Champernowne Constant is Normal
Contents
Theorem
- $0 \cdotp 12345 \, 67891 \, 01112 \, 13141 \, 51617 \, 18192 \, 02122 \ldots$
is normal.
Proof
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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): $0 \cdotp 12345 \, 67891 \, 01112 \, 13141 \, 51617 \, 18192 \, 02122 \ldots$
