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Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...

The Frucht graph is smallest cubic identity graph (Skiena 1990, p. 185). It is implemented in the Wolfram Language as GraphData["FruchtGraph"]. It has 12 vertices and 18 ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

Tietze's graph is the cubic graph on 12 nodes and 18 edges illustrated above in a number of embeddings. It is implemented in the Wolfram Language as GraphData["TietzeGraph"]. ...

The thin plate spline is the two-dimensional analog of the cubic spline in one dimension. It is the fundamental solution to the biharmonic equation, and has the form ...

There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal ...

An elliptic integral is an integral of the form int(A(x)+B(x)sqrt(S(x)))/(C(x)+D(x)sqrt(S(x)))dx, (1) or int(A(x)dx)/(B(x)sqrt(S(x))), (2) where A(x), B(x), C(x), and D(x) ...

Consider a point P inside a reference triangle DeltaABC, construct line segments AP, BP, and CP. The Ehrmann congruent squares point is the unique point P such that three ...

A curve named and studied by Newton in 1701 and contained in his classification of cubic curves. It had been studied earlier by L'Hospital and Huygens in 1692 (MacTutor ...

There exist points A^', B^', and C^' on segments BC, CA, and AB of a triangle, respectively, such that A^'C+CB^'=B^'A+AC^'=C^'B+BA^' (1) and the lines AA^', BB^', CC^' ...