Were the problems Fibonacci solved in his work "Flos" posed specifically for him?
score:10
Johannes of Palermo was a scholar in Frederick II's court. Frederick was aware of Fibonacci's work, and perhaps even an admirer. In 1225 when Frederick's court met in Pisa, Fibonacci was invited to demonstrate his works. I can't find a source for when exactly Johannes of Palermo posed his problems, but the two men certainly met in Pisa and Johannes posed his problems directly at Fibonacci:
A meeting was arranged between Fibonacci and Frederick at the Emperor's palazzo in Pisa, Frederick bringing with him an imposing retinue of people and animals. Frederick, who was about 30 years old, is described as "athletic-looking and of medium height, with reddish-blond hair and piercing blue eyes which are said to have made his courtiers tremble".
Mathematical questions for Fibonacci to solve were proposed by a scholar, Master John of Palermo. According to some writers, a mathematical tournament between Fibonacci and other mathematicians took place, but this does not seem to have been the case. Three of these problems are given later when I deal with Fibonacci's mathematical writings. At the time of his meeting with Frederick in the 1220's, Fibonacci was probably at the height of his prowess.
Source: 800 years young, A. F. Horadam, Department of Mathematics, University of New England
As for an example of the problem:
In Flos Fibonacci gives an accurate approximation to a root of 10x + 2x2 + x3 = 20, one of the problems that he was challenged to solve by Johannes of Palermo. This problem was not made up by Johannes of Palermo, rather he took it from Omar Khayyam's algebra book where it is solved by means of the intersection of a circle and a hyperbola. Fibonacci proves that the root of the equation is neither an integer nor a fraction, nor the square root of a fraction. He then continues:-
And because it was not possible to solve this equation in any other of the above ways, I worked to reduce the solution to an approximation.
Without explaining his methods, Fibonacci then gives the approximate solution in sexagesimal notation as 1.22.7.42.33.4.40 (this is written to base 60, so it is 1 + 22/60 + 7/602 + 42/603 + ...). This converts to the decimal 1.3688081075 which is correct to nine decimal places, a remarkable achievement.
Source: Leonardo Pisano Fibonacci (short biography), School of Mathematics and Statistics, University of St Andrews, Scotland
There is another example from Flos in the source of my first quote, but unfortunately without Fibonacci's solution. Perhaps you would like to try and solve it on your own? ;)
Further reading:
- The 800th birthday of the book that brought numbers to the west, Keith Devlin (Executive Director of the Center for the Study of Language and Information at Stanford University)
- Fibonacci and Square Numbers, MathDL, The Mathematical Association of America
More post
- 📝 What was used instead of toilet paper in the US and the UK prior to 1900?
- 📝 Who is Heckler?
- 📝 How can I identify the uniform and other details in this picture of my great grandfather circa 1913?
- 📝 How did women give birth in middle ages?
- 📝 According to game theory would Germany's post 1939 expansionism have provided the optimal economic benefits?
- 📝 In which East European country in the 1980s did people put their TVs in front of windows and turn them facing outside?
- 📝 Was the Vistula delta inhabited by Slavic tribes or Baltic tribes?
- 📝 What was the first recorded instance of burning a city or village in war?
- 📝 What was the last religion to become 'extinct'?
- 📝 Where in Poland and when in 1986 did stuntman Ian B. Jamieson perform?
- 📝 Were there any attempts to assassinate Joseph Stalin?
- 📝 How did the african kingdom of Carthage adapt to their environment?
- 📝 Prior to the Age of Exploration, Did Slavery Endure Anywhere in Europe?
- 📝 Was the Apostle the first Peter?
- 📝 Did the Germans try to "Pearl Harbor" Russia's Black Sea fleet?
- 📝 Did one or both sides of the cold war plan to strategically attack the others' food production?
- 📝 Why didn't Iran declare war on the United States for shooting down flight-655?
- 📝 Why was the capital of Ukraine moved in 1934?
- 📝 Why acquire real vs forged signatures?
- 📝 What types of Poison gasses were used in World War 1?
- 📝 Were ice buckets used to chill wine in Victorian England?
- 📝 How were Kurds involved (or not) in the invasion of Normandy?
- 📝 Map of/Measure of conflicted areas throughout history
- 📝 Gregório Amúrrio: dates of birth and death
- 📝 How long would it take to travel from England to western Africa in the late 1890's?
- 📝 Why did Europeans call Native Americans Indians in the 18th Century AD, After they had found out they were in the wrong continent?
- 📝 Revolutions of communication
- 📝 Why are the "Three Musketeers" called musketeers?
- 📝 Why didn't the steppe bow spread further?
- 📝 Did Russian winter seriously contribute to German defeat on the Eastern Front in WWII?
Source: stackoverflow.com
Search Posts
Related post
- 📝 Were the problems Fibonacci solved in his work "Flos" posed specifically for him?
- 📝 Why were kitchen work surfaces in Sweden apparently so low before the 1950s or so?
- 📝 Were Shakespeare's plays written for "high culture" or "entertain the bawdy masses" during his time?
- 📝 Why were the Prague Spring leaders treated more leniently than Nagy and his colleagues?
- 📝 Who were the "international statesmen" Hitler referenced in his last will as having started the war?
- 📝 Which SF author was unable to check his own work out of the library due to insufficient security clearance?
- 📝 Were China's problems in the past two centuries due to "missing out" on the industrial age?
- 📝 What were the last words of Charles the First, and Oliver Cromwell's response after his execution?
- 📝 Were there women who were against giving women the right to vote?
- 📝 Did Adolf Hitler ever address the fact that his own appearance was almost an exact opposite of what he considered the ideal Aryan appearance?
- 📝 What drugs were used in England during the High Middle Ages?
- 📝 Is there any evidence to support the claim that the United States was "suckered into WW1" by Zionists, made by Benjamin Freedman in his 1961 speech?
- 📝 What were the reasons for the Renaissance / scientific revolution in Europe?
- 📝 Why were the Romans unable to conquer Germania?
- 📝 Why were so many more Jewish men than Jewish women killed during the Holocaust?
- 📝 When did the Romans finally acknowledge that they were living in an empire?
- 📝 Why were the Allies so much better cryptanalysts?
- 📝 Were Medieval Britons aware of the existence of the Roman Empire?
- 📝 How were smallpox vaccines enforced in the US?
- 📝 Why were helmets and other body armour not commonplace in the 1800s?
- 📝 ‘Avoid sleeping on your back’ & ‘breathe in toilet smells’ were seen as precautions against the Black Death. Why did doctors think these would work?
- 📝 In the "Christmas truce" of 1914 were there any football (soccer) matches between British and German troops?
- 📝 What were the acceptance criteria in universities of medieval Europe?
- 📝 How severe were the casualties in ancient/medieval battles?
- 📝 Why were the West African islands uninhabited?
- 📝 Were defendants at the Nuremberg trial allowed to deny the holocaust?
- 📝 Were there large scale protests after earlier presidential elections in the US?
- 📝 Why were the drawings of Colossus burnt after WW2 and why was its very existence "of course" kept secret?
- 📝 What language(s) were spoken within the Holy Roman Empire?
- 📝 Did Heisenberg undermine the German atomic bomb by deliberately hiding his expertise from the Nazis?