Landau’s beautiful proofs:
1= cos 0 = cos (x-x)
Opening cos (x-x):
1 = cos x.cos (-x) – sin x.sin (-x)
=> 1= cos² x + sin² x
[QED]
Let cos x= b/c, sin x = a/c
1= (b/c)² + (a/c)²
c² = b² + a²
=> Pythagoras Theorem
[QED]
Landau (1877-1938) was the successor of Minkowski at the Gottingen University (Math) before WW II.
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