[HN Gopher] A joke in approximating numbers raised to irrational...
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A joke in approximating numbers raised to irrational powers
Author : nomemory
Score : 63 points
Date : 2024-11-18 16:41 UTC (1 days ago)
(HTM) web link (www.andreinc.net)
(TXT) w3m dump (www.andreinc.net)
| sevensor wrote:
| 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 wrote:
| 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?
| philipov wrote:
| sin(x)=x in the same way that c=p=1 when doing cosmology.
| bubblyworld wrote:
| At least you can often recover the constants after the fact
| with dimensional analysis in cosmology =P
| mr_mitm wrote:
| 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.
| adgjlsfhk1 wrote:
| the joke is that sometimes the universe is bad at making sure
| x always approaches 0.
| dotancohen wrote:
| 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
| sevensor wrote:
| 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).
| m463 wrote:
| pi = 3.2
|
| (that is an assignment statement)
|
| https://en.wikipedia.org/wiki/Indiana_pi_bill
| wmwmwm wrote:
| 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!
| setopt wrote:
| Since e^(2pi) = 1, we can also conclude that e^(2pifx) =
| 1^(fx). This makes Complex Fourier Transforms quite trivial.
| enugu wrote:
| One interesting result implies that numbers like 3^(sqrt(3)) will
| be transcendental (ie no polynomial will evaluate them to 0).
|
| https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_theo...
| immibis wrote:
| No polynomial with rational coefficients. Of course x-y
| evaluates to 0 when x=y, even if y is a transcendental number.
| wging wrote:
| Small but important correction: no polynomial with integer
| coefficients (equivalently, rational coefficients). p(x) = (x -
| 3^(sqrt(3))) is a perfectly fine polynomial with real
| coefficients.
| jbmsf wrote:
| Happy to see someone else who watches Michael Penn videos.
| epistasis wrote:
| I came here to say the same thing!
|
| YouTube has become a fantastic place for this long tail of
| content, in this particular case a bunch of interesting math
| problems and tricks presented on a blackboard. Or, even full
| classes, from a person focused on honing pedagogy.
|
| 3blue1brown is another amazing channel for math as well.
|
| I have a feeling that this sort of content is the seeds of very
| great things for humanity. In the 20th century, ET Jaynes talks
| about how people never get credit in academia for creating
| simpler paths to greater understanding. But with YouTube,
| creators can both reach an audience and also find patrons to
| support them, or maybe even make a living off of YouTube
| directly with enough viewers.
|
| Motivated students have such resources at their fingertips just
| from an internet connection, if they happen to get lucky enough
| to find the right resources.
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(page generated 2024-11-19 23:00 UTC)