Giulio Carlo de' Toschi di Fagnano

Giulio Carlo Fagnano dei Toschi (* December 6, 1682 in Senigallia, † September 26, 1766 ) was an Italian mathematician, known for his work on elliptic integrals.

Life and work

Fagnano was born into one of the leading families of his native city, which at that time belonged to the Papal States. He was council officials and Gonfaloniere 1723. Mathematics he pursued as a pastime.

Fagnano wrote a book on triangle geometry, which made him known. Today he is best known for his work on the Lemniskatenteilung in the context of determining the arc length of the lemniscate. Its publication about 1750 in his two-volume Produzioni matematiche suggested Leonhard Euler, to deal with elliptic integrals. Euler generalized the doubling formula of Fagnano to its addition formulas for elliptic integrals. Fagnano also proved that the division points of the lemniscate with ruler and compass can be constructed, if a power of 2 or the product of a power of 2 with the numbers 3 or 5. Fagnano was in his time a famous European mathematician who was also involved in priority disputes with Nicholas I Bernoulli ( published to a problem that Brook Taylor had made ​​and for both solutions).

Fagnano also found the formula:

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

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

His son Giovanni Fagnano ( born January 31, 1715 † May 14, 1797 ) was also known as a mathematician. He was a priest and archdeacon of the Cathedral of Senigallia.

Writings

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