The "greatest European mathematician of the middle ages",
his full name was Leonardo of Pisa, or Leonardo Pisano in Italian
since he was born in
Pisa,Italy (see Pisa on Google Earth), the city with the famous Leaning Tower, about 1175 AD.
Pisa was an important commercial town in its day and had links with many Mediterranean
ports. Leonardo's father, Guglielmo Bonacci, was a kind of customs officer
in the present-day Algerian town of Béjaïa,
(see Bejaia on Google Earth )
formerly known as Bugia or Bougie,
where wax candles were
exported to France. They are still called "bougies" in French.
So Leonardo grew up with a North African education under the Moors and later travelled extensively around the Mediterranean coast. He would have met with many merchants and learned of their systems of doing arithmetic. He soon realised the many advantages of the "Hindu-Arabic" system over all the others.
D E Smith points out that another famous Italian - St Francis of Assisi (a nearby Italian town) - was also alive at the same time as Fibonacci: St Francis was born about 1182 (after Fibonacci's around 1175) and died in 1226 (before Fibonacci's death commonly assumed to be around 1250).
By the way, don't confuse Leonardo of Pisa with Leonardo da Vinci! Vinci was just a few miles from Pisa on the way to Florence, but Leonardo da Vinci was born in Vinci in 1452, about 200 years after the death of Leonardo of Pisa (Fibonacci).
[The portrait here is a link to the University of St Andrew's site which has more on Fibonacci himself, his life and works.]
We shall just call him Fibonacci as do most modern authors, but if you are looking him up in older books, be prepared to see any of the above variations of his name.
[With thanks to Prof. Claudio Giomini of Rome for help on the Latin and Italian
names in this section.]
D E Smith's
History of Mathematics Volume 1,
(Dover, 1958 - a reprint of the orignal version from 1923) gives a complete
list of other books that he wrote and is a fuller reference on Fibonacci's
life and works.
There is another
brief biography of Fibonacci which is part of Karen Hunger Pashall's
(Virginia University)
The art of Algebra from
from al-Khwarizmi to Viéte: A Study in the Natural Selection of Ideas
if you want to read more about the history of mathematics.
Eight Hundred Years Young by A F Horadam (University of New England)
in The Australian Mathematics Teacher Vol 31, 1985, pages 123-134,
is an interesting and readable article on Fibonacci, his names and origins as well
as his mathematical works. He refers to and expands upon the following article...
The Autobiography of Leonardo Pisano R E Grimm, in Fibonacci
Quarterly vol 11, 1973, pages 99-104.
Leonard of Pisa and the New Mathematics of the Middle Ages
by J and F Gies, Thomas Y Crowell publishers, 1969, 127 pages,
is another book with much on the background to Fibonacci's life and work.
Della vita e delle opere di Leonardo Pisano Baldassarre Boncompagni,
Rome, 1854 is the only complete printed version of Fibonacci's 1228 edition of
Liber Abaci.
The the Math Forum's
archives of the
History of Mathematics discussion group
contain
a useful discussion
on some of the controversial topics of Fibonacci's names and life (February 1999). Use its next>> link to follow the thread of
the discussion through its 6 emailed contributions. It talks about the uncertainlty of his birth and death dates and his names.
It seems that Fibonacci never
referred to himself as "Fibonacci" but this was a nick-name given to him by later writers.
The book describes (in Latin) the rules we all now learn at elementary school for adding numbers, subtracting, multiplying and dividing, together with many problems to illustrate the methods:
1 7 4 + 1 7 4 - 1 7 4 x 1 7 4 ÷ 28
2 8 2 8 2 8 is
----- ----- -------
2 0 2 1 4 6 3 4 8 0 + 6 remainder 6
----- ----- 1 3 9 2
-------
4 8 7 2
-------
Let's first of all look at the Roman number system still in use in Europe at that time (1200)
and see how awkward it was for arithmetic.
I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1000You can still see them used on foundation stones of old buildings and on some clocks.
Sing a song of sixpenceAbove 100, the Latin words use the same order as we do in English, so that whereas 35 is quinque et triginta (5 and 30), 235 is ducenti triginta quinque (two hundred thirty five).
A pocket full of rye
Four and twenty blackbirds
Baked in a pie...
In this simple system, using addition only,
99 would be 90+9 or, using only the numbers above, 50+10+10+10 + 5+1+1+1+1 which translates to
LXXXXVIIII and by the same method 1998 would be written by the Romans as
MDCCCCLXXXXVIII.
But some numbers are long and it is this is where, if we agree to let the order of letters matter
we can also use subtraction.
But 8 is still written as VIII (not IIX). The subtraction in numbers was only of a unit (1, 10 or 100) taken away from 5 of those units (5, 50 or 500 or from the next larger multiple of 10 (10, 100 or 1000).
Using this method, 1998 would be written much more compactly as
MCMXCVIII but this takes a little more time to
interpret: 1000 + (100 less than 1000) + (10 less than 100) + 5 + 1 + 1 + 1.
Note that in the UK we use a similar system for time when 6:50 is often
said as "ten to 7" as well as "6 fifty", similarly for "a quarter to 4"
meaning 3:45. In the USA, 6:50 is sometimes spoken as "10 of 7".
Look out for Roman numerals used as the date a film was made, often recorded on the screen which gives its censor certification or perhaps the very last image of the movie giving credits or copyright information.
