![]() More generally, Mersenne primes fit the pattern 2 p –1, where p is any prime number. Among the infinity of numbers, fewer than 100 exhibit narcissism.Ĩ,191 is a prime number, because it has no divisors other than 1 and the number itself, and it is labelled a Mersenne prime because another 17th-century French mathematician, Marin Mersenne, spotted that 8,191 was equal to 2 13 – 1. The fact that 8,208 can recreate itself from its own components hints that the number is in love with itself, hence the narcissistic label. As René Descartes, the 17th-century French mathematician (and philosopher) pointed out: "Perfect numbers, like perfect men, are very rare."Ĩ,208 is a narcissistic number because it contains 4 digits, and raising each of these digits to the 4th power generates four numbers that add up to itself: 8 4 + 2 4 + 0 4 + 8 4 = 8,208. The third perfect number is 496, and the fourth one is 8,128, which appears in this episode. The second perfect number is 28, because 1, 2, 4, 7 and 14 not only divide into 28, but they also add up to 28. The smallest perfect number is 6, because 1, 2 and 3 not only divide into 6, but they also add up to 6. These digits might seem arbitrary and innocuous, but in fact they represent a perfect number, a narcissistic number and a Mersenne prime.Ĩ,128 is called a perfect number, because its divisors add up to the number itself. The screen displays three multiple choice options 8,128, 8,208 and 8,191. The Jumbo Vision screen from 'Marge and Homer Turn a Couple Play', showing a perfect number, a narcissistic number and a Mersenne prime number. More important, just before she appears on the screen, it displays a question that asks the baseball fans in the crowd to guess the attendance. The episode climaxes with Tabitha appearing on the Jumbo Vision screen at the Springfield stadium, where she publicly proclaims her love for Buck. The storyline revolves around Marge and Homer's efforts to help baseball star Buck Mitchell and his wife Tabitha Vixx, who are experiencing marital difficulties. The 2006 episode "Marge and Homer Turn a Couple Play", for example, contains a triple dose of secret mathematics. Until now, only extreme geeks have been aware that the writers have been smuggling mathematics into their scripts while the rest of the planet has been oblivious to the numerous nods to number theory and geometry. ![]() When they moved from academia to Fox Studios, these writers retained their passion for numbers and they have secretly planted mathematical references in dozens of episodes. Others have similarly impressive degrees in maths, a few can even boast PhDs, and Jeff Westbrook resigned from a senior research post at Yale University to write scripts for Homer, Marge and the other residents of Springfield. ![]() Al Jean, who worked on the first series and is now executive producer, went to Harvard University to study mathematics at the age of just 16. These examples are just the tip of the iceberg, because the show's writing team includes several mathematical heavyweights.
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