## Thursday 15 July 2010

### Holy Moly! That's a Devilish Number

It is pretty well known and accepted that the number of the beast in the Book of Revelations in the Christian Bible is 666, although apparently 616 was found in some third century works. 666 is a much more interesting number, so I thought I would point out a couple of Devilish Oddities that I learned from "Mathematical Amazements and Surprises" by Alfred S. Posamentier and Ingmar Lehmann.

If you add up the first 62 or 36 natural numbers, 1+2+3+...+ 36; you get 666... Note that six is a triangular number, 36 of course is a square, and the result, 666, must also be triangular since it it the sum of a string of consecutive natural numbers starting with one.

Of course we can make our Devilish number more holy, by using the Divine number seven. If you take the first seven primes, 2, 3, 5, 7, 11, 13 and 17, and find the sum of their squares (Holy Pythagoras, Batman!) Yeah, you guessed it.... 666.

If you factor 666 to its primes, you get 2*3*3*37.... and the sum of the digits of the factors is 2+3+3+(3+7)= 6+6+6..... spooky, huh...
The good professor has several more that I will let you pursue on your own, but hey, just one more...but as a problem... You can insert plus signs in appropriate places in the sequence 1 2 3 4 5 6 7 8 9 and the sum will be 666 in more than one way... How many can you find.

That's Captain Marvel at the top, by the way. He was born full grown in a 1939/1940 Fawcett (later DC) Comic. He is up there because "Holy Moly" was perhaps invented, but certainly popularized by the comic book hero. Moly (or Moley) itself comes from a much earlier "comic book", Homer's Odyssey. It was the herb that Hermes gave to Odysseus to protect him from Circe's magic.

Math fun and Classical Literature in one place... how cool is that?