MATHEMATICS IN POPULAR CULTUREElana ReiserSt. Joseph’s College

Can you figure out the movie title?

Solution

Snakes on a Plane!

Example 1: Cryptography

Caesar Cipher

Julius Caesar used it to send secret messages to soldiers

Shifts letters by chosen amount

Example: Shift by one

Plaintext: math is coolCiphertext: nbui jt dppm

Activity

Decode the message with a shift +2 to solve the riddle:

Question: Why did I divide sin by tan?

Answer: Lwuv equ

Solution

Question: Why did I divide sin by tan?

Answer: Lwuv equ Just cos

The Da Vinci Code

(similar to) Caesar Cipher exampleo Numbers are Fibonacci numbers out of

order13 – 3 – 2 – 21 – 1 – 1 – 8 – 5 1 – 1 – 2 – 3 – 5 – 8 – 13 – 21

o Rearrange wordsO, Draconian devil! Oh, lame saint!Leonardo Da Vinci the Mona Lisa

Vigenere Cipher

Given a key, words can be encoded and decodedA B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A A B C D E F G H I J K L M N O P Q R S T U V W X Y ZB B C D E F G H I J K L M N O P Q R S T U V W X Y Z AC C D E F G H I J K L M N O P Q R S T U V W X Y Z A BD D E F G H I J K L M N O P Q R S T U V W X Y Z A B CE E F G H I J K L M N O P Q R S T U V W X Y Z A B C DF F G H I J K L M N O P Q R S T U V W X Y Z A B C D EG G H I J K L M N O P Q R S T U V W X Y Z A B C D E FH H I J K L M N O P Q R S T U V W X Y Z A B C D E F GI I J K L M N O P Q R S T U V W X Y Z A B C D E F G HJ J K L M N O P Q R S T U V W X Y Z A B C D E F G H IK K L M N O P Q R S T U V W X Y Z A B C D E F G H I JL L M N O P Q R S T U V W X Y Z A B C D E F G H I J KM M N O P Q R S T U V W X Y Z A B C D E F G H I J K LN N O P Q R S T U V W X Y Z A B C D E F G H I J K L MO O P Q R S T U V W X Y Z A B C D E F G H I J K L M NP P Q R S T U V W X Y Z A B C D E F G H I J K L M N OQ Q R S T U V W X Y Z A B C D E F G H I J K L M N O PR R S T U V W X Y Z A B C D E F G H I J K L M N O P QS S T U V W X Y Z A B C D E F G H I J K L M N O P Q RT T U V W X Y Z A B C D E F G H I J K L M N O P Q R SU U V W X Y Z A B C D E F G H I J K L M N O P Q R S TV V W X Y Z A B C D E F G H I J K L M N O P Q R S T UW W X Y Z A B C D E F G H I J K L M N O P Q R S T U VX X Y Z A B C D E F G H I J K L M N O P Q R S T U V WY Y Z A B C D E F G H I J K L M N O P Q R S T U V W XZ Z A B C D E F G H I J K L M N O P Q R S T U V W X Y

Vigenere Cipher Example

Key = key and word to encode is mathA B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A A B C D E F G H I J K L M N O P Q R S T U V W X Y ZB B C D E F G H I J K L M N O P Q R S T U V W X Y Z AC C D E F G H I J K L M N O P Q R S T U V W X Y Z A BD D E F G H I J K L M N O P Q R S T U V W X Y Z A B CE E F G H I J K L M N O P Q R S T U V W X Y Z A B C DF F G H I J K L M N O P Q R S T U V W X Y Z A B C D EG G H I J K L M N O P Q R S T U V W X Y Z A B C D E FH H I J K L M N O P Q R S T U V W X Y Z A B C D E F GI I J K L M N O P Q R S T U V W X Y Z A B C D E F G HJ J K L M N O P Q R S T U V W X Y Z A B C D E F G H IK K L M N O P Q R S T U V W X Y Z A B C D E F G H I JL L M N O P Q R S T U V W X Y Z A B C D E F G H I J KM M N O P Q R S T U V W X Y Z A B C D E F G H I J K LN N O P Q R S T U V W X Y Z A B C D E F G H I J K L MO O P Q R S T U V W X Y Z A B C D E F G H I J K L M NP P Q R S T U V W X Y Z A B C D E F G H I J K L M N OQ Q R S T U V W X Y Z A B C D E F G H I J K L M N O PR R S T U V W X Y Z A B C D E F G H I J K L M N O P QS S T U V W X Y Z A B C D E F G H I J K L M N O P Q RT T U V W X Y Z A B C D E F G H I J K L M N O P Q R SU U V W X Y Z A B C D E F G H I J K L M N O P Q R S TV V W X Y Z A B C D E F G H I J K L M N O P Q R S T UW W X Y Z A B C D E F G H I J K L M N O P Q R S T U VX X Y Z A B C D E F G H I J K L M N O P Q R S T U V WY Y Z A B C D E F G H I J K L M N O P Q R S T U V W XZ Z A B C D E F G H I J K L M N O P Q R S T U V W X Y

