Leonardo Fibonacci, shown in this engraving, was an Italian mathematician best known for describing a famous sequence of numbers—1, 1, 2, 3, 5, 8, 13, and so on. Each number is the sum of the two numbers before it.
Credit: © Science Source/Getty Images

The countdown is over! We made it to the best day of the year. Fibonacci Day has finally presented itself on every calendar throughout the world. Every year on November 23rd, mathematicians celebrate the Leonardo Fibonacci, an Italian mathematician. Fibonacci helped introduce into Western Europe the system of numerals still widely used today. This system—which uses the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9—is known as the Hindu-Arabic numeral system. Fibonacci was known during his life as Leonardo of Pisa. He was given the nickname Fibonacci sometime after his death. But why do we celebrate him on 11/23? Fibonacci is best known today for a famous sequence of numbers—1, 1, 2, 3, 5, 8, 13, and so on—that bears his name. By definition, the first two numbers are 1 and 1. Every other number equals the sum of the two numbers immediately before it. Since the first four numbers are 1, 1, 2, 3, we dedicate 11/23 to Fibonacci each year.

Why is the Fibonacci sequence important? Good question. Mathematicians have found use for it in many branches of mathematics. The sequence has led to the discovery of the golden ratio or divine proportion. The golden ratio is a number that appears in many areas of math, nature, and art. The golden ratio is: which is equal to about 1.61803.

By dividing one number in the sequence by the number before it, you get very close to the golden ratio. The never-ending sequence gradually gets closer to this ratio, never actually equalling it. The German astronomer and mathematician Johannes Kepler discovered this pattern in the Fibonacci sequence. The Fibonacci sequence also appears in nature. The pattern of seeds on a sunflower, for example, follows the Fibonacci sequence.

The large, beautiful sunflower is raised by farmers in many parts of the world. A sunflower head may measure more than 1 foot (30 centimeters) across.
Credit: John M. Coffman, NAS

Just as the golden ratio appears in nature, so do Fibonacci numbers. For example, the kernels of a pine cone form two sets of spirals. One set runs clockwise, and the other set runs counterclockwise. The number of spirals in each set is always a Fibonacci number, usually 8, 13, or 21. This pattern is a natural consequence of mathematical principles that underlie the plant’s growth.

Around 1192, Fibonacci went to Algeria with his father, a merchant from Pisa. There he learned Arabic and studied the mathematical knowledge of the Islamic world, which in many ways surpassed that of Europe. Later, he traveled to many surrounding countries on business and became convinced that the Hindu-Arabic numeral system was superior to the Roman numeral system then being used in Europe.

April 6, 2020

Today, April 6, marks 500 years since the death of the Italian painter Raphael in 1520. Raphael was one of the greatest and most influential painters of the Italian Renaissance. His graceful figures and skillful compositions influenced artists up to the early 1900′s. The period of his activity is called the High Renaissance. Raphael painted altarpieces, frescoes (paintings on damp plaster) of historical and mythological scenes, and portraits. His most popular works include his gentle paintings of the Madonna and Child. Raphael was also an architect. From 1514 until his death, he directed the construction of St. Peter’s Basilica in Rome.

Raphael’s School of Athens shows a gathering of ancient Greek philosophers and scientists in a Roman architectural setting. Standing in the center are Plato, left, and Aristotle, right. The harmony and balance of the composition are typical of the revival of classicism in the period called the High Renaissance. Credit: Fresco (1510-1511); The Vatican, Rome (The Art Archive)

To mark the quincentenary (500th anniversary) of Raphael’s death, the National Portrait Gallery at the Smithsonian Institution in Washington, D.C., is running an exhibition called “Raphael and His Circle” from February 16 through June 14. (Unfortunately, all museums at the Smithsonian Institution were closed temporarily beginning in March because of the COVID-19 pandemic.) The exhibition includes 26 prints and drawings by Raphael’s contemporaries—his “circle”—as well as four drawings by the master himself. In Italy, the Galleria Nazionale delle Marche ran a Raphael exhibition in the artist’s hometown of Urbino from October 2019 to January 2020. Other Raphael tributes are taking place at the Scuderie del Quirinale in Rome, the Veneranda Biblioteca Ambrosiana in Milan, and at the National Gallery and the Victoria and Albert Museum in London.

