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Amazing Properties of Fractal Figures

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This article describes the process of research of the properties of geometric fractals by high school students. The general formulas of calculating the length and the area of the Sierpinski carpet have been derived in the article. The total surface area and the volume of the Menger sponge have been calculated in the paper. The amazing facts of geometric fractals have been revealed. For instance, if n→∞, the length of the Sierpinski carpet is Ln→∞, and its area is Sn→0, similarly, if n→∞, the total surface area of the Menger sponge is Sts(n)→∞, and its volume is Vn→0.


International Journal of Pure Mathematical Sciences (Volume 16)
O. Mandrazhy, "Amazing Properties of Fractal Figures", International Journal of Pure Mathematical Sciences, Vol. 16, pp. 37-43, 2016
Online since:
March 2016

[1] B. Mandelbrot, Fractal Geometry of Nature, The Institute of Computer Studies, Moscow, (2002).

[2] I. Sokolov. Fractals: submitted to the journal Quantim, (1989), 5, pp.6-13.

[3] E. Feder. Fractals, World, Moscow, (1991).

[4] O. Shkolniy. The Study of Elements of Fractal Theory at School: submitted to the journal Mathematics at School, (2004), 9-10, pp.42-47.

[5] Information on http: /ru. wikipedia. org/wiki/Мандельброт, _Бенуа.

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