Tiling by rectangles and alternating current

This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings by R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses direct-current circuits. The new approach of this paper is an application of alternating-current circuits. The following results are obtained:• ssary condition for a rectangle to be tilable by rectangles of given shapes; erion for a rectangle to be tilable by rectangles similar to it but not all homothetic to it; erion for a “generic” polygon to be tilable by squares. results generalize those of C. Freiling, R. Kenyon, M. Laczkovich, D. Rinne, and G. Szekeres.