◀ ▲ ▶History / 16th-century / Person: Van Ceulen, Ludolph

Person: Van Ceulen, Ludolph

Ludolph Van Ceulen was a German mathematician who is famed for his calculation of $\pi$ to 35 places. In Germany, $\pi$ used to be called the Ludolphine number.

Mathematical Profile (Excerpt):

• Van Ceulen could receive no more than an elementary education and, certainly, he did not have a university education as his parents were not sufficiently wealthy to pay for one.
• First let us give the few details of Van Ceulen's life prior to 1578.
• Van Ceulen tells us in his Preface that he made a trip to Germany in 1569 when he visited Cologne and purchased a book there.
• The information from the Preface also tells us that Van Ceulen earned his living teaching mathematics beginning around 1566.
• Van Ceulen was a member of the Calvinist church of the Netherlands, so like thousands of others, suffered from the attempts of the Spanish to subdue rebellions in the Netherlands.
• It is likely that at this time Van Ceulen was still in Antwerp which had became a centre of Protestant activity and was most at risk.
• It is likely that Van Ceulen was among the large numbers who fled to Delft in 1576.
• Like Mariken Van Ceulen, Bartholomew Cloot died in 1590.
• After arriving in Delft, Van Ceulen taught mathematics there then, on 13 May 1580, he submitted a request to the Delft town council to be allowed to open a fencing school in the town.
• To understand why Van Ceulen was being offered a church in which to hold his fencing school, one has to understand that Delft was largely a Calvinist city and many of the buildings previously owned by the Roman Catholic Church had been taken over and put to other uses.
• The Council were obviously very pleased to have Van Ceulen open a fencing school in the city for, in addition to offering him the building, they awarded him an annual allowance of 25 guilders.
• During his time in Delft, Van Ceulen was involved in a number of mathematical disputes.
• Goudaan had posed a geometric problem which Van Ceulen solved but his solution was not accepted by Goudaan.
• When Goudaan published his own solution to the problem, Van Ceulen realised that it was incorrect.
• In 1584 Van Ceulen published Solutie ende werckinghe op twee geometrische vraghen by Willem Goudaen inde jaeren 1580 ende 83 binnen Haerlem aenden kerckdeure ghestelt: mitsgaders propositie van twee andere geometrische vraghen Ⓣ(Solution of two geometric problems posed by William Goudaen in 1580 and 83 in Haarlem and corrections: together with two other geometric problems) putting his side of the dispute.
• A second dispute from this period was with Simon van der Eycke who had published an incorrect proof of the quadrature of the circle in 1584.
• Van Ceulen showed van der Eycke's error in two publications: Kort claar bewijs dat die nieuwe ghevonden proportie eens circkels iegens zyn diameter te groot is ende ouerzulcx de quadratura circuli des zeluen vinders onrecht zy Ⓣ(Short clear proof that the new-found proportion of a circle to his diameter is too big, whence the quadrature of the circle of this discoverer is not correct.) (1585) and Proefsteen ende claerder wederleggingh dat het claarder bewijs (so dat ghenaempt is) op de gheroemde ervindingh vande quadrature des circkels een onrecht te kennen gheven, ende gheen waerachtich bewijs is: hier by gevoeght Een corte verclaringh aengaende het onverstant ende misbruyck inde reductie op simpel interest.
• This proved a significant point in Van Ceulen's life for he spent the rest of his life obtaining better approximations to π using Archimedes' method with regular polygons with many sides.
• They offered Van Ceulen the Faliedenbegijnkerk for, as in Delft, former Roman Catholic churches were being put to different uses.
• However, included in the letter of permission was a clause with made Van Ceulen responsible for any damage caused to the building by either him or his students.
• Nobody else was allowed to run a fencing school in Leiden and in 1602, when he realised that his assistant Pieter Bailly was running his own school, Van Ceulen complained to the Council who forced the closure of Bailly's fencing school.
• Van Ceulen knew that was incorrect - he already had an accurate value of π with √10 well outside his bounds.
• However, he now had a problem since he felt he could not openly criticise Scaliger, given his position, and he also he had the problem that Scaliger's book was in Latin which he could not read (a friend must have translated the relevant parts).
• However Scaliger was not going to be told how to do mathematics by a fencing instructor, and challenged Van Ceulen to put his objections in writing.
• Van Ceulen never did so, perhaps because he felt he could not enter a public dispute with a leading professor at the university, perhaps also because his inability to write Latin would have meant that he could not take part in the dispute on the usual terms.
• 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.
• The first and second sections are the most original; they contain not only the best approximation of π reached at that time but also shows Van Ceulen to be as expert in trigonometry as his contemporary Viète.
• Van Ceulen was appointed to a number of committees by the States-General.
• On 10 January 1600, Van Ceulen was appointed to the Engineering School.
• The School was set up in the Faliedenbegijnkerk so Van Ceulen could teach fencing and mathematics in the same building.
• Van Ceulen had several friends among the mathematicians of the time.
• In particular his friendships with Simon Stevin and Adriaan van Roomen were important for his career.
• Snell translated two of Van Ceulen's works into Latin to make them more accessible to the world-wide mathematical community.
• In 1615 his widow Adriana Simondochter published a posthumous work by Van Ceulen entitled De arithmetische en geometrische fondamenten Ⓣ(On arithmetic and fundamental geometry).
• Having spent most of his life computing this approximation, it is fitting that the 35 places of π were engraved on Van Ceulen's tombstone.
• Van Ceulen had purchased a grave in the Pieterskerk on 11 November 1602 but, after Van Ceulen's death on 31 December 1610, his widow Adriana exchanged this grave for another, still in the Pieterskerk, and it was in this second grave that Van Ceulen was buried on 2 January 1611.
• The tombstone gave both Van Ceulen's lower bound of 3.14159265358979323846264338327950288 and his upper bound of 3.14159265358979323846264338327950289.
• A replica of the original tombstone of Ludolph Van Ceulen was placed into the Church since the original disappeared.
• It was therefore a tribute to the memory of Ludolph Van Ceulen, when on Wednesday 5 July, 2000 prince Willem-Alexander (heir to the throne), unveiled the memorial tombstone in the St Peter's Church, in Leiden.
• In Germany π was called the "Ludolphine number" for a long time.

Born 28 January 1540, Hildesheim, Germany. Died 31 December 1610, Leiden, Netherlands.

View full biography at MacTutor

Tags relevant for this person:

Origin Germany, Number Theory, Special Numbers And Numerals

Thank you to the contributors under CC BY-SA 4.0!

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@J-J-O'Connor

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive