Monday, April 7, 2008

Learning math with The Simpsons

Ok. I like math, and I like really strange math. Perfect numbers, friendly numbers, some special prime numbers like Mersenne prime numbers, and things like that. During my college years I did some computer algorithms to get these humbers (the problem was when the numbers overflowed the long double format numbers). Anyways, surfing the Internet I found something interesting. Something that only few people would have think about.

There is a chapter in 'The Simpsons' that a singing star tells her baseball player husband that she won't go back with him unless he guess correctly the number of attendance to the game. The numbers are: 8191, 8128, 8208. But guess what... The writters didn't take just numbers from nowhere.

8191 - It is a Mersenne prime number. The Mersenne numbers are any number that is one less than a power of two. ((2^n) − 1). So the Mersenne prime number has the characteristic of being a Mersenne number and prime number. 8191 is the fifth Mersenne prime number.

Some facts: The 8th Mersenne prime number was discovered by Euler; and the largest known Mersenne number has
9,808,358 digits (pretty big, huh?).


8128 - It is the fourth perfect number. A perfect number is defined as a positive integer which is the sum of its proper positive divisors. For example: the first perfect number is 6. Its proper positive divisors are 1, 2 and 3, and 1+2+3=6. The equation to get perfect numbers is: (2^(n-1))((2^n) − 1). And the first four perfect numbers were discoverd by... guess who... Exactly!!! Euclid (man... these people had nothing to do... Euclid, Euler, Newton, Gauss... they are everywhere!!!) So, are you wondering which numbers are the first four (you know the first one and the fourth, right?):
  1. 6
  2. 28
  3. 496
  4. 8128
If you don't beleave me, do the maths. The first two are easy, but the third and the fourth... good luck!!!


8208 - This is beautiful. I mean, because I didn't know about these kind of numbers until I read about The Simpsons. Funny, isn't it? Ok. Now, these kind of numbers are called narcissistic number or pluperfect digital invariant (PPDI) or Armstrong number (phew... hard to remember). The characteristics of these numbers is that the number is equal to the sum of each digit to the power of the number of digits. Got lost? Let's see 8208. It has 4 digits, so:

(8^4) + (2^4) + (0^4) + (8^4)
= 2 * (8 * 8 * 8 * 8) + (2 * 2 * 2 * 2)
= 2 * 4096 + 16
= 8192 + 16
= 8208.

8208 is the 15th PPDI number. There are only three 4-digit PPDI numbers, the other two are 1634 and 9474. There are 88 known PPDI, and the largest PPDI number is a number with 39 digits:

115,132,219,018,763,992,565,095,597,973,971,522,401

(Do you want to do the maths?)



Did you enjoy it? It's interesting. Who would have ever say that there was so much to learn watching The Simpsons? So next time someone says that The Simpsons are stupid or nonsence, you can invite him to think about it twice before he says so. Hahahaha...

Want more? Follow this link: http://www.simpsonsmath.com

One question... does someone remember wich was the correct answer??? A, B, C or D??? I don't remember.

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