A joke in approximating numbers raised to irrational powers

    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.

I am not sure I understand. Sin(x) approaches x only when x approaches 0. When else does the universe does a bad job with this approximation?

sin(x)=x in the same way that c=π=1 when doing cosmology.

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

At least you can often recover the constants after the fact with dimensional analysis in cosmology =P

1=c=G=hbar and sometimes =k is not even a joke, that's just natural units. Pi=e=1 however ... is only half a joke, because cosmologists are often only interested in orders of magnitudes, and even those are sometimes approximated.

the joke is that sometimes the universe is bad at making sure x always approaches 0.

pi = 3.2

(that is an assignment statement)

https://en.wikipedia.org/wiki/Indiana_pi_bill

Since e^(2πi) = 1, we can also conclude that e^(2πifx) = 1^(fx). This makes Complex Fourier Transforms quite trivial.

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).

My aero engineering friend from university winds me up every time I see him saying that pi = 22/7 - I finally stopped getting angry, checked and it’s pretty good! I’m still glad he didn’t decide to design planes after he graduated though!

That was a near miss for the industry, real aerospace nerds use 355/113 ...

Fun fact, in the book Life Of Pi, the kid stays exactly 227 days on the boat with the tiger.

> 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.

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.

Any sources to Bach that up?

I wonder what Grassmann did

Was thinking of organ pipes and imagining it as the first tune. Might also be fitting.