## Wednesday, July 22, 2020

### Happy casual π day!

Today is also known as π approximation day. Today is July 22, which is written as 22/7 in many countries.

22/7 is a rational number with repeating digits in decimal 3.14285714285714... and is one of the earliest approximation (besides the number 3) to π = 3.141592653589...  and has been used since antiquity. 22/7 approximates π to 2 decimal digits. 22/7 is also the second convergent in the simple continued fraction expansion of π. The convergents in this continued fraction are the best rational approximation of π, in the sense that if n/d with n and d coprime is a convergent, then no other rational number m/c with c ≤ d is closer to π.  It is interesting to note some other convergents have also been used as approximation to π. For instance the fourth convergent 355/113 = 3.141592920... matches up with π to 6 decimal places and was discovered by astronomer Zu Chongzhi (祖沖之) in the fifth century A.D.

I talked about these 2 approximations in my blog post from Pi Day 2017. For countries where the date format is YY/MM, we have to wait 2 years before we have a casual π or π approximation month during July 2022!