An Inscribed Jewish Ossuary

Containment and Inscribed Simplices

Let K and L be compact convex sets in Rn. The following two statements are shown to be equivalent: (i) For every polytope Q ⊆ K having at most n+ 1 vertices, L contains a translate of Q. (ii) L contains a translate of K. Let 1 ≤ d ≤ n − 1. It is also shown that the following two statements are equivalent: (i) For every polytope Q ⊆ K having at most d+ 1 vertices, L contains a translate of Q. (i...

Enumeration of inscribed polyominos

We introduce a new family of polyominos that are inscribed in a rectangle of given size for which we establish a number of exact formulas and generating functions. In particular, we study polyominos inscribed in a rectangle with minimum area and minimum area plus one. These results are then used for the enumeration of lattice trees inscribed in a rectangle with minimum area plus one. Résumé. No...

Hereditary chondrocalcinosis in an Ashkenazi Jewish family.

A hereditary chondrocalcinosis is described for the first time in an Ashkenazi Jewish kindred. Of 34 family members in five generations, seven had medical history suggesting the disease. Five of 25 members of generations III-V had direct evidence for their disease. Characteristically, symptoms started at a fairly early age (third decade) while radiological evidence of chondrocalcinosis was dela...

An Area Inequality for Ellipses Inscribed in Quadrilaterals

If E is any ellipse inscribed in a convex quadrilateral, D – , then we prove that Area (E) Area(D – ) π 4 , and equality holds if and only if D – is a parallelogram and E is tangent to the sides of D – at the midpoints. We also prove that the foci of the unique ellipse of maximal area inscribed in a parallelogram, D – , lie on the orthogonal least squares line for the vertices of D – . This doe...

A New Palmprint Segmentation Method Based on an Inscribed Circle