AVirtualMachineForExploringSpaceTimeAndBeyond : Visualization of the Newton's method when computing the roots of Z_____AnTi_QuOtE__QuOtE_____MiseEnExposant(7)=1 (Visualisation de la methode de Newton lors du calcul des racines de Z_____AnTi_QuOtE__QuOtE____

Visualization of the Newton's method when computing the roots of Z⁷=1 [Visualisation de la méthode de Newton lors du calcul des racines de Z⁷=1].

The seven black squares display the seven complex roots Z=cos(2.k.pi/7)+i*sin(2.k.pi/7) for k={0 -middle right-,1,2,3,4,5,6}.

[Plus d'informations à propos de la Méthode de Newton -en français/in french-]

See some related pictures (possibly including this one) displaying the computation of the roots of Zⁿ=1 using Newton's method:

Z²=1

Z³=1

Z⁴=1

Z⁵=1

Z⁶=1

Z⁷=1

Z⁸=1

See some related pictures (possibly including this one) displaying the Newton's method when computing the roots of Zⁿ=1 -sixteen trajectories are exhibibited, their starting points being the big circular dots-: