An Inscribed Scarab

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...

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

an inscribed cylindrical seal with ostrich image from lama cemetery

in the third season excavation of lama cemetery (chal shahin lama), a cylindrical seal with inscription was found and because of its significance, it was introduced, compared and analyzed. existence of this seal indicates the continuation of nomadic practices of the people of this cemetery in spite of change of material culture (for example, ceramic). the seal of lama and its grave reflect the ...