Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)

Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.

And what better way to start your week, then by discussing math Monday morning?

In honour of last nights 666th episode, **THOH XXX**, we will look at some of the properties of 666.

In last nights **Treehouse of Horror XXX (Season 31, Episode 04)**, The Simpsons celebrated episode 666 in style, as they planned from the beginning:

The number has made many appearances in the show itself, with my personal favourite being in **Bart Star (S09, E06)**, wherein we can catch the Flanders boys wearing the number on their jerseys:

So let’s look at a couple of the properties of 666:

**Smith Numbers**

As discussed last week, Smith number is a number for which the sum of its digits is equal to the sum of the digits in its prime factorization.

The sum of the digits are 6 + 6 + 6 = 18.

The prime factorization of 666 is 2 x 3 x 3 x 37. The sum of the digits of the prime factorization are 2 + 3 + 3 + 3 + 7 = 18.

As the two values are equal, 666 is a Smith number.

**Triangular Numbers**

A few weeks back, we looked at square pyramidal numbers. Triangular numbers are essentially a two dimensional version of the three dimensional square pyramidal numbers.

The *T*th triangular number is the number of dots in the triangular arrangement with *T* dots on a side, and is equal to the sum of the *T* natural numbers.

So T1 = 1, T2 = 1 + 2 = 3, T3 = 1 + 2 + 3 = 6, etc.

T36 = 1 + 2 + 3 + … + 35 + 36 = 666

666 is the 36th triangular number and can be graphically depicted by a triangular arrangement with 36 dots on a side, and is equal to the sum of the first 36 natural numbers.

**Square of Primes**

Square pyramidal numbers you may recall is the sum of the square of these numbers; such that T1 = 1^{2}, T2 = 1^{2} + 2^{2} = 5, T3 = 1^{2} + 2^{2} + 3^{2} = 14, etc. While 666 is not a square pyramidal number, it is the sum of the squares of the first seven prime numbers.

2^{2} + 3^{2} + 5^{2} + 7^{2} + 11^{2} + 13^{2} + 17^{2} = 4 + 9 + 25 + 49 + 121 + 169 + 289 = 666

**Roman Numerals**

Way back in February, we looked at roman numerals. 666 has the unique feature of using exactly one occurrence of all symbols whose value is less than 1000 in decreasing order (D = 500, C = 100, L = 50, X = 10, V = 5, I = 1).

666 in roman numerals is DCLXVI.

**Cultural Significance**

For those who are unfamiliar of the cultural significance of 666, in Christianity, it is often known as the number of the beast as Revelations 13:15-18 reads:

“*And that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name. Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.*”

However, in China, 666 is considered a very lucky number and often displayed in homes and storefronts. The pronunciation of 6 is very similar to the pronunciation of smooth. So 666 is considered to mean “*everything goes smoothly.*”

Now that we’ve completed a look at some properties of the number 666, why not spend a fraction of 666 on your own Math Mayhem shirt or hoodie.

If you love math or enjoy reading these posts, don’t forget to stop by the Addicts Shop and check out all the paraphernalia, including the Math Mayhem shirts and hoodies.

Were you familiar with these properties of the number 666? Did you watch last nights episode 666? Do you remember some more occurrences of 666 in the show? Sound off in the comments below. You know we love hearing from you.

Will this be on the test?

Roman numerals, they never even tried to teach us that in school. Rocky V plus Rocky II equals Rocky 7 Adrian’s Revenge.

Is a number a triangle number ?? This will tell you –

Double your number

666 x 2 = 1332

Find the Square Root

√ 1332 = 36.49657518

Take the whole number from the result and subtract it from your doubled number

1332 – 36 = 1296

Find the Square Root

√ 1296 = 36

If the result is a whole number that is your Triangle Number

To get the sum of a Triangle Number 1 + 2 + 3 + … + Base where Base is the largest number –

( ( Base + 1 ) / 2 ) x Base

36 + 1 = 37

37 / 2 = 18.5

18.5 x 36 = 666

About last night

This is so cool Safi! I wasn’t aware of the “square of primes” property 😀

You may also add that 666 is the sum of the numbers you can find on a roulette (0 to 36) 🙂