The equal internal bisectors theorem

Equal Opportunity Law and the Construction of Internal Labor Markets

The internal consistency of Easton's theorem

Let Card denote the class of infinite cardinals and Reg the class of infinite regular cardinals. The continuum function on regulars is the function κ 7→ 2, defined on Reg. This function C has the following two properties: α ≤ β → C(α) ≤ C(β) and α < cof (C(α)). Easton [2] showed that, assuming GCH, any function F : Reg → Card with these two properties (any “Easton function”) is the continuum fu...

Internal Analogy in Theorem Proving

Internal analogy tries to reuse solutions of subproblems within the same problem solving process. In mathematical theorem proving several patterns are known where internal analogy suggests itself. Hence, we propose the use of internal analogy in automated theorem proving. This paper investigates the possibility of incorporating internal analogy into the inductive proof planner CL A M. It introd...

On the Area Bisectors of a Polygon

We consider the family of lines that are area bisectors of a polygon (possibly with holes) in the plane. We say that two bisectors of a polygon P are combinatorially distinct if they induce di erent partitionings of the vertices of P . We derive an algebraic characterization of area bisectors. We then show that there are simple polygons with n vertices that have (n) combinatorially distinct are...

On bisectors in normed planes

In this note, we completely describe the shape of the bisector of two given points in a two-dimensional normed vector space. More precisely, we show that, depending on the position of two given points with respect to the shape of the unit circle, the following holds: the bisector of a non-strict pair of points consists of two cones and a curve, which has properties similar to those of bisectors...