# Champernowne Constant is Normal

## Theorem

$0 \cdotp 12345 \, 67891 \, 01112 \, 13141 \, 51617 \, 18192 \, 02122 \ldots$

is normal.

## Historical Note

The Champernowne constant was constructed by David Gawen Champernowne as an example of a real number which was demonstrably normal.

He did this in the paper of 1933: The Construction of Decimals Normal in the Scale of Ten (J. London Math. Soc. Vol. 8: 254 – 260), while still an undergraduate.