Fermi Problems

Описание: Fermi Problems

📫𝐎𝐮𝐫 𝐅𝐁 𝐏𝐚𝐠𝐞:
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🎬𝐈𝐦𝐚𝐠𝐞𝐬, 𝐚𝐧𝐢𝐦𝐚𝐭𝐢𝐨𝐧𝐬 𝐚𝐧𝐝 𝐯𝐢𝐝𝐞𝐨𝐬 𝐜𝐫𝐞𝐝𝐢𝐭𝐬:
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The World Of Enrico Fermi - Project Physics Incorporated (Harvard University - https://archive.org/details/TheWorldO...)

🎼𝗠𝘂𝘀𝗶𝗰:
Undercover Vampire Policeman by Chris Zabriskie is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/...
Source: http://chriszabriskie.com/uvp/
Artist: http://chriszabriskie.com/

📚𝐃𝐚𝐯𝐢𝐝'𝐬 𝐁𝐨𝐨𝐤𝐬
📕 𝗪𝗲𝗶𝗿𝗱 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗘𝗱𝗴𝗲 𝗼𝗳 𝗜𝗻𝗳𝗶𝗻𝗶𝘁𝘆 𝗮𝗻𝗱 𝗕𝗲𝘆𝗼𝗻𝗱
(https://www.amazon.com/Weird-Maths-Ag...)
📙 𝗪𝗲𝗶𝗿𝗱𝗲𝗿 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗘𝗱𝗴𝗲 𝗼𝗳 𝘁𝗵𝗲 𝗣𝗼𝘀𝘀𝗶𝗯𝗹𝗲
(https://www.amazon.com/Weirder-Maths-...)
📗 𝗪𝗲𝗶𝗿𝗱𝗲𝘀𝘁 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗙𝗿𝗼𝗻𝘁𝗶𝗲𝗿𝘀 𝗼𝗳 𝗥𝗲𝗮𝘀𝗼𝗻
(https://www.amazon.com/Weirdest-Maths...)
** The kindle versions are available
*** For more details : http://weirdmaths.com/

📄𝗧𝗿𝗮𝗻𝘀𝗰𝗿𝗶𝗽𝘁𝗶𝗼𝗻:
Enrico Fermi was an Italian physicist famous because of his achievements in nuclear physics, quantum theory and particle physics. He and his team built the world's first nuclear reactor and he also worked on the development of the atomic bomb.

Fermi was present at the Trinity test, the first nuclear weapons test on 16th July 1945. Because a nuclear bomb had never been detonated before, no one had any idea of the strength of the weapon. But Fermi was able to make a reasonable estimate based simply on watching pieces of papers. Here’s what he wrote:

“About 40 seconds after the explosion the air blast reached me, I tried to estimate its strength by dropping from about six feet small pieces of paper before, during and after the passage of the blast wave. Since, at the time, there was no wind I could observe very distinctly and actually measure the displacement of the pieces of paper that were in the process of falling while the blast was passing. The shift was about 2½ meters, which, at the time, I estimated to correspond to the blast that would be produced by ten thousand tons of TNT.”

Later, after detailed calculations and further experiments, the actual power was found to have been about 21 kilotons of TNT. Yes, Fermi was wrong but his quick and simple estimate was reasonable. It wasn’t, for instance, 1,000 kilotons or 0.1 kiloton of TNT. His estimate made sense and was within acceptable limits.

When we come across a problem and need to make an estimate with little or no actual data, we use Fermi’s technique. Since he was very good at carrying out estimations, the kind of problems that allow this approach are called Fermi problems.

As a lecturer, Fermi used to challenge his students with problems that, at first sight, seemed impossible. One such problem was to estimate the number of piano tuners in Chicago given only the population of the city. Let’s look at how this can be done using Fermi’s approach.

In 1957, Chicago’s population was approximately 3.5 million. This is the only actual information we’re given. Now, assume that an average family has 4 members, so that the number of families in Chicago was about 875,000. If one in 10 families owned a piano, that makes a total of 87,500 pianos in the city. If the average piano tuner works 5 days a week and takes a two-week vacation during the summer, he works 246 days in a year. If he services 4 pianos every day, that’s 984 pianos per year. So if there are 87,500 pianos, there must be about 89 piano tuners.

In fact, there were 83 piano tuners in Chicago in 1957. So our estimate is very close.

We might have found that there were 50 or 150 piano tuners, but that doesn’t matter. The point is we can make an estimate within acceptable limits. That’s the important thing about this approach. Thanks to Fermi we have a way of making reasonable estimates for almost everything starting from very little data.

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