Definition:Ludolphine Number
Definition
The Ludolphine number is the expression of the value of $\pi$ to $35$ decimal places:
- $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \ldots$
Also known as
The Ludolphine number is also referred to as the Ludolphian number.
Source of Name
This entry was named for Ludolph van Ceulen.
Historical Note
Ludolph van Ceulen published a $20$-decimal approximation for pi in his $1596$ book Van den Circkel ("On the Circle").
He later expanding this result to $32$ decimal places, and finally to $35$ decimal places.
He did not live to see the $35$-decimal-place value published, but it was carved onto his tombstone in a churchyard in Leyden.
The church was subsequently rebuilt and his tomb was destroyed, but his epitaph had by then been recorded in a survey of Leyden. Hence his lifework was preserved.
He obtained his value by using Archimedes' technique, taking the number of sides of the inscribed and circumscribed polygons to be $2^{62}$.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41972 \ldots$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$