Gino Fano (5 January 1871 – 8 November 1952) was an Italian mathematician, best known as the founder of the finite geometry. He was born in Mantua, in Italy and died in Verona, also in Italy.

Fano made various contributions on projective and algebraic geometry. His work in the foundations of geometry predates the similar, but more popular, work of David Hilbert by about a decade. Ugo Fano and Robert Fano were his sons.

Fano is an early writer in the area of finite projective spaces. In his article on proving the independence of his set of axioms for projective n-space, among other things, he considered the consequences of having a fourth harmonic point be equal to its conjugate. This leads to a configuration of seven points and seven lines contained in a finite three-dimensional space with 15 points, 35 lines and 15 planes, in which each line contained only three points. All the planes in this space consist of seven points and seven lines and are now known as Fano planes:

Fano goes on to describe finite projective spaces of arbitrary dimension and prime orders.

Fano [ˈfaːno] is a town and comune of the province of Pesaro and Urbino in the Marche region of Italy. It is a beach resort 12 kilometres (7 miles) southeast of Pesaro, located where the Via Flaminia reaches the Adriatic Sea. It is the third city in the region by population after Ancona and Pesaro.

History

An ancient town of Marche, it was known as Fanum Fortunae after a temple of Fortuna located there. Its first mention in history only dates from 49 BC, when Julius Caesar held it, along with Pisaurum and Ancona. Caesar Augustus established a colonia, and built a wall, some parts of which remain. In 2 AD Augustus also built an arch (which is still standing) at the entrance to the town.

In January 271, the Roman Army defeated the Alamanni in the Battle of Fano that took place on the banks of the Metauro river just inland of Fano.

Fano was destroyed by Vitiges' Ostrogoths in AD 538. It was rebuilt by the Byzantines, becoming the capital of the maritime Pentapolis ("Five Cities") that included also Rimini, Pesaro, Senigallia and Ancona. In 754 it was donated to the Popes by the Frank kings.

Fano is a parish of the municipality of Gijón / Xixón, in Asturias, Spain. In 2012, its population was 220. Located in the south-east of the municipality, Fano is a rural area which borders the municipality of Siero in the south, and with the district of Valdornón in the east.

Toponym comes from Latin Fanum, a kind of temples ancient romans built in pre-Roman cults sacred places. A Benedictine monastery existed in Fano from 12th to 17th centuries. Its front romanesque façade is nowadays part of the San Juan Evangelista de Fano church.

Villages and their neighbourhoods

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Coordinates: 43°27′18″N 5°37′33″W / 43.4551°N 5.6259°W / 43.4551; -5.6259

Fano may refer to: