4 ms·
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.
by sevensor 2y ago
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.
- pkoird 2y agoI 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?
- philipov 2y agosin(x)=x in the same way that c=π=1 when doing cosmology.
- bubblyworld 2y agoAt least you can often recover the constants after the fact with dimensional analysis in cosmology =P
- mr_mitm 2y ago1=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.
- adgjlsfhk1 2y agothe joke is that sometimes the universe is bad at making sure x always approaches 0.
- dotancohen 2y agoAre 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 https://dotancohen.com/eng/taylor-sine.php
- sevensor 2y agoOh 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).
- xelxebar 2y ago> 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.
- seanhunter 2y agoNo 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.
- brookst 2y agoAny sources to Bach that up?
- selimthegrim 2y agoI wonder what Grassmann did
- xg15 2y agoWas thinking of organ pipes and imagining it as the first tune. Might also be fitting.
- m463 2y agopi = 3.2 (that is an assignment statement) https://en.wikipedia.org/wiki/Indiana_pi_bill https://en.wikipedia.org/wiki/Indiana_pi_bill
- wmwmwm 2y agoMy 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!
- setopt 2y agoSince e^(2πi) = 1, we can also conclude that e^(2πifx) = 1^(fx). This makes Complex Fourier Transforms quite trivial.