Giulio Carlo, Count Fagnano, Marquis de Toschi (26 September 1682 — 18 May 1766) was an Italian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He was probably the first to direct attention to the theory of

elliptic integral In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (). Their name originates from their originally arising i ...

s. Fagnano was born in

Senigallia Senigallia (or Sinigaglia in Old Italian; ) is a ''comune'' (municipality) and port town on Italy's Adriatic Sea, Adriatic coast. It is situated in the province of Ancona, in the Italian region of Marche, and lies approximately 30 kilometres nor ...

(at the time spelled "Sinigaglia"), and also died there.

Life

Giulio Fagnano was born to Francesco Fagnano and Camilla Bartolini in

(at the time spelled "Sinigaglia") in 1682. Fagnano had twelve children. One, Giovanni Fagnano, was also well-known as a mathematician. Another of Fagnano's children became a Benedictine nun. In 1721, Fagnano was made a

count Count (feminine: countess) is a historical title of nobility in certain European countries, varying in relative status, generally of middling rank in the hierarchy of nobility. Pine, L. G. ''Titles: How the King Became His Majesty''. New York: ...

Louis XV Louis XV (15 February 1710 – 10 May 1774), known as Louis the Beloved (), was King of France from 1 September 1715 until his death in 1774. He succeeded his great-grandfather Louis XIV at the age of five. Until he reached maturity (then defi ...

; in 1723, he was appointed ''

gonfaloniere The Gonfalonier (Italian: ''Gonfaloniere'') was the holder of a highly prestigious communal office in medieval and Renaissance Italy, notably in Florence and the Papal States. The name derives from '' gonfalone'' (English: "gonfalon"), the term ...

'' of Senigallia and elected to the

Royal Society of London The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...

; in 1745 he was made a

marquis A marquess (; ) is a nobleman of high hereditary rank in various European peerages and in those of some of their former colonies. The German-language equivalent is Markgraf (margrave). A woman with the rank of a marquess or the wife (or wido ...

of Sant' Onofrio.

Mathematical work

Fagnano made his higher studies at the

Collegio Clementino The Collegio Clementino is a palace in Rome, central Italy, sited between the Strada del'Orso and the banks of the Tiber. It was founded by Pope Clement VIII in 1595, to host Slavonian refugees. Giacomo della Porta was commissioned to erect a su ...

Rome Rome (Italian language, Italian and , ) is the capital city and most populated (municipality) of Italy. It is also the administrative centre of the Lazio Regions of Italy, region and of the Metropolitan City of Rome. A special named with 2, ...

, and there won great distinction — except in mathematics, to which his aversion was extreme. Only after his college course did he take up the study of mathematics; but then, without help from any teacher, he mastered mathematics from its foundations. Most of his important researches were published in the ''Giornale de' Letterati d'Italia''. Fagnano is best known for investigations on the length and division of arcs of certain curves, especially the

lemniscate In algebraic geometry, a lemniscate ( or ) is any of several figure-eight or -shaped curves. The word comes from the Latin , meaning "decorated with ribbons", from the Greek (), meaning "ribbon",. or which alternatively may refer to the wool fr ...

(cf.

Lemniscate elliptic functions In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied by Giulio Carlo de' Toschi di Fagnano, Giulio Fagnano in 1718 and later by Leonhard Euler ...

); this seems also to have been in his own estimation his most important work, since he had the figure of the lemniscate with the inscription "Multifariam divisa atque dimensa Deo veritatis gloria" engraved on the title-page of his ''Produzioni Matematiche'', which he published in two volumes (Pesaro, 1750), and dedicated to

Pope Benedict XIV Pope Benedict XIV (; ; 31 March 1675 – 3 May 1758), born Prospero Lorenzo Lambertini, was head of the Catholic Church and ruler of the Papal States from 17 August 1740 to his death in May 1758. Pope Benedict X (1058–1059) is now con ...

. The same figure and words "Deo veritatis gloria" also appear on his tomb. Failing to

rectify ''Rectify'' is an American television drama series exploring the life of a man after he is released from prison after nearly 20 years on death row following a wrongful conviction. It was created by Ray McKinnon and is the first original series ...

the

ellipse In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...

hyperbola In mathematics, a hyperbola is a type of smooth function, smooth plane curve, curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected component ( ...

, Fagnano attempted to determine arcs whose difference is rectifiable. The word "rectifiable" meant at that time that the length can be found explicitly, which is different from its modern meaning. He also pointed out the remarkable analogy existing between the

integral In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental oper ...

s which represent the arc of a

circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...

and the arc of a lemniscate. He also proved the formula :

\pi = 2i\log

where

i

stands for

\sqrt

. Some mathematicians objected to his methods of analysis founded on the

infinitesimal calculus Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of ...

. The most prominent of these were Viviani, De la Hire and

Rolle Rolle () is a Municipalities of Switzerland, municipality in the Cantons of Switzerland, Canton of Vaud in Switzerland. It was the seat of the district of Rolle (district), Rolle until 2006, when it became part of the district of Nyon District, N ...

References

External links

* {{DEFAULTSORT:Fagnano, Giulio Carlo 1682 births 1766 deaths People from Senigallia 18th-century Italian mathematicians 17th-century Italian mathematicians Fellows of the Royal Society Scientists from the Papal States