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 CONTENTS Introduction Fermi's Piano Tuner Problem How Old is Old? If the Terrestrial Poles were to Melt... Sunlight Exerts Pressure Falling Eastward What if an Asteroid Hit the Earth Using a Jeep to Estimate the Energy in Gasoline How do Police Radars really work? How "Fast" is the Speed of Light? How Long is a Light Year? How Big is a Trillion? "Seeing" the Earth, Moon, and Sun to Scale Of Stars and Drops of Water If I Were to Build a Model of the Cosmos... A Number Trick Designing a High Altitude Balloon Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water Calendar Calculations Telling Time by the Stars - Sidereal Time Fields, an Heuristic Approach The Irrationality of The Irrationality of The Number (i)i Estimating the Temperature of a Flat Plate in Low Earth Orbit Proving that (p)1/n is Irrational when p is a Prime and n>1 The Transcendentality of Ideal Gases under Constant Volume, Constant Pressure, Constant Temperature and Adiabatic Conditions Maxwell's Equations: The Vector and Scalar Potentials A Possible Scalar Term Describing Energy Density in the Gravitational Field A Proposed Relativistic, Thermodynamic Four-Vector Motivational Argument for the Expression-eix=cosx+isinx Another Motivational Argument for the Expression-eix=cosx+isinx Calculating the Energy from Sunlight over a 12 hour period Calculating the Energy from Sunlight over actual full day Perfect Numbers-A Case Study Gravitation Inside a Uniform Hollow Sphere Further note on Gravitation Inside a Uniform Hollow Sphere Pythagorean Triples Black Holes and Point Set Topology Additional Notes on Black Holes and Point Set Topology Field Equations and Equations of Motion (General Relativity) The observer in modern physics A Note on the Centrifugal and Coriolis Accelerations as Pseudo Accelerations - PDF File On Expansion of the Universe - PDF File

## Fermi's Piano Tuner Problem

As a lecturer, Enrico Fermi used to challenge his classes with problems that, at first glance, seemed impossible. One such problem was that of estimating the number of piano tuners in Chicago given only the population of the city. When the class returned a blank stare at their esteemed professor, he would proceed along these lines:

1. From the almanac, we know that Chicago has a population of about 3 million people.
2. Now, assume that an average family contains four members so that the number of families in Chicago must be about 750,000.
3. If one in five families owns a piano, there will be 150,000 pianos in Chicago.
4. If the average piano tuner
1. serviced four pianos every day of the week for five days
2. rested on weekends, and
3. had a two week vacation during the summer,
1. then in one year (52 weeks) he would service 1,000 pianos. 150,000/(4 x 5 x 50) = 150, so that there must be about 150 piano tuners in Chicago.

This method does not guarantee correct results; but it does establish a first estimate which might be off by no more than a factor of 2 or 3--certainly well within a factor of, say, 10. We know, for example, that we should not expect 15 piano tuners, or 1,500 piano tuners. (A factor of 10 error, by the way, is referred to as being 'to within cosmological accuracy.' Cosmologists are a somewhat different breed from physicists, evidently!!!)