Geodesic
Geometrical definition of Pi and its approximations by nested radicals
The Teaching of Mathematics, XI (2008) no. 1, p. 25

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper the length of the arc of a circle and the area of a circular sector are defined in an elementary way. From this we derive the geometrical definition of the number $\pi$, in two equivalent ways. Formulas for the area and the perimeter of a circle are proved. Also, the number $\pi$ is represented as a limit of several sequences involving nested radicals. From this some approximations of $\pi$ are obtained. One of them is in terms of Golden ratio.
Classification : 00A35 G39
Keywords: Circle, circular sector, area, length. 
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     author = {Milan Janji\'c},
     title = {Geometrical definition of {Pi} and its approximations by nested radicals},
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Milan Janjić. Geometrical definition of Pi and its approximations by nested radicals. The Teaching of Mathematics, XI (2008) no. 1, p. 25 . http://geodesic.mathdoc.fr/item/TM2_2008_XI_1_a2/