In mathematics, the Champernowne constant C10 is a transcendental real constant whose decimal expansion has important properties. It is named after mathematician D. G. Champernowne, who published it as an undergraduate in 1933.
For base 10, the number is defined by concatenating representations of successive integers:
- C10 = 0.12345678910111213141516… (sequence A033307 in OEIS).
Champernowne constants can also be constructed in other bases, similarly, for example:
- C2 = 0.11011100101110111… 2
- C3 = 0.12101112202122… 3.
The Champernowne constant can be expressed exactly as an infinite series:
and this series generalizes to arbitrary bases b by replacing 10 and 9 with b and b − 1 respectively.
The Champernowne word or Barbier word is the sequence of digits of Ck.
Read more about Champernowne Constant: Continued Fraction Expansion
Famous quotes containing the word constant:
“It is useless to contend with the irresistible power of Time, which goes on continually creating by a process of constant destruction.”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)