pictures from 'A Mathematical Bridge'

I have been reading a book named 'A Mathematical Bridge' and have come across a couple of proofs which make an entertaining read:

First, showing the the square root of 2 is irrational

Second, A proof that all integers >1 have a prime decomposition

Both of these a brilliant, short proof which really mainly on logic rather than mathematical skill, credit goes to Stephen Fletcher Hewson for writing the book.