Enrico Fermi (September 29, 1901 – November 28, 1954) An Italian-born physicist Known for his work on the development of the first nuclear reactor, and contributions to quantum theory, nuclear and particle physics Fermi was known for his ability to make good approximate calculations

Fermi Problems (aka Fermi Estimates) Named after Enrico Fermi, they are problems that require making educated guesses using estimation skills and prior knowledge They are solved by breaking what seems like an impossible problem into smaller/simpler problems, and using estimation skills to continuously refine your answer These problems often involve making justified guesses about quantities that seem impossible to compute given limited available information

How do I solve a Fermi Problem? Most of the time, you will need to ask questions! A Fermi question demands communication A Fermi question utilizes estimation Write these down! A Fermi question might require you to make assumptions Write these down! A Fermi question emphasizes process rather than “the” answer. Show how you got to your answer

The Classic Fermi Problem “How many piano tuners are there in Chicago?”

Sample Solution to the Classic Problem Typical solution involves multiplying a bunch of estimates that leads to the correct answer if the estimates are correct Sample solution: There are ~ people living in Chicago On average, there are 2 people in each household in Chicago Roughly one household in 20 has a piano that is tuned regularly Pianos that are tuned regularly are tuned once a year Each piano tuner works 8 hours a day, 5 days a week, and 50 weeks a year

Sample Solution to the Classic Problem Typical solution involves multiplying a bunch of estimates that leads to the correct answer if the estimates are correct Sample solution: There are ~ people living in Chicago On average, there are 2 people in each household in Chicago Roughly one household in 20 has a piano that is tuned regularly Pianos that are tuned regularly are tuned once a year Each piano tuner works 8 hours a day, 5 days a week, and 50 weeks a year With all of these assumptions…we get 125 piano tuners in Chicago. See SAMPLE WRITE UP

Why do these ‘work’? Fermi estimates generally work because… The estimations of the individual terms are often close to correct Over- and under- estimates help cancel each other out

So,if we can’t get the answer, what’s the point? Looking for Fermi estimates of the answer to a problem before turning to calculations provides you with a useful check on your results Although Fermi estimates are often not accurate (it depends on how good your estimates are), this type of analysis does tell us what to look for in order to get a better answer (e.g. is one of your estimates really off?) Fermi estimates give us a rough idea of the answer… which may be enough in some cases

What’s the point (continued)… They are good brain exercise They often don’t have an exact answer, forcing you to… Use your imagination Think outside the box (sometimes)

Your task… Work in groups to tackle a fermi problem Do a written report (see sample report) Present your solution to the class