Giulio Carlo Fagnano dei Toschi

Giulio Carlo Fagnano dei Toschi (born December 6, 1682 in Senigallia ; † September 26, 1766 ibid) was an Italian mathematician who is known for his work on elliptical integrals .

Live and act

Produzioni matematiche , 1750

Fagnano was born into one of the leading families in his hometown, which was then part of the Papal States. Fagnano was gifted at an early age and wrote poetry at the age of ten. At fourteen he was sent to the Collegio Clementino in Rome, where he stayed for three years and mainly studied theology and philosophy, but avoided mathematics, although his mathematical talent was noticed by his teacher there, Domenico Quateroni (around 1660-1735). He became a council official and in 1723 a gonfalonier . He practiced mathematics as a pastime. He was also the consul of the King of Spain and Sicily in Senigallia.

At school he also studied the works of Nicolas Malebranche , with whom he then corresponded, including on transubstantiation . After reading De la recherche de la vérité by Malebranche, he recognized the importance of mathematics and, as he matured, turned intensively to mathematical studies. Although he was relatively isolated, he soon made remarkable advances, so that he turned entirely away from philosophy.

Fagnano wrote a book on triangular geometry that made him famous. Today he is best known for his work on the lemniscate division in the context of determining the lemniscate arc length . His publication about it in 1750 in his two-volume Produzioni matematiche encouraged Leonhard Euler to deal with elliptical integrals (he should go through Fagnano's collected works because it was proposed to admit him to the Berlin Academy of Sciences). Euler generalized Fagnano's doubling formula to his addition formulas for elliptic integrals. Fagnano also proved that the -partition points of the lemniscate can be constructed with a compass and ruler if is a power of 2 or the product of a power of 2 with the numbers 3 or 5. The work on the lemniscate and Euler's work stimulated by it (1751), according to Carl Gustav Jacobi, gave birth to the theory of elliptic integrals. ${\displaystyle n}$ ${\displaystyle n}$

Fagnano was a well-known European mathematician in his day who was also involved in priority disputes with Nikolaus I Bernoulli (about a problem that Brook Taylor had posed and for which both published solutions).

Fagnano also found the formula:

${\displaystyle \pi =2i\ln {1-i \over 1+i}\!\,,}$

which, from today's perspective, is a simple consequence of the geometric interpretation of the complex numbers.

In 1721 Giulio Carlo Fagnano dei Toschi was appointed Count and in 1723 admitted to the Royal Society . He was also a member of the Berlin Academy of Sciences and should be accepted into the French Academy, but died before that. In 1745 he became Marquis of St. Onofrio.

In 1743 he was called in as an appraiser to assess the stability of the dome of St. Peter's Basilica, as were Ruger Boscovich , Thomas Le Seur and other mathematicians known at the time. This also showed his reputation as an engineer at the time. Pope Benedict XIV commissioned the publication of his collected works, which appeared in 1750. He was a humorous, jovial personality. Fagnano suffered from kidney stones and was buried in the church of St. Maria Magdalena in Senigallia. His funerary inscription begins Veritas Deo gloria. ${\displaystyle \infty }$ There is a portrait as an oil painting in Senigallia town hall, in which he is holding a drawing of a lemniscate in his hand.

He was married to Francesca Sassofrato, with whom he had six daughters and six sons. Only four of his children survived him. His son Giovanni Fagnano (born January 31, 1715, † May 14, 1797) was also known as a mathematician. He was a priest and archdeacon at Senigallia Cathedral .

Fonts

• Giulio Carlo di Fagnano: Produzioni matematiche . 2 vols. ( Vol. 1 , vol. 2 ). Pesaro 1750.

literature

• Raymond Ayoub: The lemniscate and Fagnano's contributions to elliptic integrals , Arch. Hist. Exact Sciences, Vol. 29, 1984, pp. 131-149

Web links

• John J. O'Connor, Edmund F. Robertson :  Giulio Carlo Fagnano dei Toschi. In: MacTutor History of Mathematics archive .
• Entry on Toschi, Giulio Carlo Fagnano dei (1682 - 1766), Marquis of Sant 'Onofrio in the Archives of the Royal Society , London

Individual evidence

1. ↑ He is the author of a book on military fortifications (1709)
2. ↑ Raymond Ayoub, Arch. Hist. Exact Sci., See literature
3. ↑ Dionisio Gambioli, biography in Volume 3 of Fagnanos Collected Works, 1750, quoted by Ayoub.