The Prophets Hosea and Jonah by Raphael. Credit: The Prophets Hosea and Jonah (1510), pen and brown ink with brown wash over black chalk, heightened with white and squared for transfer on laid paper by Raphael; National Gallery of Art

Raphael was born in Urbino on March 28 or April 6, 1483. His real name was Raffaello Sanzio. His father served as court painter to the Duke of Urbino. About 1494, Raphael went to Perugia to study with Perugino, an important painter. Perugino introduced Raphael to the latest ideas in Italian art and greatly influenced his student’s style.

Raphael settled in Florence in 1504. In Florence, Raphael studied the paintings of the great Italian artist Leonardo da Vinci. Leonardo da Vinci’s balanced compositions and idealized figures had a strong influence on all Renaissance painters, including Raphael.

Late in 1508, Pope Julius II asked Raphael to work for him in Rome. Julius wanted to rebuild and redecorate Rome to reflect its ancient glory. He gathered together the most illustrious architects, painters, and sculptors from all parts of Italy. Raphael created his finest work while in the service of Julius and his successor, Pope Leo X. With the assistance of a large workshop, Raphael produced religious paintings, tapestry designs, palace decorations, and portraits. He died in Rome at age 37 on April 6, 1520, after a short illness.

May 14, 2018

Italian is the national language of Italy and an official language of the European Union. It is also a second language in Switzerland, Vatican City, and the small republic of San Marino. Italian is recognized as a minority language in Brazil, Croatia, and Slovenia. In addition, it is spoken in countries that have large Italian immigrant populations. For example, about 1 million people speak Italian in the United States.

The Italian flag is often referred to as il Tricolore (the Tricolor) in Italian. Credit: © T. Lesia, Shutterstock

Italian belongs to the Indo-European family of languages. It is a Romance language, one of the modern languages that developed from Latin. Many forms of Italian are spoken throughout Italy. They are commonly called dialects, but they are more like separate languages than variations of one language.

When Italy became a unified country in 1861, more than 90 percent of the population spoke regional dialects. Today, Standard Italian is used throughout Italy, but it is the first language of few Italians. Most people speak a regional dialect, such as Milanese, Neapolitan, Sicilian, or Venetian, as their first language.

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Italy. Credit: WORLD BOOK map

The sounds of Italian are more simply organized than the sounds of English. Italian spelling is more consistent than English spelling, because each letter or combination of letters usually represents only one distinct sound. As a result, an Italian word is generally pronounced exactly as it is spelled.

Italian and English have similar systems of grammar. In both, the nouns, pronouns, adjectives, and adverbs have inflections, which are changes of form. More than 80 percent of the Italian vocabulary is shared with the French, Spanish, and Portuguese languages. Many Italian words have been absorbed into English, such as balcony, carnival, cash, costume, laundry, opera, and piano.

Italian gradually developed from Latin. It emerged as a separate language about A.D. 1000. It consisted of several local dialects that had formed in different regions. After about 1250, the region of Tuscany in northern Italy became the center of cultural life in Italy. The Tuscan dialect of the city of Florence and surrounding areas became the language of literature and culture. Tuscan was the language used by Boccaccio, Dante, and Petrarch, the three greatest Italian writers of the 1300’s.

From the 1300’s to the 1500’s, Italian was widely used as the language of commerce in the eastern Mediterranean area. By the mid-1500’s, Italian had almost completely replaced Latin as a written and spoken language.

The first novel written in Italian was I Promessi Sposi (The Betrothed) by Alessandro Manzoni. The historical work was first published in 1827. Its story took place during the 1600’s in the Lombardy region of northern Italy and set the standard for modern Italian prose.

