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
Double Tally Stick
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
c
b
a
Right Triangle
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
c
"The sum of the squares
upon the legs of a right triangle
is equal to the square
upon the hypotenuse".
b
a
Right Triangle
b
a
a
c
b
c
c
b
c
a
b
a
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
1
5
1
Mary paints
3
Together they paint 1 1
5
3
Bill paints
housein one hour
housein one hour
housein one hour
1 1 houses  
n hours1 houses(painted)
5
3 hour
1 1 n 1
5
3
3 5 n 1
3 5
n  15 1 7 hours
8
8
m houses  
n hoursmnhouses(painted)
hour
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
160000 mi
This is 
400 2
 3. 14
Is his calculationcorrect?
502, 400 mi
????
An error of about .04%. Wow!!
A 
r2
Exact
math

400 2 160 000

502654. 8246 mi
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…
How did he make the computation? It is a units
conversionproblem and a rate equation.
Rate of travel  Time traveled  Distance covered.
First convertminutes to hours:
1 hour
90 minutes 
 1.5 hours
60 minutes
4 miles/hour  1.5 hours6 miles
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 $16,000,000.
Assemble the facts
Compiling our data. Let us supposea bar of gold is 30cm
5cm 2cm. Then
 The volume of one bar of gold is 30  5  2 300
cm3
 Gold w eighs19320 kg/ 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 w emultiply:
0 cm3 kg
300 cm3 
19320 kg/ m3 
$1. 13/ g 6549480.

gm3

$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 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
1h
1 min
30 mi/ h 30 mi/ h
60 min
60 s
30 5280
ft/ s 44 ft/ s
2
60
5280 ft
1 mi
Thus the subway moves 180 feet in
288 ft
6. 54 s
44 ft / s
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?
(1) Fill the five gallon jug. Three gallon jug is empty.
(2) Empty three gallons from the five gallon jug into the three
gallon jug.
(3) There remains tw o gallons in the five gallon jug. Empty the
three gallon jug.
(4) Pour the tw o gallons into the three gallon jug.
(5) Fill the five gallon jug and pour one gallon from it into the
three gallon jug - filling the three gallon jug.
(6) Four gallons remain in the five gallon jug. We havesolved
the 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
f xdx
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.
“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
Integrate

/2
0
1 k 2 sin 2 d,
0 k 1
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.
Mail
Club
Diner
Shower