Blog
Happy -10+e√2+5√3 Approximation Day!
2020-07-29
A week ago, it was 22 July: Pi Approximation Day.
22/7 (22 July in DD/M format) is very close to pi, closer in fact than 14 March's
approximation of 3.14 (M.DD).
During this year's Pi Approximation Day, I was wondering if there are other days that give good
approximations of interesting numbers. In particular, I wondered if there is a good 2π (or τ)
approximation day.
π is close to 22/7, so 2π is close to 44/7—but sadly there is no 44th July.
The best approximation day for 2π is 25th April, but 25/4 (6.25) isn't really close to
2π (6.283185...) at all. The day after Pi Approximation Day, however, is a good approximation of 2π-3 (as π-3 is
approximately 1/7). After noticing this, I realised that the next day would be a good approximation
of 3π-6, giving a nice run of days in July that closely approximate expressions involving pi.
After I tweeted about these three, Peter Rowlett suggested
that I could get a Twitter bot to do the work for me. So I made one:
@HappyApproxDay.
Since writing this post, Twitter broke @HappyApproxDay by changing their API, but the bot lives on on
Mathstodon (@HappyApproxDay@mathstodon.xyz)
and Bluesky (@happyapproxday.bsky.social).
@HappyApproxDay is currently looking for days that approximate expressions involving
π, τ, e, √2 and √3, and approximate the chosen expression better than
any other day of the year. There are an awful lot of ways to combine these numbers, so @HappyApproxDay@mathstodon.xyz
looks like it might be tooting quite a lot...
Edit: Added Mastodon and Bluesky links
×4 ×4 ×4 ×5 ×6(Click on one of these icons to react to this blog post)
You might also enjoy...
Comments
Comments in green were written by me. Comments in blue were not written by me.
⭐ top comment (2020-07-30) ⭐
June the 28th (6.28) isn't too bad for 2 Pi.steve
×4 ×6 ×2 ×2 ×2 Add a Comment