In the plane, the way to enclose the most area with a given perimeter and to use the shortest perimeter to enclose a given area, is always to use a circle. If we replace the plane by a regular tiling of it, and construct polyforms i.e. shapes as sets of tiles, things become more complicated. We need to redefine the area and perimeter measures, and study the consequences carefully. A spiral cons...

Perimeter surveillance is one of the major applications of sensor networks. The perimeter represents the physical extent of the region to be monitored and depending on the application, it is required to sense the intrusion enter the monitored region or leave from the monitored region of the object being monitored. In this paper, the problem of identifying the perimeter of the wireless network’s...

The number of essentially different square polyominoes of order n and minimum perimeter p(n) is enumerated.

Two natural foliations, guided by area and perimeter, of the configurations spaces planar polygons are considered topology their leaves is investigated in some detail. In particular, homology groups homotopy type determined. The with fixed perimeter also Besides, we extend classical isoperimetric duality to all critical points. conclusion a few general remarks on dual extremal problems polygon ...