February 13, 2018

Today, February 13, people in Ivrea, Italy, wrapped up the Battaglia delle Arance (Battle of the Oranges), the traditional end of the city’s Carnival celebrations and the nation’s largest fruit fight. Ivrea is a town near Turin in the Piemonte (Piedmont) region of northwestern Italy. The messy three-day battle uses up more than 550,000 pounds (250,000 kilograms) of oranges, and stems from a revolt against an unpopular lord of Ivrea some 800 years ago.

People of Ivrea, Itlay, defend the town against “an invasion” of the lord’s aranceri (orange throwers) during the annual Battle of the Oranges. Credit: © Pecold/Shutterstock

According to legend, sometime around the year 1200, the lord of Ivrea tried to force his romantic attentions on a local miller’s daughter (known as Violetta) on the eve of her wedding to someone else. The bride-to-be did not take kindly to the lord’s actions. Instead of submitting to his advances, Violetta killed him. The townspeople, fed up with years of oppression, rallied around the miller’s daughter, defeated the lord’s soldiers, and then stormed and burned the lord’s palace.

The people of Ivrea began celebrating their liberation with an annual event that was eventually tied to the end of carnival. Different missiles have been used to “re-create” the battle over the years, including beans and apples (representing arrows). Oranges—still a bit hard, prompting many people to wear protective helmets and masks—have been the battle’s ammunition since the late 1800′s.

Today, a horse-drawn cart loaded with the lord’s aranceri (orange throwers) runs the gauntlet of Ivrea’s streets three days in a row. The lord’s aranceri, protected in plastic “suits of armor,” are pummeled with oranges as they navigate the town streets—but they too throw oranges, and the entire scene is soon one of citrus carnage. Teams of orange throwers on foot defend different parts of the town, and each is identified by medieval uniforms and even coats of arms. Nets protect local store fronts and non-participants from wayward citrus fruit missiles. The oranges, imported from the southern Italian island of Sicily, are the remnants and rejects of the winter harvest. La Mugnaia (the miller’s daughter) Violetta, played by a local woman dressed in red and white, oversees the activities, hands out sweets to children, and throws flowers to admirers. A symbolic funeral ends the battle on Shrove Tuesday, followed by a more traditional parade of bands and floats.

The week-long Carnevale di Ivrea celebration draws some 100,000 people each year. Carnival is a lively time of dancing, feasting, music, pageants, and parades prior to the beginning of Lent, a strict religious season observed in the spring by most Christians. People celebrate Carnival around the world. The largest and most famous Carnaval draws millions of people each year to Rio de Janeiro, Brazil. In the United States, the best-known Carnival is held in New Orleans, Louisiana—an event capped by the city’s famous celebration of Mardi Gras (French for Fat Tuesday).

March 22, 2017

On Saturday, March 18, the Irish men’s national Rugby Union team defeated the English team 13-9 at Aviva Stadium in Dublin, Ireland. The win was satisfying for Ireland and the majority of the 51,700 fans in attendance, but it was England that still came out on top, winning its second-straight Six Nations Championship title. The Six Nations is an annual tournament that also includes the national rugby teams of France, Italy, Scotland, and Wales. The popular rough-and-tumble tournament is one of the biggest outside the Rugby World Cup (last won by New Zealand—in England—in 2015). The Royal Bank of Scotland (RBS) has sponsored the tournament—officially called the RBS 6 Nations—since 2003.

On March 18, 2017, England’s Anthony Watson (in white) and Jared Payne of Ireland compete for a high ball during Ireland’s 13-9 victory at Aviva Stadium in Dublin, Ireland. Credit: © Shaun Botterill, Getty Images

Ireland controlled the first half of Saturday’s match. The Irish players kept the ball in their hands 74 percent of the time, clamped down on England’s bruising offense, and scored the day’s only try (akin to a touchdown in American football) en route to a 10-3 halftime lead. Ireland held on during a grinding second half to secure the 13-9 win and second place in the tournament. Irish forward Peter O’Mahony—a last-minute starter because of an injury—won the man of the match award as the game’s outstanding player.

