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

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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
  / 1129114614321618951  

The reddit post
  / got_this_while_doing_some_calculations_why...  

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

This is the 'best rational approximation' algorithm I used:
https://www.johndcook.com/blog/2010/1...

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.

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