Problem of the Week: Finding the Polynomial

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3 TV Shows for Math Geeks

Normally math and television are thought of like oil and water: they don't really mix well when thrown together. Even in science fiction, math is exaggerated or ignored altogether. (why were people able to stand on spaceships in Star Trek? The force of gravity shouldn't be that strong!)

However, as these three examples show, sometimes the two can mix for compelling entertainment for everyone!


Numb3rs



On a show about solving crimes, it may seem a little strange to see someone writing formulas on a chalkboard. However, it isn't done just for show. The show employed several mathematical consultants to help when writing the equations. While the show has received a little criticism for sometimes scrupulously connecting the math with the situation, the math on the show has been deemed accurate and valid by several mathematicians!

Big Bang Theory

 


In a show about four physicists, math inevitably makes an appearance. Often the mathematical references on the show become a part of the pop culture lexicon (Schrodinger's Cat, for example). It has even inspired a mathematical proof! On one episode of the show, Sheldon, the main character, said that his favorite number was 73. Why? 73 has a prime index is 21. This means that 73 is the 21st smallest prime number. Flipping around 21 results in 12. What number has a prime index of 12? 37, which is, of course, 73 flipped around. Dartmouth College professor and fan of the show Carl Pomerance was curious as to whether or not this was the only case in which this was possible, and wrote a proof on the subject. A section of the proof even appeared in the background of the episode titled "The Inspiration Deprivation!" The proof can be found here.

 
Futurama



Even though this show is animated and features a fair amount of science fiction elements, a lot of the math featured in the show is fairly accurate - several of the writers on the show had Ph.D's in math. One of them, Ken Keeler, wrote a proof that ended up tying into the show's plot! WARNING: The following will contain mild spoilers of "The Prisoner of Benda".
In the episode, Professor Farnsworth creates a machine that will allow two people to switch bodies. However, the machine won't allow two people to swap back if they have switched minds with each other already. Thus, when characters on the show want to try out the machine, they end up in entirely different bodies with no clear way to get them out. However, a few mathematicians are summoned by the professor, and eventually figure out a solution: if two additional people are added, there exists a way for people to return to their original bodies despite the limitations of the machine! This proof is allegedly the first time a television show has been used to prove something, and it makes for compelling TV! The proof can be found here.

Problem of the Week 7-23-19: Shaking Hands at a Party [Combinatorics]

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What is Yellow Pig's Day?

You are perhaps wondering what the Center of Math is doing posting about a holiday dedicated to yellow pigs. Was this meant for another blog? Is the Center of Math announcing that they're now the Center of Pork Artistry? To answer those questions, no, and not in the foreseeable future.

Yellow Pig's day is actually a celebration of the number 17. In the 1960's, a pair of math students at Princeton were discussing the many properties of 17, and decided that there should be a day to celebrate it. Ultimately the date they decided was July 17th! Thus, Yellow Pig's Day was born. Why Yellow Pig's Day? One of the students discussing 17 decided that the mascot of the holiday should be a yellow pig with 17 eyelashes, 17 teeth, and 17 toes.

Here are some of the properties of 17 that make it worthy of a mathematical holiday:

-17 is the smallest number that can be written as the sum of a cube and a square in 2 different ways (8+9=17 and 1+16=17)

-It is also the smallest number that is the sum of two powers of 4 (1+16=17)

-17 is the minimum number of givens in a Sudoku puzzle for the puzzle to have a unique solution

-In Italy, 17 is a lucky number. In Roman numerals, 17 is written as XVII, which is an anagram of VIXI, which means 'my life is over' in Italian.

-Depending on how you look at it, 17 is either the most random or the least random number. In a study in which respondents were asked to pick a random number between 1 and 20, 17 was the number that was selected the most. Is it the most random because the most people decided it was the most random? Or is it the least random because the most people chose that number?

-17 is the only prime number that is the sum of 4 consecutive prime numbers (2+3+5+7=17), which is possible because 2 is the only even prime number and the smallest prime number. The sum of any other 4 consecutive primes will be even, and thus won't be prime.

-And, finally, as all ABBA fans know, 17 is the age of all young, sweet Dancing Queens

There is no one way to celebrate the holiday, but this haiku (a poem with 17 syllables!) should offer a good starting point:

Spend time with some friends,
Hug a mathematician,
And have a good time!

Problem of the Week 7-16-19: Counting Lattice Paths [Combinatorics]

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Problem of the Week 7-11-19: Find the Sum [Algebra]

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Advanced Knowledge Problem of the Week 7-9-19: Polynomial Function in Numerator [Analysis]

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Problem of the Week 7-4-19: A 7-Tuple of Integers [Algebra]

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Advanced Knowledge Problem of the Week 7-2-19: A Binary Operation [Algebra]

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