Ludolph van Ceulen devoted a considerable part of his life to the subject (= finding p { pi (:number)} digits). In 1596 he gave the result to 20 places of decimals: this was calculated by finding the perimeters of the inscribed and circumscribed regular polygons of 60*(2^33) sides, obtained by the repeated use of a theorem of his discovery equivalent to the formula 1-cosA =2*((sin(A/2))^2). I posses a finely executed engraving of him of this date, with the result printed round a circle which is below his portrait.
He died in 1610, and by his directions the result to 35 places of decimals (which was as far as he had calculated it) was engraved on his tombstone# in St. Peter's Church, Leyden. His posthumous arithmetic contains the result to 32 places; this was obtained by calculating the perimeter of a polygon, the number of whose sides is 2^62, i.e. 4,611686,018427,387904. Van Ceulen also compiled a table of the perimeters of varous regular polygons.
# The inscription is quoted by Prof. de Haan in the
Messenger of Mathematics, 1874, (N.S.) vol. III, p. 25
Ball 1, pp. 353-354
2
Ludolph van Ceulen (1539-1610) devoted his life to finding a numerical approximation to the value of p {pi (:number)}. Before death overtook him, in 1610, he suceeded in making his approximation correct to 35 places of decimals. In 1596 he had the result worked out to 20 places, and this value was calculated by using regular inscribed and circumscribed polygons of 60*(2^33) sides. It will be seen that the last 15 places cost him fourteen years work. Just how many sides Van Ceulen's polygons had, at the time of his death, I do not know; but, according Professor Ball, they must have been above 2^62, i.e. 4,611686,018427,387904 in number. Polygons with 2^62 sides give a result correct to 32 places. It should be remembered that Van Ceulen did not have the aid of logarithms in his day, and that his calculations were necessarily made in a very laborious manner. These calculations, indeed, were considered so remarkable that the value of p {pi (:name)} has, in his honor, been called "Ludolph's number"; and his approximation to the value of p {pi (:symbol)} (3.141,592,653,589,793,238,462,643,383,279,502,88) was, in compliance with his request, carved on his tombstone in St. Peter's churchyard at Leyden. "Ludolph's number" has been carried now {=1901} to more than 700 places; but the greater accuracy has been attained by using modern methods which are as far superior to those at Ceulen's command as steam and electricity are superior to human muscle.
Rupert, pp. 97-98
3
The most successful and the most obsessive was Ludolph van Ceulen who spent much of his life on the calculation of p {pi (:number)}, first finding it correct to 20 decimal places, then to 32, and finally to 35 places. He did not live to publish his final achievement, but it was engraved on his tombstone in a Leyden Church. When the church was rebuilt and his tomb destroyed, his epitaph had already been recorded in a survey of Leyden, and his lifework preserved, but a more lasting monument is the name "Ludolphian number" which has been used for p {pi (:name)} in Germany.
Wells-N, p. 49
4
He is famed for his calculation of p {pi (:number)} to 35 places which he did using polygons with 2^62 sides. He spent most of his life doing this and it is fitting that the 35 places of p {pi (:number)} are engraved on his tombstone. In Germany p {pi (:name)} was called the Ludolphine number for a long time.
