Why do calculators get this wrong? (We don’t know!)

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From Standup Mathematician.

Women in Trading and Technology: https://www.janestreet.com/witt.html
21 to 23 September 2020 (deadline to apply: Friday 7 August 2020)

These are all of the almost-π calculations I showed:
11^6 ÷ 13 ≈ (156158413/3600)π
17^5 ÷ 11 ≈ (366494029/8920)π
11^6 ÷ 17 ≈ (119415257/3600)π
19^9 ÷ 2^3 ≈ (65249503235207/5082)π
5^9 ÷ 3 ≈ (1226819353/5920)π
7^9 ÷ 19 ≈ (2623750469/3881)π
13^5 ÷ 7 ≈ (154266801/9137)π
21^6 ÷ 5 ≈ (27818908094/5095)π
23^9 ÷ 5^4 ≈ (4030701961529/4394)π

Sheena’s tweet
https://mobile.twitter.com/Sheena2907/status/1129114614321618951

The reddit post
https://www.reddit.com/r/CasualMath/comments/bn0k9f/got_this_while_doing_some_calculations_why_does/

Farey sequence
https://en.wikipedia.org/wiki/Farey_sequence

This is the ‘best rational approximation’ algorithm I used:
https://www.johndcook.com/blog/2010/10/20/best-rational-approximation/

I’ve tested it on the Casio FX-83GT PLUS and Casio FX-991EX CLASSWIZ. Let me know what calculators you have checked!

CORRECTIONS:
– At 8:30 I say "13" when I mean "11". Ignore what I say: the on-screen number is correct!
– Let me know if you spot anything else.

Thanks to my Patreon supports who do support these videos and make them possible. Here is a random subset:
Alan Flett
Nikola Studer
Philippe von Bergen
Alan McNea
Derek Chandler
Jeremy Buchanan
Alan H.
Malcolm Rowe
Glenn Watson
Patrick Stover

Support my channel and I can make more videos:
https://www.patreon.com/standupmaths

And of course thanks to Jane Street who support my channel. They’re amazing.
https://www.janestreet.com/

Filming and editing by Matt Parker
Additional camera work by Lucie Green
That piano music is No.8 Requiem by Esther Abrami
All other music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
US book: https://www.penguinrandomhouse.com/books/610964/humble-pi-by-matt-parker/
UK book: https://mathsgear.co.uk/products/5b9fa76f230ffa140094dc43
Nerdy maths toys: http://mathsgear.co.uk/

A transcendental number is not the root of any integer polynomial!
https://mathworld.wolfram.com/TranscendentalNumber.html

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