Medieval Times Mathematics

by Liliana Usvat

During the centuries in which the Chinese, Indian and Islamic mathematicians had been in the ascendancy, Europe had fallen into the Dark Ages, in which science, mathematics and almost all intellectual endeavour stagnated. Scholastic scholars only valued studies in the humanities, such as philosophy and literature, and spent much of their energies quarrelling over subtle subjects in metaphysics and theology, such as "How many angels can stand on the point of a needle?"

Persian and Middle Eastern scholars made great contributions to math during this time. Muhammad ibn Musa Al-kharizmi made great advances in algebra being able to solve quadratic equations with positive roots. Al-Karaji also made several advances in algebra which is sometimes termed algebraic calculus nowadays. Spherical trigonometry, algebraic notation, and algebraic geometry were some other developments of the time.

The High Middle Ages brought a huge increase in the study of mathematics and in the abilities of mathematicians because of the introduction of practices developed in Islamic countries in the East and introduced to Europe primarily through Spain. These included the use of Arabic numerals, which replaced the very clunky Roman system and remain in use today. Algebra was developed by Islamic people, as was algebraic geometry, from its rudimentary beginnings in Greece. These developments, and others, made it possible for Medieval mathematicians to do easily what Roman mathematicians had not dreamed of, and engineering developed as a result.

From the 4th to 12th Centuries, European knowledge and study of arithmetic, geometry, astronomy and music was limited mainly to Boethius’ translations of some of the works of ancient Greek masters such as Nicomachus and Euclid. All trade and calculation was made using the clumsy and inefficient Roman numeral system, and with an abacus based on Greek and Roman models.

By the 12th Century, though, Europe, and particularly Italy, was beginning to trade with the East, and Eastern knowledge gradually began to spread to the West. Robert of Chester translated Al-Khwarizmi's important book on algebra into Latin in the 12th Century, and the complete text of Euclid's “Elements” was translated in various versions by Adelard of Bath, Herman of Carinthia and Gerard of Cremona.

The great expansion of trade and commerce in general created a growing practical need for mathematics, and arithmetic entered much more into the lives of common people and was no longer limited to the academic realm. The advent of the printing press in the mid-15th Century also had a huge impact. Numerous books on arithmetic were published for the purpose of teaching business people computational methods for their commercial needs and mathematics gradually began to acquire a more important position in education.;

Fibonacci, writing in the Liber Abaci, in 1202 and updated in 1254, produced the first significant mathematics in Europe since the time of Eratosthenes, a gap of more than a thousand years. The work introduced Hindu-Arabic numerals to Europe, and discussed many other mathematical problems.

The 14th century saw the development of new mathematical concepts to investigate a wide range of problems.One important contribution was development of mathematics of local motion.

Thomas Bradwardine proposed that speed (V) increases in arithmetic proportion as the ratio of force (F) to resistance (R) increases in geometric proportion. Bradwardine expressed this by a series of specific examples, but although the logarithm had not yet been conceived, we can express his conclusion anachronistically by writing: V = log (F/R).

Bradwardine's analysis is an example of transferring a mathematical technique used by al-Kindi and Arnald of Villanova to quantify the nature of compound medicines to a different physical problem.

The Europeans learned Arabic in the 12 century. All mathematics and astronomy was written in Arabic.

By the end of the 12 century the best mathematics was done in Christian Italy.

During this century there was a spate of translations of Arabic works to Latin

Leonardo Pisano Fibonacci Born: 1170 in (probably) Pisa (now in Italy) Died: 1250 in (possibly) Pisa (now in Italy)

Fibonacci or Leonard of Pisa, played an important role in reviving ancient mathematics and made significant contributions of his own.

Leonardo Pisano is better known by his nickname Fibonacci. He played an important role in reviving ancient mathematics and made significant contributions of his own. Fibonacci was born in Italy but was educated in North Africa where his father held a diplomatic post. He travelled widely with his father, recognising and the enormous advantages of the mathematical systems used in these countries.

Fibonacci Liber abaci (Book of the Abacus), published in 1202 after his return to Italy, is based on bits of arithmetic and algebra that Fibonacci had accumulated during his travels. Liber abaci introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe.

Liber abaci did not appear in print until the 19 century. A problem in Liber abaci led to the introduction of the Fibonacci numbers and the Fibonacci sequence for which Fibonacci is best remembered today.

Fibonacci's other books of major importance are Practica geometriae in 1220 containing a large collection of geometry and trigonometry. Also in Liber quadratorum in 1225 he approximates a root of a cubic obtaining an answer which in decimal notation is correct to 9 places.

Features of Liber abaci: - a treatise on algebraic methods and problem which advocated the use of Hindu-Arabic numerals.
used the horizontal bar for fractions. In fractions though the older systems of unit and sexigesimal were maintained!
contained a discussion of the now-called Fibonacci Sequence -inspired by the following problem:

`How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on.''