Use column with word to encode letters and row with key letters

Column row resultm k wa e et y rh k r

Gossip Girl

Example 2: Taxicab Numbers

History

British mathematician G.H. Hardy mentored Indian mathematician Ramanujan

Definition

Smallest number that can be expressed as sum of two positive cubes in two ways:

13+123 = 1+1728 93+103 = 729+1000

1729 (2nd taxicab number)

Smallest number that can be expressed as sum of two positive cubes in n ways

nth taxicab number

Example

87539319: 3rd taxicab number87539319 = 1673 +4363 = 2283 + 4233 = 2553 + 4143

From Futurama

Futurama

Activity

What is the smallest number that can be expressed as the sum of two positive squares in two ways?

Solution

What is the smallest number

that can be expressed as the

sum of two positive squares

in two ways?

50 = 12 + 72 = 52 + 52

Example 3: Logic

Die Hard

Activity

Make exactly 4 gallons using 3 gallon and 5 gallon jugs

Die Hard

Solution

Fill 3 gallon jug and pour into 5 gallon jug

Fill 3 gallon jug and pour into 5 gallon jug until full, leaving 1 gallon in 3 gallon jug

Solution cont.

Empty 5 gallon jug and pour 1 gallon into 5 gallon jug

Fill 3 gallon jug and pour into 5 gallon jug, leaving 4 gallons in 5 gallon jug

Example 4: Transitivity

Definition

A BB C A C

30 Rock

Activity

Use transitivity to find the conclusion:

If I eat my spinach then I’ll become muscularIf I become muscular then I’ll become a wrestlerIf I am a wrestler then I’ll wear sequined tightsIf I wear sequined tights then I’ll be ridiculous

Solution

If I eat my spinach then I’ll become muscularIf I become muscular then I’ll become a

wrestlerIf I am a wrestler then I’ll wear sequined tightsIf I wear sequined tights then I’ll be ridiculous

ConclusionIf I eat my spinach then I will be ridiculous

Example 5: The Monty Hall Problem

What is it?

A game show contestant picks one of three doors.

Goats are behind two doors and a car is behind the third.

The host, who knows what is behind each door, opens one of the doors the contestant didn’t pick to reveal a goat.

Activity

Should the contestant stick with the original door or switch to

the remaining one?

Activity cont.

Let’s play!

Numb3rs

21

Example 6: Infinity

What is up with infinity?

Is infinity a number?What is ∞+1?What about 2 ∙∞?What about ∞ ∙∞?

Still not convinced?

Infinity divided by infinity doesn’t equal one

Assume it does

.

FAIL

Revenge

It gets weirder

There is more than one kind of infinity Countably infinite

Integers

Uncountable Real numbers between 0 and 1

Activity

True or False:

There are more numbers between 0 and 2 than

there are between 0 and 1.

Solution

FALSE

There are the same amount of numbers between 0 and 1 as there are between 0

and 2

The Fault in Our Stars

Songs With Math

o U+ Me = Us 2gethero 4 out of 5 Soul Coughingo Mathematics Mos Defo (Lord It's Hard to Be Happy When You're

Not) Using the Metric System Atom and His Package