“The Ludolphian number is fixed in eternity— not a digit out of place, all characters in their proper order, an endless sentence written to the end of the world by the division of the circle’s diameter into its circumference.”
― Richard Preston
In addition to teaching mathematics and fencing, Van Ceulen was writing his most famous work, the book Vanden circkel (On the Circle) which he published in 1596. In this book he gave π correct to 20 decimal places using a regular polygon of 15 × 231 sides. It was split into four sections.
First Section: The first contained the computation of Pi.

Second Section:The second shows how to compute the sides of regular polygons of any number of sides, which in modern terms amounts to the expression of sin nA in terms of sin A (n an integer).

Third & Fourth Sections:The third and fourth sections are tables that don’t consist of very unoriginal information or discoveries.

Van Ceulen is famed for his calculation of Pi to 35 places which he did using polygons with 262 sides. Having published 20 places of Pi in his book of 1596, the more accurate results were only published after his death. In 1615 his second wife,Adriana Simondochter, published a postdeath work by Van Ceulen entitled De arithmetische en geometrische fondamenten. This contained his computation of 33 decimal places for Pi. The complete 35 decimal place approximation was only published in 1621 in Snell's Cyclometricus. Having spent most of his life computing this approximation, it is fitting that the 35 places of Pi were engraved on Van Ceulen's tombstone.
For many years following this Pi was called the Ludolphian number after Ludolph Van Cuelen.
For many years following this Pi was called the Ludolphian number after Ludolph Van Cuelen.