It was England, however, that dominated this year’s Six Nations, barely missing the so-called Grand Slam (an undefeated tournament). If Ireland had not happily stepped in the way, England would have won its second-straight Grand Slam, a difficult feat last accomplished by France in 1997 and 1998. Back then, it was only the Five Nations tournament (Italy joined the fray in 2000), so England’s back-to-back Grand Slam titles would have been the first in the modern Six Nations era. Alas, it was not to be. Saturday’s defeat also prevented England from setting a new record with its 19^th consecutive Test match victory. Test matches represent the highest level of international rugby competition. England instead remained tied with New Zealand’s powerful All Blacks for the all-time record of 18 straight Test wins.

The Six Nations tournament began as a competition among the British “Home Nations” of England, Ireland, Scotland, and Wales in 1883. The 1910 addition of France made it a Five Nations Championship. France bowed out of the tournament in 1932, and the tournament halted altogether during World War II (1939-1945). But the competition returned—with France included—in 1947. Since the modern Six Nations format began in 2000, England has now won the tournament six times. France is second with five championships. Wales has four Six Nations titles, and Ireland has three. Scotland and Italy have yet to win the Six Nations.

Within the Six Nations tournament, other team awards—aside from the championship and Grand Slam—include the Triple Crown, which goes to any Home Nation team that defeats the other three in a given year. The worst team in the tournament “wins” the Wooden Spoon each year. Individual nations also swap annual trophies. The Calcutta Cup goes to the winner of the England-Scotland match. Scotland and Ireland play for the Centenary Quaich (a quaich «kwaykh» is a ceremonial drinking cup), while Ireland competes with England for the Millennium Cup. France and Italy play each year for the Giuseppe Garibaldi Trophy.

January 5, 2017

Last month, in December 2016, new prime ministers took office in two of Europe’s largest nations, France and Italy. In France, Bernard Cazeneuve, a member of the ruling Socialist Party, took over for Prime Minister Manuel Valls, who resigned to run for president in 2017. In Italy, Paolo Gentiloni replaced Matteo Renzi, who resigned as prime minister but retained his leadership of the ruling Democratic Party.

Bernard Cazeneuve. Credit: Toms Norde, State Chancellery (licensed under CC BY-SA 2.0)

Bernard Cazeneuve was born on June 2, 1963, in Senlis, a small city in the northern Oise department (administrative district). Cazeneuve worked as a lawyer before taking on a political career. In 1994, he moved to the northwestern city of Octeville in the Manche department of Normandy. He was elected to the departmental council and, in 1995, he was elected mayor of Octeville. In 1997, Cazeneuve was also elected to the National Assembly, where he successfully petitioned for the merger of Octeville with the neighboring port city of Cherbourg in 2000. Cazeneuve then served as mayor of newly created Cherbourg-Octeville. In 2002, he lost his bid for reelection to the National Assembly.

Cazeneuve rejoined the National Assembly in 2007. In 2012, Cazeneuve ended his tenure as mayor of Cherbourg-Octeville and began a series of ministerial Cabinet positions under Socialist Party prime ministers Jean-Marc Ayrault and Manuel Valls. Cazeneuve served as interior minister from April 2014 until his appointment as prime minister on Dec. 6, 2016.

In Italy, Paolo Gentiloni took office as the nation continued to absorb large numbers of refugees fleeing poverty and violence in the Middle East and northern Africa. Within Italy, his government faced a financial crisis and political challenges from populist and far-right movements.

Paolo Gentiloni. Credit: © Presidency of the Republic

Gentiloni was born in Rome on Nov. 22, 1954. He studied political science before beginning a career in journalism. In 1993, he entered politics as spokesman for Francesco Rutelli, who became mayor of Rome in 1994. Gentiloni served in Rome’s city council until 2001, when he was elected to parliament. In 2002, he helped found the Daisy, a political party that merged with Democrats of the Left to form the current Democratic Party in 2007. Gentiloni served as foreign minister in Matteo Renzi’s government from 2014 until becoming prime minister on Dec. 12, 2016.

