AMDM Project News

Fermi Project

Who is Fermi?

Would it be possible to fit everyone in the world into a cube that measures one mile by one mile by one mile?

This is an example of a Fermi Question—an estimation problem designed to teach dimensional analysis, approximation, and the importance of clearly identifying one’s assumptions.

“How large is the crowd?” is an another example of a Fermi Question, which requires estimating physical quantities to produce an answer.

Enrico Fermi was an Italian physicist known for his ability to take limited information and arrive at a reasonable numerical estimate. He approached a problem by setting a lower estimate—a value that the item in question was more than—and an upper estimate—a value that the item in question was smaller than. Fermi then worked through the problem using this approach and reached a numerical estimate within identified limits. Fermi worked at the University of Chicago, and his classic question was “How many piano tuners are there in the city of Chicago?”

Fermi questions rely on making logical assumptions about a situation to reach an estimate to an order of magnitude (usually a power of 10). That is, the estimate is expressed in hundreds, thousands, millions, and so on—whatever unit is appropriate for the question.

The Project

Select a Fermi Question

Three group members* should devise an estimation process that can be used to answer one of the following questions. Use input from all group members to describe the best estimation process possible.

  1. Is it possible to walk from San Francisco to New York in a year?
  2. If the land area of Earth was divided equally for each person on the planet, about how much would you get?
  1. What is the weight of solid garbage thrown away by Americans families each year?
  2. How many jelly beans fill a 1 liter jar?
  3. What is the mass in kilograms of the student body of your school?
  4. How many gallons of gasoline are used by cars each year in the United States?
  5. How many flat toothpicks would fit on the surface of a sheet of poster board?
  6. If Bill Gates’ net worth was doled out to him by the hour, how much is his time worth per hour?

*You may work with family and friends or someone from our class.

Required Components

Your project must have the following components:

Assumptions: List and explain all assumptions that you made (or had to make) to answer your Fermi question.

Math work: Explain your plan, show ALL your math work, AND the process used to come up with your rough prediction. You need to use this information to come up with your rough prediction.

Prediction: Use your information from your initial math work to predict an answer to your Fermi question. This must be noted before you move on.

Research with MORE math: You will go online and use reliable sources and the support, (dis)prove, conclude, and/or justify your prediction and completely answer your Fermi question. Use your new found information and include all steps in your mathematical (re)calculations. Site your sources.

Power Point or some type of Presentation:

  1. Assumptions
  2. Math work done BEFORE research (estimations)
  3. Prediction of the answer to your Fermi question bases on your estimations
  4. Results of Research (include website(s) with your (re)calculations)
  5. Explanation of how/why your prediction was (in)accurate.
  6. Creativity

**Know your topic in great detail, be prepared for any question.**