The Indo-Arabic numeral system

Our current decimal numeral system with the digits 1 to 9, supplemented by zero, is said to have its origins in India around the middle of the first millennium CE. From there it was transmitted via the trading routes into the Middle East. In the eighth and ninth centuries the Arab world enjoyed a cultural and intellectual heyday under the enlightened caliphs Al-Mansur, Harun al-Rashid and Al-Ma'mun. The Indian digits 0 to 9 and the associated method for writing calculations were adopted in the time of Al-Mansur (755–775). Harun al-Rashid commissioned a translation of Euclid's "Elements". In Baghdad, Al-Ma'mun founded the "House of Wisdom", an academy along the lines of the Musaeum of Alexandria, and had all the Greek works then available translated into Arabic, including classical writers on mathematics like Euclid, Archimedes, Apollonius of Perga and Ptolemy. In some cases these translations are the only sources of the lost Greek originals. Arabic culture thus formed an important link in handing down the ancient sciences.

Origin of the terms "algorithm" and "algebra"

Two Arab scholars are particularly worthy of mention in this context since Fibonacci refers to them: al-Khwarizmi and Abu Kamil. The lives of these two Arab mathematicians are largely unknown. Al-Khwarizmi lived in the first half of the ninth century. His work on arithmetic was decisive in spreading the Indian numeral system in the Middle East and Western Europe. The word "algorithm" is derived from his name, and the term "algebra" can be traced back to one of his works. Abu Kamil came from Egypt and lived there from about 850 to 930. He continued al-Khwarizmi's algebraic work and was an important source for Fibonacci.

The abacus – a simple calculating machine

While Arab culture was flourishing, feudalism dominated in Europe and scientific and cultural life stagnated at a low level. Economic transactions, still mainly by barter, placed low demands on mathematical skills. Anyone having to perform calculations, and these were mainly merchants, needed an abacus. The abacus is the simplest form of calculating machine: beads are pushed up and down along wires or tracks. Another form consisted of a table with specified columns in which marks were made and later numbers were inscribed. This made the four basic types of calculation feasible.