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A double point at which two (or more) osculating curves are tangent. The above plot shows the tacnode of the curve 2x^4-3x^2y+y^2-2y^3+y^4=0. The capricornoid and links curve ...

A 3-coloring of graph edges so that no two edges of the same color meet at a graph vertex (Ball and Coxeter 1987, pp. 265-266).

A set of circuits going along the graph edges of a graph, each with an even number of graph edges, such that just one of the circuits passes through each graph vertex (Ball ...

An (n,k)-talisman hexagon is an arrangement of nested hexagons containing the integers 1, 2, ..., H_n=3n(n-1)+1, where H_n is the nth hex number, such that the difference ...

An n×n array of the integers from 1 to n^2 such that the difference between any one integer and its neighbor (horizontally, vertically, or diagonally, without wrapping ...

A knot equivalent to a polygonal knot. Knots which are not tame are called wild knots.

The external (internal) similarity point of two fixed circles is the point at which all the circles homogeneously (nonhomogeneously) tangent to the fixed circles have the ...

Two curves both containing the point P are tangent at P if they share the same tangent line at P.

A ruled surface M is a tangent developable of a curve y if M can be parameterized by x(u,v)=y(u)+vy^'(u). A tangent developable is a developable surface.

Let the speed sigma of a closed curve on the unit sphere S^2 never vanish. Then the tangent indicatrix, also called the tantrix, tau=(sigma^.)/(|sigma^.|) is another closed ...