You already knew that adding two consecutive Fibonacci numbers results in a third Fibonacci number... But, did you know that adding the squares of two consecut

You already knew that adding two consecutive Fibonacci numbers results in a third Fibonacci number... But, did you know that adding the squares of two consecutive Fibonacci numbers -- results in a non-squared Fibonacci number from the original Fibonacci sequence? (See the video for a more visual representation...) To me, the fact that it does that is nothing short of fascinating...