Euler's formula, and why complex analysis is where the Riemann Hypothesis lives.
e^{iθ} = cos θ + i sin θ turns rotation into exponentiation, and it is the first step into a subject where differentiable functions are astonishingly rigid: knowing one on a small disc determines it everywhere. The zeta function ζ(s) of the Riemann Hypothesis is such a function; its zeros are the whole story.
Indi sen
Bir meseläni saýla, ýa-da ýaz ýa-da özüňi surata çek. Her ädim, bir resim, jogap sorag berlençä gizlenýär.
Özüň işle
Mugt hasap her bir ders üçin notlar goşýar, tamamlanan zadyňyzyň ýazgysyny, çözen problemaňyzy bir ýerde, we bu sahypa barada sorap biljek mugallymy. Matematika özüçe her kim üçin açyk, girseň ýa girmeseň.
Eň täze düşündirme, surat, we her harpyň manysy üçin her bir simwoly basyň.
Her bir bölegiň manysy
Resim
Bilen
Mysal
Bu beýanda hem ulanylan
Nädip: Functions of a complex variable
Power: E^(I·π) = -1.
Adamlar soraýan soraglar
What is the ε, δ definition actually saying?
That you can make the output as close to the limit as anyone demands (within ε) by keeping the input close enough (within δ). It replaces "approaches" with a challenge-and-response that can be checked.
Why does the harmonic series diverge when its terms go to zero?
Because the terms shrink too slowly: group them as 1/3 + 1/4 > 1/2, 1/5 + … + 1/8 > 1/2, and so on: infinitely many halves.