Math, asked by karanpro739, 5 hours ago

Second Question So what is The Value of Pie When Divided By 22/7

Answers

Answered by xXmonaXx99
1

{\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Question}}}}}}}}}}}}}

So what is The Value of Pie When Divided By 22/7

{\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Answer}}}}}}}}}}}}}

I interpret “value” in your question as “how valuable is this expression”.

22/7 is one of the so-called “best rational approximations” for pi, that is, it is closer to pi than any approximation with a smaller or equal denominator.

These “best approximations” roll out of the continued fraction expansion of pi, which is given by [3; 7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,2, …], see e.g. Continued fraction expansion of pi, on Wikipedia

From this, the following are the first “best rational approximations” for pi:

3

22/7

333/106

355/113

(which is accurate to six decimal places!

this approximation was already discovered by the Chinese astronomer Tsu Ch'ung-Chih in the fifth century A.D.)

103993/33102

104348/33215

\huge\sf\fbox\red{Ans By Mona}

Similar questions