That has to be how I would want to pitch a movie to mathematically unwary movie executives. Do they know that Spiderman and Waterworld both show exponential behavior?
This is a page with information on
a presentation from Math in Action 2004 by John Golden . It is inspired by the article Big Box-Office Bucks , in the Mathematics Teacher , by Robert A. Powers, February 2001, Volume 94, Issue 2, Page 112. It is a great example of how hand held calculators enable us to do interesting things with real life data that just would have been too computationally intensive before. It is made possible by the amazing data collection done by Bruce Nash at The Numbers .
Now here is a chart of Summer 2003 blockbusters, from the-numbers.com:
What is exponential about this data? Where are the clues to an underlying exponential structure? Don't exponentials either decrease rapidly to zero or zoom off to infinity? It only takes a little investigation to find the link.
Some documents for you to download and use. (Permission for reproduction granted for educational use.)
Other mathematical uses:
this is really a discrete math game. Start with a set of actors for vertices. Students fill in edges between vertices that represent a movie that each made together. If you just have the actors from one movie, this makes a complete graph. The traditional Kevin Bacon game is to get from Kevin Bacon to any other actor in 6 movies. You might try this with Johnny Depp nowadays. The most useful reference for this game is clearly the Internet Movie Database . Students can investigate completeness, paths, circuits and distance in a strangely interesting setting.
For example, two movie math problems I wrote for the Menu of Problems in Mathematics Teaching in the Middle School , in February 2003.
1. Critics explain that movies are getting shorter in running time so that theaters can show them more times during normal operating hours. In 1997, the average length of a movie was 109 minutes; in 2002, the average length was 103 minutes. On a typical weekend, a movie theater is open from noon until midnight and schedules at least 15 minutes between showings. If the theater is full, seats 150 people, and charges an average of $6 per ticket, how much more money does an 82-minute movie like Men in Black II make compared with a typical 1997 movie on one Saturday?
2. Men in Black II grossed $19,821,658 on 3557 screens on the opening Friday. Use the information from question 1 to find the average number of people who attended each showing.
Virtually all of the cool math that can be done with the stock market, can be done with the hollywood stock exchange, but centering around information that many teens have more at hand than financial information. The downside is that it is one more step away from the real world careers and data. The upside is that it is a great introduction to financial markets through commodities that students may find very engaging.
National Council of Teachers of Mathematics