I'd be curious how that works? I always hated memorizing those things, and I'd love it if there was some way to easily derive those from a single relationship.
That is the euler relationship. You can use that relationship to convert any expression with a trig function into an expression of exponentials and imaginary numbers. "Euler's formula" is a good search term if you want to learn more
Euler thought up or improved way too many things for them all to be named after him, it would get too confusing.
From his wiki: "Euler's work averages 800 pages a year from 1725 to 1783. He also wrote over 4500 letters and hundreds of manuscripts. It has been estimated that Leonhard Euler was the author of a quarter of the combined output in mathematics, physics, mechanics, astronomy, and navigation in the 18th century." https://en.m.wikipedia.org/wiki/Leonhard_Euler
9 Comments
Gustephan@lemmy.world · 15 pts · 328d
Shout out to the euler relationship for allowing me to forget every single trig identity I ever learned
Trashbones@lemmy.sdf.org · 6 pts · 328d
I'd be curious how that works? I always hated memorizing those things, and I'd love it if there was some way to easily derive those from a single relationship.
Gustephan@lemmy.world · 13 pts · 328d
e^(ix) = cos(x) + i sin(x)
That is the euler relationship. You can use that relationship to convert any expression with a trig function into an expression of exponentials and imaginary numbers. "Euler's formula" is a good search term if you want to learn more
DevCuber@sh.itjust.works · 11 pts · 328d
I don't know what any of those are, but surely lagrangian mechanics was invented by Lagrange, right
RunawayFixer@lemmy.world · 16 pts · 328d
Euler thought up or improved way too many things for them all to be named after him, it would get too confusing.
From his wiki: "Euler's work averages 800 pages a year from 1725 to 1783. He also wrote over 4500 letters and hundreds of manuscripts. It has been estimated that Leonhard Euler was the author of a quarter of the combined output in mathematics, physics, mechanics, astronomy, and navigation in the 18th century." https://en.m.wikipedia.org/wiki/Leonhard_Euler
And a relevant xkcd:
ChrysanthemumIndica@discuss.tchncs.de · 7 pts · 328d
I guess Euler-Langrangian mechanics was too much of a mouthful!
umbraroze@slrpnk.net · 5 pts · 328d
An old bit of wisdom: "Most scientific concepts are named after the second person to discover them"
humanspiral@lemmy.ca · 1 pts · 328d
hmmm... I was going to go with continuum mechanics as that seems made up. Maybe Euler contributed something to Lagrange.
marcos@lemmy.world · 6 pts · 328d
https://en.wikipedia.org/wiki/Continuum_mechanics
I guess F = ma is pure Newton + Galileo + Kepler + a bunch of people that weren't Euler.