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!

80's, 90's and today

I have been listening to a music channel called "80's, 90's and today" and it occurs to me that while there is only 1 decade between 80's and 90's, there are now 3 decades between 90's and today. When I was growing up, music from the 60's are considered oldies, perhaps the oldies today should include 80's and 90's music. Maybe the music channel should change its title, unless the implication is that "today" consists of music of the last 2+ decades (the 00's, the 10's and the start of the 20's) rather than grouped by a single decade, as was done before.