Great link! It explains clearly that the ancient civilizations before the “Common Era” CE, or before the time of Christ, were not able to be accurate beyond 2 decimal places.
“[FONT="]The best known approximations to [/FONT]
π[FONT="] dating to [/FONT]
before the Common Era[FONT="] were accurate to two decimal places; this was improved upon in [/FONT]
Chinese mathematics[FONT="] in particular by the mid-first millennium, to an accuracy of seven decimal places. After this, no further progress was made until the late medieval period.”
Sadly for you, and I did not know this, today, Pi has been calculated to 22.4 trillion decimal points.
“[/FONT][FONT="]The record of manual approximation of [/FONT]
π[FONT="] is held by [/FONT]
William Shanks[FONT="], who calculated 527 digits correctly in the years preceding 1873. Since the middle of the 20th century, the approximation of [/FONT]
π[FONT="] has been the task of electronic digital computers; as of November 2016[/FONT][FONT="], the record is 22.4[/FONT][FONT="] [/FONT][FONT="]trillion digits.”
So, you can’t claim your approximation is even close! (Yes, I did miss that one after .14. Thanks for pointing it out. My hands are in very bad shape, unfortunately, and I either missed it, or didn’t see it. My bad!)
As for your “approximations” what does your lovely link say?
”[/FONT][FONT="]Depending on the purpose of a calculation, [/FONT]
π[FONT="] can be approximated by using fractions for ease of calculation. The most notable such approximations are [/FONT][FONT="][SUP]22[/SUP]⁄[SUB]7[/SUB][/FONT][FONT="] (accuracy 2·10[/FONT][SUP]−4[/SUP][FONT="]) and [/FONT][FONT="][SUP]355[/SUP]⁄[SUB]113[/SUB][/FONT][FONT="] (accuracy 8·10[/FONT][SUP]−8[/SUP][FONT="]).”
Hmm! No 111/106 listed. Because it deviates so rapidly from Pi, the 6th decimal place. Yes, I got that wrong, based on that missed number 1. So, I am correcting it from 3rd decimal place to 6th. Anything you want to correct?
Nor have you explained your random choice of 111/106. Next time, if you want an approximation, try 22/7 or 355/113.
As for now, you have picked the wrong numbers! But, then, you do have no methods whatsoever for the numbers you pull out of a hat. Spare me the rhetoric and don’t bother going over your mishmash again. I have to go do things![/FONT]