August 26, 2016

Two days ago, on August 24, a 6.2-magnitude earthquake shook the mountains of central Italy. The earthquake struck in the early morning, toppling homes and buildings in the region of Latium (often called Lazio) and causing damage in nearby Marche (or Marches) and Umbria as well. The earthquake killed 278 people and several people remain missing. About 400 people were injured. The mountain towns hit by the quake are popular with tourists, and many of the dead were travelers staying in hotels and hostels. Because many of the missing people are not residents, authorities are not sure how many people may yet be found buried in the devastation.

Survivors and rescue workers begin searching the ruins of Amatrice, Italy, after an earthquake struck on Aug. 24, 2016. Credit: © Antonio Nardelli, Shutterstock

The earthquake struck at 3:36 a.m. local time and centered near the mountain village of Amatrice, about 85 miles (140 kilometers) east of Rome, the Italian capital. The quake reduced much of the town to ruins, including several historic buildings dating from the 1400’s. The majority of the earthquake victims were in Amatrice, but scores died in such nearby villages as Accumoli, Arquata del Tronto, and Pescara del Tronto. The earthquake woke startled residents in Rome, and was felt as far away as Bologna to the north and Naples to the south. In the first 12 hours after the initial quake, the region trembled through some 150 aftershocks, the strongest of which measured 5.5 on the Richter scale. Survivors stumbled about the destruction, helping those who could be reached, and huddled in vehicles and tents as rescue workers arrived on the scene. Helicopters carried rescue workers to the area’s more isolated villages to retrieve survivors trapped by landslides and rubble.

This map shows the location of the earthquake that devastated Amatrice and other mountain towns in central Italy on Aug. 24, 2016. Credit: WORLD BOOK map

Amatrice has a population of about 2,000 people, but that number swells many times during the summer tourist season. Last year, Amatrice was voted one of Italy’s most beautiful historic towns, and the town’s popular spaghetti festival was scheduled for this weekend. Amatrice’s heartbroken mayor, Sergio Pirozzi, surveyed the destruction, saying, “The town is no more.”

Wednesday’s earthquake was the worst in Italy since 2009 when 308 people died in a powerful quake just south of Amatrice in the region of Abruzzo. That earthquake destroyed parts of the medieval city of L’Aquila. Italy sits on a major fault line, making it one of the most seismically active areas of Europe.

Nov. 13, 2011

Mario Monti, a highly respected economist and a former European Union (EU) commissioner, has been nominated to become Italy’s prime minister and form a new government to tackle the acute national debt crisis. (National debt is the total amount that a federal government owes because of money it has borrowed by selling bonds or other securities.) Italy’s former prime minister, Silvio Berlusconi, formally resigned on November 12 after a new austerity package (strict economic measures) were passed by both houses of parliament. The austerity package includes a mixture of tax increases and spending cuts with the aim of saving 59.8 billion euros ($89.6 billion) to balance the budget by 2014. On November 9, the yield, or rate of interest, on 10-year Italian government bonds shot above 7 percent. (A bond is a certificate issued by a government promising to pay back money it has borrowed). Higher-risk bonds must pay a higher interest rate to attract buyers. When the interest rate on the government bonds of Greece and Ireland in 2010 and Portugal in 2011 climbed to 7 percent, the three countries were forced to seek bailouts from the European Union to avoid bankruptcy (the state of being legally unable to pay debts).

The euro has replaced the individual currencies of 17 member nations of the European Union, including Italy and Greece. European Central Bank

On November 10, Greek political leaders named Lucas Papademos as prime minister. Papademos, also a respected economist, is a former vice president of the European Central Bank. The coalition (multiparty) government he will lead has pledged to save Greece from bankruptcy by quickly approving the tough terms of the second bailout package that was approved by European Union leaders on October 26.

Additional World Book articles:

• Economics
• Crisis in the Eurozone (a special report)