified by Cundy and Rowllet (1989, p. 72) is the quartic curve given by the implicit equation ...

Given a set of n+1 control points P_0, P_1, ..., P_n, the corresponding Bézier curve (or Bernstein-Bézier curve) is given by C(t)=sum_(i=0)^nP_iB_(i,n)(t), where B_(i,n)(t) ...