Clock Arithmetic and Prime Numbers
One of the greatest mathematicians of all time was Carl Gauss . One of his earliest achievement was the invention of clock arithmetic, writes Marcus du Sautoy in Music of the Primes . It is easy to understand. It is 10 o’clock. If someone says they will be back in 4 hours, we add 4 to 10 to get 14. But since the clock only has 12 hours, we don’t say the person will be back at 14 o’clock; instead we say 2 o’clock. Stop for a moment and think of how you knew 14 meant 2 o’clock. Because it is the remainder when 14 (the answer) is divided by 12 (the number of hours on the clock). That’s clock arithmetic. Gauss found a different use for it. Say, you want to find the remainder when 3 x 9 x 12 is divided by 1 1. You start by calculating 3 x 9 = 27. Find the remainder when 27 is divided by 11 – the answer is 5. Now multiply this remainder (5) by the other number (12) to get 5 x 12 = 60. Again, find the remainder when 60 is divided by 11 – the answer is 5. That’s your fina...