 Rumsey presented results that angle-defined scaling was one of the underlying requirements to make antennas "invariant" (have same radiation properties) at a number, or range of, frequencies.Work by Y. Mushiake in Japan starting in 1948 demonstrated similar results of frequency independent antennas having self-complementarity.It was believed that antennas had to be defined by angles for this to be true, but in 1999 it was discovered that "self-similarity was one of the underlying requirements to make antennas frequency and bandwidth invariant".