Solcius

09-19-2008, 10:20 AM

I thought of posting this in the "I hate math" thread but the info. was too long and it was kinda different topic so.......................

The number 666 is cool. Made famous by the Book of Revelation (Chapter 13, verse 18, to be exact), it has also been studied extensively by mathematicians because of its many interesting properties. Here is a compendium of mathematical facts about the number 666. Most of the well-known "chestnuts" are included, but many are relatively new and have not been published elsewhere.

1. The number 666 is a simple sum and difference of the first three 6th powers:

666 = 1(raised to 6) - 2(raised to 6) + 3(raised to 6).

2. It is also equal to the sum of its digits plus the cubes of its digits:

666 = 6 + 6 + 6 + 6³ + 6³ + 6³.

There are only five other positive integers with this property. Exercise: find them, and prove they are the only ones!

3. The sum of the squares of the first 7 primes is 666:

666 = 2² + 3² + 5² + 7² + 11² + 13² + 17²

4. There are exactly two ways to insert '+' signs into the sequence 123456789 to make the sum 666, and exactly one way for the sequence 987654321:

666 = 1 + 2 + 3 + 4 + 567 + 89 = 123 + 456 + 78 + 9

666 = 9 + 87 + 6 + 543 + 21

but also

666 is a divisor of 123456789 + 987654321.

5. The following fact is quite well known, but still interesting: If you write the first 6 Roman numerals, in order from largest to smallest, you get 666:

DCLXVI = 666.

More inscriptions to come sooonnn.............................

The number 666 is cool. Made famous by the Book of Revelation (Chapter 13, verse 18, to be exact), it has also been studied extensively by mathematicians because of its many interesting properties. Here is a compendium of mathematical facts about the number 666. Most of the well-known "chestnuts" are included, but many are relatively new and have not been published elsewhere.

1. The number 666 is a simple sum and difference of the first three 6th powers:

666 = 1(raised to 6) - 2(raised to 6) + 3(raised to 6).

2. It is also equal to the sum of its digits plus the cubes of its digits:

666 = 6 + 6 + 6 + 6³ + 6³ + 6³.

There are only five other positive integers with this property. Exercise: find them, and prove they are the only ones!

3. The sum of the squares of the first 7 primes is 666:

666 = 2² + 3² + 5² + 7² + 11² + 13² + 17²

4. There are exactly two ways to insert '+' signs into the sequence 123456789 to make the sum 666, and exactly one way for the sequence 987654321:

666 = 1 + 2 + 3 + 4 + 567 + 89 = 123 + 456 + 78 + 9

666 = 9 + 87 + 6 + 543 + 21

but also

666 is a divisor of 123456789 + 987654321.

5. The following fact is quite well known, but still interesting: If you write the first 6 Roman numerals, in order from largest to smallest, you get 666:

DCLXVI = 666.

More inscriptions to come sooonnn.............................