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An important result in valuation theory which gives information on finding roots of polynomials. Hensel's lemma is formally stated as follows. Let (K,|·|) be a complete ...

Given a circle C with center O and radius k, then two points P and Q are inverse with respect to C if OP·OQ=k^2. If P describes a curve C_1, then Q describes a curve C_2 ...

Kepler's folium is a folium curve explored by Kepler in 1609 (Lawrence 1972, p. 151; Gray et al. 2006, p. 85). When used without qualification, the term "folium" sometimes ...

If a points A^', B^', and C^' are marked on each side of a triangle DeltaABC, one on each side (or on a side's extension), then the three Miquel circles (each through a ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

A projection of the Veronese surface into three dimensions (which must contain singularities) is called a Steiner surface. A classification of Steiner surfaces allowing ...

A surface (or "space") of section, also called a Poincaré section (Rasband 1990, pp. 7 and 93-94), is a way of presenting a trajectory in n-dimensional phase space in an ...

The "binary" Champernowne constant is obtained by concatenating the binary representations of the integers C_2 = 0.(1)(10)(11)(100)(101)(110)(111)..._2 (1) = ...

A folding function is a function that maps the integers Z={...,-3,-2,-1,0,1,2,3,...} onto the nonnegative integers Z^*={0,1,2,3,...}. This type of function arises naturally ...

The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...