Difference between revisions of "Talk:2205: Types of Approximation"

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(Added note about curved spaces to highlight the importance of circle size.)
 
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The cosmologist is probably using Fermi's a la [https://what-if.xkcd.com/84/ What-If 84: Paint the Earth][[User:OhFFS|OhFFS]] ([[User talk:OhFFS|talk]]) 20:34, 20 September 2019 (UTC)
 
The cosmologist is probably using Fermi's a la [https://what-if.xkcd.com/84/ What-If 84: Paint the Earth][[User:OhFFS|OhFFS]] ([[User talk:OhFFS|talk]]) 20:34, 20 September 2019 (UTC)
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: In that What-If, the rounding formula for Fermi problem estimation is given as "Fermi(x) = round10(log10(x))".  [https://www.google.com/search?&q=log10%28pi%29 log10(pi)] (Google search, shows calculator) is roughly .4971... so close enough that someone could do a "Fermi rounding" to either 1 or 10 and not really care one way or another. [[Special:Contributions/162.158.142.118|162.158.142.118]] 21:19, 20 September 2019 (UTC)
  
 
As a physics Phd (though not working in astrophysics), approximating pi to 1 is not all that bad. Especially when the measurable quantities that go into the calculation usually have huge error bars.--[[Special:Contributions/172.68.59.120|172.68.59.120]] 21:03, 20 September 2019 (UTC)
 
As a physics Phd (though not working in astrophysics), approximating pi to 1 is not all that bad. Especially when the measurable quantities that go into the calculation usually have huge error bars.--[[Special:Contributions/172.68.59.120|172.68.59.120]] 21:03, 20 September 2019 (UTC)
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Using natural units (setting c=hbar=1) is different from setting pi to 1. Using different units is always allowed and not an approximation. Setting pi to 1 on the other hand, is an approximation and is only justifiable if the other quantities in the calculation have huge uncertainty. --[[Special:Contributions/172.68.59.120|172.68.59.120]] 21:07, 20 September 2019 (UTC)
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In curved spaces, size of a circle also matters a lot. Small circles will always have circumference/diameter ratio closer to pi than larger circles, no matter where they are.

Latest revision as of 08:29, 21 September 2019

The cosmologist is probably using Fermi's a la What-If 84: Paint the EarthOhFFS (talk) 20:34, 20 September 2019 (UTC)

In that What-If, the rounding formula for Fermi problem estimation is given as "Fermi(x) = round10(log10(x))". log10(pi) (Google search, shows calculator) is roughly .4971... so close enough that someone could do a "Fermi rounding" to either 1 or 10 and not really care one way or another. 162.158.142.118 21:19, 20 September 2019 (UTC)

As a physics Phd (though not working in astrophysics), approximating pi to 1 is not all that bad. Especially when the measurable quantities that go into the calculation usually have huge error bars.--172.68.59.120 21:03, 20 September 2019 (UTC)

Using natural units (setting c=hbar=1) is different from setting pi to 1. Using different units is always allowed and not an approximation. Setting pi to 1 on the other hand, is an approximation and is only justifiable if the other quantities in the calculation have huge uncertainty. --172.68.59.120 21:07, 20 September 2019 (UTC)

In curved spaces, size of a circle also matters a lot. Small circles will always have circumference/diameter ratio closer to pi than larger circles, no matter where they are.