proof ch:08-phonons-lattices@proof-1

open in the book · parts/12-statistical-mechanics/08-phonons-lattices.tex:132

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proof : ch:08-phonons-lattices@proof-1proofproposition 125.2: Crystallographic restriction125.2definition 7.74: π7.74lemma 7.71: Derivatives; the Pythagorean identity7.71lemma 7.75: The first quadrant7.75lemma 7.72: Addition theorems7.72proposition 7.91: The golden ratio7.91proposition 7.77: Special values, periodicity, and the kernel7.77theorem 29.3: Euler's rotation theorem29.3remark 125.3: What the theorem does and does not forbid125.3

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proves Crystallographic restriction declared parts/12-statistical-mechanics/08-phonons-lattices.tex:132