math at the movies
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/1.jpg)
Math at the Movies
Dr. Don Allen
Department of Mathematics
Texas A&M
![Page 2: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/2.jpg)
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
![Page 3: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/3.jpg)
Counting
![Page 4: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/4.jpg)
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.
![Page 5: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/5.jpg)
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!
![Page 6: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/6.jpg)
Chinese counting
![Page 7: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/7.jpg)
Oceana – base 5
![Page 8: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/8.jpg)
Ancient carvings
6,500
![Page 9: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/9.jpg)
Blombos Cave
Purpose???
70,000 years70,000 years
![Page 10: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/10.jpg)
American Indians
Apache Navaho Sioux
![Page 11: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/11.jpg)
Double tally stick
D o u b le Ta lly S tick
Banking
![Page 12: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/12.jpg)
Quipu
![Page 13: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/13.jpg)
Comedy and Counting
???7 × 13 = 28
![Page 14: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/14.jpg)
Abbott & Costello
![Page 15: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/15.jpg)
Abbott & Costello
13
13
13
13
13
13
13
28
![Page 16: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/16.jpg)
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
![Page 17: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/17.jpg)
The Wizard of Oz
a
c
R ig h t T rian g le
b
![Page 18: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/18.jpg)
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???
![Page 19: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/19.jpg)
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
![Page 20: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/20.jpg)
Pythagorean Theorem
…from an Arabic translation of Euclid
Proposition I-47
![Page 21: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/21.jpg)
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
![Page 22: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/22.jpg)
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
![Page 23: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/23.jpg)
Here is what we see
![Page 24: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/24.jpg)
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
![Page 25: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/25.jpg)
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
![Page 26: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/26.jpg)
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
![Page 27: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/27.jpg)
Computation, anyone?
What’s the search area?
Math modeling
![Page 28: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/28.jpg)
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!!
![Page 29: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/29.jpg)
Tom and pal Wilson
![Page 30: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/30.jpg)
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."
![Page 31: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/31.jpg)
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
![Page 32: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/32.jpg)
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?
![Page 33: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/33.jpg)
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
![Page 34: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/34.jpg)
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!
![Page 35: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/35.jpg)
In 12 Angry Men a young manis accused of murdering his father. All jurors but one want to convict him immediately.
![Page 36: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/36.jpg)
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.
![Page 37: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/37.jpg)
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.
![Page 38: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/38.jpg)
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
![Page 39: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/39.jpg)
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
![Page 40: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/40.jpg)
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.
![Page 41: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/41.jpg)
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.
![Page 42: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/42.jpg)
Step-by-step
![Page 43: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/43.jpg)
Step-by-step
![Page 44: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/44.jpg)
Step-by-step
![Page 45: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/45.jpg)
Given 11 and 4. Make 8
Step 1 Step 2
Step 3 Step 4
11 gallon
4 gallon
![Page 46: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/46.jpg)
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
![Page 47: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/47.jpg)
Calculus, anyone?
Richard challenges the Chinese shopkeeper to a dual. Who can compute faster?
![Page 48: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/48.jpg)
The abacist
The shopkeeper wins at addition, easily.
They tie at multiplication.
But when taking a cube root, Richard wins. But …
Was he correct?
![Page 49: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/49.jpg)
He was correct – applying calculus
Binomial theorem
Approximation
![Page 50: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/50.jpg)
The calculation
Richard gives 12.00238
![Page 51: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/51.jpg)
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
![Page 52: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/52.jpg)
“I can’t do calculus.”
![Page 53: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/53.jpg)
He makes a classic mistake
![Page 54: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/54.jpg)
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
![Page 55: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/55.jpg)
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
![Page 56: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/56.jpg)
Higher math
In the movie Bedazzled, our hero Elliot Richards is tempted by the devil to choose any seven wishes.
![Page 57: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/57.jpg)
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.
![Page 58: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/58.jpg)
What was that problem?
Find positive integer solutions of the equation
Show your work!!!
![Page 59: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/59.jpg)
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.
![Page 60: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/60.jpg)
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.
![Page 61: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/61.jpg)
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.
![Page 62: Math at the Movies](https://reader033.vdocuments.us/reader033/viewer/2022052204/5681492c550346895db6671c/html5/thumbnails/62.jpg)
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