Math at the Movies Dr Don Allen Department

Math at the Movies Dr. Don Allen Department of Mathematics Texas A&M

Topics • Counting. • You're not in Kansas anymore, Todo. • The ball game • Calculations • • The Die Hard 3 problem Calculus, anyone? Higher mathematics Hiding in the train

Counting

Finger counting In the movie The Clan of the Cave Bear, Ayla is adopted into a clan of Neanderthals. Her adoptive father is teaching her to count.

Give me a high-five… He can count to five. "Only Mog-ur knows this much. " She then shows him how to count to ten and then to twenty. Ayla is at the head of this class!

Chinese counting

Oceana – base 5

Ancient carvings 6, 500

Blombos Cave 70, 000 years Purpose? ? ?

American Indians Apache Navaho Sioux

Double tally stick Banking

Quipu

Comedy and Counting 7 × 13? ? ? 28 =

Abbott & Costello

Abbott & Costello 13 13 28

Topics • Counting. • You're not in Kansas anymore, Todo. • The ball game • Calculations • • The Die Hard 3 problem Calculus, anyone? Higher mathematics Hiding in the train

The Wizard of Oz

Scarecrow – with brain "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. " What? ? ?

Pythagorean Theorem "The sum of the squares upon the legs of a right triangle is equal to the square upon the hypotenuse".

Pythagorean Theorem …from an Arabic translation of Euclid Proposition I -47

Topics • Counting. • You're not in Kansas anymore, Todo. • The ball game • Calculations • • The Die Hard 3 problem Calculus, anyone? Higher mathematics Hiding in the train

Baseball and math? ? ? Homework problem Bill can paint the house in five hours, and Mary can paint the house in three hours. How many hours did it take both to paint the house?

Here is what we see

Painting the house

Filling the tank Of the four spouts, one fills the whole tank in one day, one in two days, one in three days, and one in four days. What time will it take all four to fill the tank? From a Greek Anthology, c. 500 CE Not such a new problem…

Topics • Counting. • You're not in Kansas anymore, Todo. • The ball game • Computations • • The Die Hard 3 problem Calculus, anyone Higher mathematics Hiding in the train

Computation, anyone? What’s the search area? Math modeling

Did he get it correct? Our Hero An error of about. 04%. Wow!! Exact math

Tom and pal Wilson

The Fugitive "Our fugitive has now been on the run for 90 minutes. Foot speed over uneven ground is four miles per hour. That gives us a radius of six miles. "

It’s a rates problem, plus…

Gold and more gold Is he right? …and a quotation of the price of gold on the Paris commodity exchange, and the fact that there are 14, 000 bars of gold, he computes the value to be $16, 000.

Assemble the facts

For just one bar and… To get the value of all the gold we multiply by the number of bars He’s way off!

In 12 Angry Men a young man is accused of murdering his father. All jurors but one want to convict him immediately.

The hypothesis During the course of the deliberations, the jurors discuss how long a six car elevated subway would take to pass the window of the victim. "It takes about 10 seconds, " he said. Other jurors agreed. Does this value hold up?

Assemble the facts - compute Let us suppose that • Each subway car is 48 feet long • The subway travels at 30 mi/hr So, the subway is 6 × 48= 288 feet long.

Now compute We have Thus the subway moves 180 feet in They’re way off!

Topics • Counting. • You're not in Kansas anymore, Todo. • The ball game • Calculations • • The Die Hard 3 problem Calculus, anyone? Higher mathematics Hiding in the train

The Die Hard 3 problem The bad guy tells our heros that they must make exactly four gallons from five and three gallon jugs. They did it just in time.

How did they do it?

Step-by-step

Step-by-step

Step-by-step

Given 11 and 4. Make 8 Step 1 Step 2 Step 3 Step 4

Topics • Counting. • You're not in Kansas anymore, Todo. • the ball game • Calculations • • The Die Hard 3 problem Calculus, anyone? Higher mathematics Hiding in the train

Calculus, anyone? Richard challenges the Chinese shopkeeper to a dual. Who can compute faster?

The abacist The shopkeeper wins at addition, easily. They tie at multiplication. But when taking a cube root, Richard wins. But … Was he correct?

He was correct – applying calculus Binomial theorem Approximation

The calculation Richard gives 12. 00238

More calculus In the movie Stand Deliver, Jaime Escalante takes a group of East Los Angeles high school students to the AP Calculus exam. They must prepare for two years to get ready.

“I can’t do calculus. ” X

He makes a classic mistake

Inspirational This film is about the remarkable spirit, perseverance and mental toughness of a teacher and his inspiration to a whole class of students to achieve what they thought was impossible. Edward James Olmos Integrate

Topics • Counting. • You're not in Kansas anymore, Todo. • The ball game • Calculations • • The Die Hard 3 problem Calculus, anyone? Higher mathematics Hiding in the train

Higher math In the movie Bedazzled, our hero Elliot Richards is tempted by the devil to choose any seven wishes.

Homework we’d like to see In one part of the film the devil plays a teacher for a group of school boys and "blows them away" by not making any assignments.

What was that problem? Find positive integer solutions of the equation Show your work!!!

Can we solve it for extra credit? Had the movie been made just 10 years earlier, this would have constituted a 360 year old unsolved problem known as Fermat's Last Theorem. It is named after Pierre de Fermat (1601 -1665) who discovered it. Fermat conjectured that there are no solutions.

It has been resolved… In 1994, Princeton mathematician Andrew Wiles, after seven years of concentrated effort, produced a proof that indeed there are no solutions. It shocked the world.

There is still an open question Goldbach conjecture: Any even number (>2) can be written as the sum of exactly two prime numbers. A prime number is one which is divisible only by itself and one.

Hiding in the train Try to hide in the train. You cannot. . . I will find you.