You are right
this formula discovered by Euler is a magic formula connecting all known units ,zero and the magic numbers π and e .
Hello all, are there any formulae that mathematicians love for any particular reason? I think I remember someone saying that
is some kind of magical thing. Sorry if I'm being totally random but it's something like that and people say it's stuff like this that makes math magical...
are there any other formulae that make maths "magical"
The history of mathematics is fascinating. The number zero was not accepted for years: the is a year 1BCE and a year 1CE but no year zero. If fact, we think that the symbol 0 was adopted because that is the impression left when a counting stone was removed from a counting table made of sand.
Negative numbers have had a troubled history not even to mention irrational numbers.
Therefore, there was a real debate about complex numbers. We wanted to extend as many properties of real numbers to complex numbers as possible.
To that end if is a real number, define . Thus it is perfectly clear that .
There is no magic there. It is just a definition extending definitions for real numbers to complex numbers in such a way to make them consistent.
I think you are referring to Richard Feynman saying is the most beautifu of abstract algebra facsinates me l equation because it includes transcendental, natural numbers, with addition, multiplication and exponentiation.(Someone else probably said it as well, but since Feynman was such a popularizer of science, i think most people probably heard it from him, including me).
For me, its not a thrm but the massive role that poylnomials and their roots have in modern algebra is just fascinating.