Tiling by rectangles and alternating current

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