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Nan had alerted me to an interesting lecture at Stanford quite a while
ago. I didn't attend but later he shared a link to the video which I
just watched last night and enjoyed very much. You can find it here:
https://mrc.stanford.edu/content/rubik-escher-bank-brian-conrad
The answer is surprising and deep.
Thank you Nan!
-Melinda
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https://mrc.stanford.edu/content/rubik-escher-bank-brian-conrad