the primitive arab people ruled women’s (body) covering as well as chastity, and the poets were honored to praise these qualities in their poems.in the present article reasons of women’s (body) covering are studied.the main reasons to be mentioned are grief and sorrow, fear of captivity in wars, enthusiasm and interests and poverty.

We prove the following theorems: (1) every spherical convex body W of constant width $$ \varDelta (W)\ge \frac{\uppi}{2} can be covered by a disk radius (W)+\arcsin \left(\frac{2\sqrt{3}}{3}\cos \frac{\varDelta (W)}{2}\right)-\frac{\uppi}{2}; (2) reduced R thickness (R)<\frac{\uppi}{2} arctan \left(\sqrt{2}\tan (R)}{2}\right).

Covering a convex body by its homothets is a classical notion in discrete geometry that has resulted in a number of interesting and long-standing problems. Swanepoel introduced the covering parameter of a convex body as a means of quantifying its covering properties. In this paper, we introduce two relatives of the covering parameter called covering index and weak covering index, which upper bo...

Covering a convex body by its homothets is a classical notion in discrete geometry that has resulted in a number of interesting and long-standing problems. Swanepoel [Mathematika 52 (2005), 47–52] introduced the covering parameter of a convex body as a means of quantifying its covering properties. In this paper, we introduce a relative of the covering parameter called covering index, which turn...

We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...