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 "raenil" backwards 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

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

Archive

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