mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 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      ×4      ×5
(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.
June the 28th (6.28) isn't too bad for 2 Pi.
steve
×4   ×6   ×2   ×2   ×2     Reply
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "rotcaf" backwards in the box below (case sensitive):

Archive

Show me a random blog post
 2025 

Jan 2025

Christmas (2024) is over
Friendly squares
 2024 
▼ show ▼
 2023 
▼ show ▼
 2022 
▼ show ▼
 2021 
▼ show ▼
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

trigonometry approximation video games turtles game show probability harriss spiral convergence radio 4 youtube dataset flexagons manchester science festival runge's phenomenon gerry anderson python asteroids bodmas accuracy craft edinburgh programming books braiding sound numbers regular expressions big internet math-off game of life sobolev spaces hannah fry countdown polynomials sport phd inverse matrices dinosaurs cambridge misleading statistics gather town news squares errors frobel weather station golden ratio crochet probability oeis the aperiodical christmas card tennis javascript fonts mathsjam martin gardner draughts matrix of minors stirling numbers propositional calculus graphs 24 hour maths royal institution bubble bobble inline code interpolation london underground platonic solids guest posts map projections mathsteroids pizza cutting friendly squares gaussian elimination weak imposition rugby data finite element method data visualisation menace preconditioning crossnumber light palindromes kings folding tube maps latex dragon curves noughts and crosses sorting quadrilaterals london advent calendar rhombicuboctahedron final fantasy bots boundary element methods ucl pi approximation day correlation reddit world cup arithmetic pythagoras stickers logs chebyshev recursion puzzles matt parker plastic ratio hats determinants hyperbolic surfaces standard deviation logic wave scattering hexapawn games live stream go reuleaux polygons geogebra triangles logo mean golden spiral raspberry pi zines a gamut of games finite group graph theory manchester fractals football wool tmip coins computational complexity mathslogicbot chalkdust magazine chess newcastle signorini conditions dates error bars matrix multiplication pascal's triangle royal baby simultaneous equations electromagnetic field fence posts binary talking maths in public geometry matrix of cofactors curvature databet realhats speed european cup bempp matrices captain scarlet folding paper exponential growth national lottery machine learning people maths pi datasaurus dozen statistics pac-man estimation christmas cross stitch anscombe's quartet nine men's morris php numerical analysis ternary

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2025