# Blog

## Happy e+τ-5 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.

@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
looks like it might be tweeting quite a lot...

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⭐ top comment (2020-07-30) ⭐