Geodesic
Geometrical definition of Pi and its approximations by nested radicals
The Teaching of Mathematics, XI (2008) no. 1, p. 25 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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},
     journal = {The Teaching of Mathematics},
     pages = {25 },
     year = {2008},
     volume = {XI},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM2_2008_XI_1_a2/}
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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/