Geometric

 I think I am meeting the limits of how AI can help with mathematics. They

are large language models, not math tutors. I've been trying to get them to 

explain to me how, in quantum computing, repeating or adding a gate can

improve precision, and all I am getting back is discussions on error correction, 

not really the topic here.

https://meta.ai/s/1qM8d5oxcoR9PoZS/

One thing of interest that did emerge is that spectral decomposition takes us to

a geometric view:

https://www.getmerlin.in/fr/chat/9dac5c03-ceea-4edb-8b36-6b971e282469

                                                           *     *     *

 Amplitude, Period, Phase Shift and Frequency (mathsisfun.com)     

https://www.mathsisfun.com/calculus/fourier-series.html

  https://forums.parallax.com/uploads/FileUpload/d0/6f7868d8263988b52359e71f4721c5.pdf