# Champernowne Constant is Normal

## Contents

## Theorem

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

is normal.

## Proof

## 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.

## Sources

- 1933: D.G. Champernowne:
*The Construction of Decimals Normal in the Scale of Ten*(*J. London Math. Soc.***Vol. 8**: 254 – 260) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $0 \cdotp 12345 \, 67891 \, 01112 \, 13141 \, 51617 \, 18192 \, 02122 \ldots$