Giacomo Candido

For the 17th century Italian Roman Catholic bishop, see Giacomo Candido (bishop).

Giacomo Candido
Born	(1871-07-10)10 July 1871 Guagnano
Died	30 December 1941(1941-12-30) (aged 70) Galatina
Nationality	Italian
Alma mater	University of Pisa
Known for	Candido's identity
Scientific career
Fields	Mathematics, History of mathematics

Giacomo Candido (10 July 1871, in Guagnano – 30 December 1941, in Galatina) was an Italian mathematician and historian of mathematics.

Education and career

In 1897 Candido received his Laurea (teaching degree) from the University of Pisa and started to teach mathematics: first, at the Liceo of Galatina, then at the Liceo of Campobasso and from 1927 at the Liceo of Brindisi.[1]

He was an editor and contributor for the Periodico di Matematica per l'Insegnamento secondario and was one of the founders of the journal La Matematica elementare (an intermediate-level journal for teachers, engineers and students).[2]

He was an Invited Speaker of the ICM in 1928 in Bologna[3] and in 1932 in Zürich. In 1934 he founded the Apulian branch of Mathesis, an Italian association of mathematics teachers.

He is also remembered for his work on the history of mathematics.

Candido's identity

Main article: Candido's identity

Candido devised his eponymous identity to prove that

${\displaystyle (F_{n}^{2}+F_{n+1}^{2}+F_{n+2}^{2})^{2}=2(F_{n}^{4}+F_{n+1}^{4}+F_{n+2}^{4})}$

where F_n is the nth Fibonacci number.
The identity of Candido is that, for all real numbers x and y,[4][5]

${\displaystyle (x^{2}+y^{2}+(x+y)^{2})^{2}=2(x^{4}+y^{4}+(x+y)^{4})}$

It is easy to prove that the identity holds in any commutative ring.[4]

Selected publications

• Sulle funzioni U_n , V_n di Lucas in Periodica matematica, anno XVII, 1901–1902
• La formola di Waring e sue notevoli applicazioni, Tipografia editrice salentina, 1903
• Su d'un' applicazione delle funzioni U_n , V_n di Lucas in Periodica matematica, anno XX, 1904–1905
• Le equazioni reciproche in senso generale in Periodico matematica, anno XXI, 1905–1906
• Il fondo Palagi-Libri della Biblioteca Moreniana di Firenze, in Atti del II Congresso della Unione Matematica Italiana, ed. Cremonese, 1941
• Sulla mancata pubblicazione nel 1826 della celebre memoria di Abel, ed. Marra, Galatina, 1942
• Conferenze e discorsi, ed. Marra, Galatina, 1943
• Scritti matematici, ed. Marzocco, Firenze, 1948

References

1. "Biografia SISM". Archived from the original on 2012-07-17.
2. Goldstein, Catherine; Schappacher, Norbert; Schwermer, Joachim (2007). The Shaping of Arithmetic after C.F Gauss's Disquisitiones Arithmeticae. p. 438.
3. Candido, G. "Applicazione delle funzioni U_n e V_n di Lucas all'analisi indeterminata." In Atti del Congresso Internazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928, vol. 2, pp. 17–24. 1929.
4. Alsina, Claudi; Nelsen, Roger B. (2007). "On Candido's Identity" (PDF). Mathematics Magazine. 80 (3): 226–228. Archived from the original (PDF) on 2008-07-05.
5. Koshy, Thomas (2014). "Candido's Identity and the Pell Family". Pell and Pell-Lucas Numbers with Applications. p. 169.