Fractal Analysis of Pi Normality

ABSTRACT

π, the ratio between a circumference of a circle to its diameter, is a transcendental (and hence irrational) number. Fractal analysis is used here to show that π’s digit sequence corresponds to a uniformly distributed random succession of independent decimal digits, and that these properties get clearer as the number of digits in the series grows towards infinity; 10⁹ digits were tested in this work. This is consistent with the hypothesis that π is normal.

KEYWORDS:

• Pi normality
• fractals
• transcendental numbers
• irrational numbers

2000 AMS SUBJECT CLASSIFICATION:

• 11K16

Acknowledgments

This article was written using TEXstudio for Linux (also available for Apple OS X and MS Windows, http://www.texstudio.org), an open source free editor.