Arithmetic was not easy in the Roman system:
CLXXIIII added to XXVIII is CCII CLXXIIII less XXVIII is CXXXXVI
For more on Roman Numerals, see the excellent
Frequently Asked Questions
on Roman Numerals at Math Forum.
This decimal positional system, as we call it, uses the ten symbols of Arabic origin and the "methods" used by Indian Hindu mathematicians many years before they were imported into Europe. It has been commented that in India, the concept of nothing is important in its early religion and philosophy and so it was much more natural to have a symbol for it than for the Latin (Roman) and Greek systems.
Earlier the Persian author Abu ‘Abd Allah, Mohammed ibn Musa al-Khwarizmi (usually abbreviated to Al-Khwarizmi had written a book which included the rules of arithmetic for the decimal number system we now use, called Kitab al jabr wa‘l-muqabala (Rules of restoring and equating) dating from about 825 AD. D E Knuth (in the errata for the second edition and third edition of his "Fundamental Algorithms") gives the full name above and says it can be translated as Father of Abdullah, Mohammed, son of Moses, native of Khwarizm. He was an astromomer to the caliph at Baghdad (now in Iraq).
Al-Khowârizmî is the region south and to the east of the Aral Sea around the town now called Khiva (or Urgench) on the Amu Darya river. It was part of the Silk Route, a major trading pathway between the East and Europe. In 1200 it was in Persia but today is in Uzbekistan, part of the former USSR, north of Iran, which gained its independence in 1991.
Our modern word "algorithm" does not just apply to the rules of arithmetic
but means any precise set of instructions
for performing a computation whether this be
![[]](../images/purplesq.gif)
a method followed by humans, for example:
a cooking recipe;
or mechanically by machines (such as placing chips and components at correct
places on a circuit board to go inside your TV) or automatically by electronic computers which store the
instructions as well as data to work on.
See D E Knuth,
The Art of Computer Programming
Volume 1: Fundamental Algorithms (now in its Third Edition, 1997)pages 1-2.
There is an English translation of the ".. al jabr .." book:
L C Karpinski Robert of Chester's Latin Translation ... of al-Khowarizmi
published in New York in 1915. [Note the variation in the spelling of
"Al-Khowârizmî"
here - this is not unusual! Other spellings include al-Khorezmi.]
Ian Stewart's The Problems of Mathematics
(Oxford) 1992, ISBN: 0-19-286148-4 has a chapter on algorithms and the
history of the name: chapter 21: Dixit Algorizmi.
How Many Pairs of Rabbits Are Created by One Pair in One YearHe then goes on to solve and explain the solution:
A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear also.
Because the above written pair in the first month bore, you will double it; there will be two pairs in one month. |
beginning 1 first 2 second 3 third 5 fourth 8 fifth 13 sixth 21 seventh 34 eighth 55 ninth 89 tenth 144 eleventh 233 end 377 |
Before Fibonacci wrote his work, the sequence F(n) had already been discussed by Indian scholars, who had long been interested in rhythmic patterns that are formed from one-beat and two-beat notes. The number of such rhythms having n beats altogether is F(n+1); therefore both Gospala (before 1135) and Hemachandra (c. 1150) mentioned the numbers 1, 2, 3, 5, 8, 13, 21, ... explicitly.
Knuth refers to an article by
P Singh in Historia Mathematica vol 12 (1985) pages 229-244.
It was the French mathematician Edouard Lucas (1842-1891) who gave the name Fibonacci numbers to this series and found many other important applications as well as having the series of numbers that are closely related to the Fibonacci numbers - the Lucas Numbers: 2, 1, 3, 4, 7, 11, 18, 29, 47, ... named after him.
He died in the 1240's and there is now a
statue commemorating him located at the Leaning Tower end of
the cemetery next to the Cathedral in Pisa.
[With special thanks to Nicholas Farhi, an ex-pupil of Winchester College,
for the picture of the statue.]
The picture of Pisa's cathedral and leaning tower is a link to more information on Pisa.
Clark Kimberling, Professor of Mathematics at Evansville University, Indiana, has
a
Fibonacci biography page.
It shows the face of another Fibonacci statue down by
the Arno river off the Via Fibonacci.
Another article about this
book:
Leonardo of Pisa and his Liber Quadratorum by
R B McClenon in American Mathematical Monthly vol 26, pages 1-8.
Fibonacci's Mathematical Letter to Master Theodorus
A F Horodam, Fibonacci Quarterly 1991, vol 29, pages 103-107.
The most comprehensive translation of the manuscripts of the 5 works above is:
Scritti di Leonardo Pisano B Boncompagni, 2 volumes,
published in Rome in 1857 (vol 1) and 1862 (vol 2).
Leonardo of Pisa and the New Mathematics of the Middle Ages J Gies, F Gies,
Crowell press, 1969.
The Autobiography of Leonardo Pisano R E Grimm, in
Fibonacci Quarterly, vol 11, 1973, pages 99-104 with corrections
on pages 162 and 168.
800 Years young A F Horodam in
Australian Mathematics Teacher vol 31, 1975, pages 123-134.
The Golden String
|
Fibonacci Home Page
WHERE TO NOW?
This is the only page on |
The next topic is...
Pi and the Fibonacci Numbers
|
© 1996-2009 Dr Ron Knott
