====== Pi (π) normality ======

A 'normal' sequence of numbers is one in which no digit occurs more frequently than any other. The mathematical equivalent of White Noise.

'Normality' is usually considered to be one of the tests for [[content:mathematics:random_numbers|randomness]].

The //**π**// sequence has now been computed to [[https://www.theguardian.com/science/2021/aug/16/swiss-researchers-calculate-pi-to-new-record-of-628tn-figures|many trillions]] of digits, and appears to pass all tests for randomness, including 'normality'. But the conjecture that //**π**// is 'normal' has not yet been proved or disproved.

See: [[https://www2.lbl.gov/Science-Articles/Archive/pi-random.html|Are the digits of Pi random?]] US Berkeley Lab.

//Notes : //

1) No 'naturally occurring' mathematical constant has ever been proved to be 'normal' (or// not //normal) Examples include the square root of 2, and the natural logarithm of 2.

2) 2024. A group of researchers studying [[content:physics:cosmology:string_theory]] have accidentally discovered a new formula for calculating - or rather approximating -  **π**. See [[https://www.scientificamerican.com/article/string-theorists-accidentally-find-a-new-formula-for-pi/|Scientific American, Aug 2024]]