It is called a rational approximation of Pi, but I guess they didn't reach you that in "calculus."
https://en.wikipedia.org/wiki/Approximations_of_π
Oh by the way , Pi is 3.14159.... and not 3.1459...like you have posted.
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]