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 "q" then "u" then "o" then "t" then "i" then "e" then "n" then "t" in the box below (case sensitive):

Archive

Show me a random blog post
 2025 

Mar 2025

How to write a crossnumber

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

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

Archive

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