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 totwenty. Ayla is at the head of this class!

Chinese counting

Oceana – base 5

Ancient carvings

6,500

Blombos Cave

Purpose???

70,000 years70,000 years

American Indians

Apache Navaho Sioux

Double tally stick

D o u b le Ta lly S tick

Banking

Quipu

Comedy and Counting

???7 × 13 = 28

Abbott & Costello

Abbott & Costello

13

13

13

13

13

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

a

c

R ig h t T rian g le

b

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 triangleis equal to the square upon the hypotenuse".

b

a

b a

b

a

ba

c

c

c

c

a

c

R ig h t T rian g le

b

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???

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?

Homework problem

Here is what we see

Painting the house

Bill paints 15 house in one hour

Mary paints 13 house in one hour

Together they paint 15 1

3 house in one hour

m houseshour

n hours mn houses(painted)

15 1

3houses

hour n hours 1 houses(painted)

15 1

3 n 1

3 53 5 n 1

n 158 1 7

8 hours

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?

Not such a new problem…

From a Greek Anthology, c. 500 CE

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?

160000 mi This is 4002

3.14 Is his calculationcorrect?

502,400 mi ????

A r2

4002 160000 502654.8246mi

OurHero

Exactmath

An error of about .04%. Wow!!

Tom and pal Wilson

The Fugitive

"Our fugitive has nowbeen 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…

How did he make the computation? It is a unitsconversionproblem and a rate equation.

Rate of travel Time traveled Distance covered.

First convertminutesto hours:

90 minutes 1 hour

60 minutes 1.5 hours

4 miles/hour 1.5 hours 6 miles

Gold and more gold

…and a quotation of the priceof gold on the Paris commodityexchange, and the fact that thereare 14,000 bars of gold, he computesthe value to be $16,000,000.

Is he right?

Assemble the facts

Compilingour data. Let us suppose a bar of gold is 30cm 5cm 2cm. Then The volumeof one bar of gold is 30 5 2 300

cm3

Gold weighs 19320kg/ m3

Gold sells for $1.13/g ($32/oz) Number of gold bars 14,000

For just one bar and…

To get the valueof one bar of gold we multiply:

300cm319320kg/ m3 $1.13/ g 6549480.0gm3

cm3 kg

$6549. 48

To get the value of all the gold we multiply by the number of bars

14000 bars $6549.48/bar $91,692,720

He’s way off!

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

The hypothesis

"It takes about 10 seconds," he said. Other jurors agreed.

Does this value hold up?

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.

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

30mi/ h 30mi/ h 1h60min

1min60s

5280ft1mi

30 5280602

ft/ s 44ft/ s

Thus the subway moves 180 feet in

They’re way off!

288 ft44 ft / s

6. 54 s

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 herosthat they must make exactly four gallons from five and three gallon jugs. They did it just in time.

How did they do it?

(1) Fill the five gallon jug. Three gallon jug is empty.(2) Empty three gallons from the five gallon jug into the threegallon jug.(3) There remains two gallons in the five gallon jug. Empty thethree gallon jug.(4) Pour the two gallons into the three gallon jug.(5) Fill the five gallon jug and pour one gallon from it into thethree gallon jug - filling the three gallon jug.(6) Four gallons remain in the five gallon jug. We have solvedthe problem.

Step-by-step

Step-by-step

Step-by-step

Given 11 and 4. Make 8

Step 1 Step 2

Step 3 Step 4

11 gallon

4 gallon

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 and 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.

f x dx

“I can’t do calculus.”

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

0

/21 k2 sin2 d , 0 k 1Integrat

e

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. Itshocked 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.

Din er

Clu b

Sh ower

M a i l