Square root application

[ari.archeology]

Has the sum of the square roots of 2 & 3 ever been used as an alternative form of Pi?

 

[SoggyTissue]

pi = 3.141592
root 2 + root 3 = 3.14626 etc

the answers are the same to 2dp, so any calculation that does not ned to be precise could use it as a substitution, but in pythag the minute decimal places can affect results. (since there are 57.2958 degrees to a radian - which is 4 decimal places NOT 2) it is therefore benificial to have at least a 5 dp accuracy with all calculations (eg at least 1 more dp than the required answer format).

many people will tell you different things. I would not use root 2 plus root 3 due to the fact that many calculators will not compute the input.

 

[ari.archeology]

pi = 3.141592
root 2 + root 3 = 3.14626 etc

the answers are the same to 2dp, so any calculation that does not ned to be precise could use it as a substitution, but in pythag the minute decimal places can affect results. (since there are 57.2958 degrees to a radian - which is 4 decimal places NOT 2) it is therefore benificial to have at least a 5 dp accuracy with all calculations (eg at least 1 more dp than the required answer format).

many people will tell you different things. I would not use root 2 plus root 3 due to the fact that many calculators will not compute the input.

Makes good sense for our needs today. So, anciently, when 2 to 3 dp was about as accurate as was needed, the application of root 2 + root 3, or 3.14626, would have sufficed and been more accurate than the Babylonians at 3.125 or the Egyptians at 3.1605. I just can't identify in the literature any use of the root 2 + root 3 formula being used as a solution. If you have seen anything, please let me know.

 

[camieabz]

The older way that was taught was simply 22/7 (3.14285), which is closer to 3.14159 than the sum of root 2 plus root 3 (3.14626), is closer to PI than 3.14, and lot easier to remember.

Five decimal places ought to be enough for general purposes - https://blogs.scientificamerican.com/observations/how-much-pi-do-you-need/

If you were building a fence around a giant circular swimming pool with a radius of 100 meters and used that approximation to estimate the amount of fencing you would need, you would be half a millimeter short. Half a millimeter is tiny compared with the total fence length, 628.3185 meters. Being within half a millimeter is surely sufficient, and the tools you are using to make the fence probably introduce more uncertainty into your structure than your approximation of pi.