←back to thread

A joke in approximating numbers raised to irrational powers

(www.andreinc.net)
104 points nomemory | 7 comments | 18 Nov 24 16:41 UTC | HN request time: 1.026s | source | bottom
Show context
sevensor ◴[19 Nov 24 18:13 UTC] No.42186490[source]▶

    sin x = x
Half the problems in EE become trivial once you learn this. Sometimes the universe does a bad job of complying with the approximation though.
replies(4): >>42186803 #>>42186842 #>>42187116 #>>42187823 #
1. dotancohen ◴[19 Nov 24 18:51 UTC] No.42186842[source]▶
Are you familiar with the Taylor series? That's the first organ of the Taylor series, something like two decades ago I checked how accurate it goes past 20 organs:

https://dotancohen.com/eng/taylor-sine.php

replies(2): >>42188006 #>>42190301 #
2. sevensor ◴[19 Nov 24 20:56 UTC] No.42188006[source]▶
Oh yeah, for sure. And if you like a good time, compare the Taylor series at x=0 for sin(x) to that for exp(jx).
3. xelxebar ◴[20 Nov 24 02:27 UTC] No.42190301[source]▶
> That's the first organ of the Taylor series

Guessing that "organ" is a typo for "order", but somehow I kind of like envisioning Taylor series as living organisms, with terms being individual organelles.

Thanks for the smile in the morning.

replies(2): >>42190683 #>>42198121 #
4. seanhunter ◴[20 Nov 24 03:50 UTC] No.42190683[source]▶
No Taylor liked to communicate the series musically on various organs. IT got expensive and that’s why noone ever goes beyond the first two or three terms.
replies(2): >>42193766 #>>42194118 #
5. brookst ◴[20 Nov 24 13:28 UTC] No.42193766{3}[source]▶
Any sources to Bach that up?
6. selimthegrim ◴[20 Nov 24 14:19 UTC] No.42194118{3}[source]▶
I wonder what Grassmann did
7. xg15 ◴[20 Nov 24 21:08 UTC] No.42198121[source]▶
Was thinking of organ pipes and imagining it as the first tune. Might also be fitting.