## Arabic and Babylonian MathematicsManuela Zea, Juan Diego Moya and Cayetana Llano

### Events

Sexagesimal (base 60): is a numeral system with sixty as its base. It originated with the ancient Sumerian in the 3rd millennium BC, was passed down to the ancient Babylonian and is still used—in a modified form—for measuring time, angles and geographic coordinates.

Babylonian numerals: were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record.

This period begins under the Caliph Harun al-Rashid, the fifth Caliph of the Abbasid dynasty. He help the first translations of Greek texts into Arabic, such as Euclid’s Elements by al-Hajjaj. The next Caliph, al-Ma'mun, encouraged learning even more strongly than his father al-Rashid, and he set up the House of Wisdom in Baghdad which became the centre for both the work of translating and of of research. Al-Kindi (born 801) and the three Banu Musa brothers worked there, as did the famous translator Hunayn ibn Ishaq.

Indian numeral system: The third system was the arithmetic of the Indian numerals and fractions with the decimal place-value system. The numerals used were taken over from India, but there was not a standard set of symbols. Different parts of the Arabic world used slightly different forms of the numerals. At first the Indian methods were used by the Arabs with a dust board. A dust board was needed because the methods required the moving of numbers around in the calculation and rubbing some out as the calculation proceeded. The dust board allowed this to be done in the same sort of way that one can use a blackboard, chalk and a blackboard eraser. However, al-Uqlidisi (born 920) showed how to modify the methods for pen and paper use. Al-Baghdadi also contributed to improvements in the decimal system.

### BIOGRAPHY

#### Al-Khwarizmi

• Born on c. 780 and died c. 850. Lived in Baghad.
• A muslim mathematician and astronomer.
• His book "The Compendious Book on Calculation by Completion and Balancing" was translated to latin in the 12th century.
• The term Algebra, "a compilation of rules, together with demonstrations, for finding solutions of linear and quadratic equations based on intuitive geometric arguments, rather than the abstract notation now associated with the subject"(Log in), comes from this book.
• It also contains geometry aspects.
• "Elements within the work can be traced from Babylonian mathematics of the early 2nd millennium bce through Hellenistic, Hebrew, and Hindu treatises"(Log in).
• His second book was "Algoritmi de numero Indorum", in which he introduced Hindu-Arabic numerals, and arithmetic.
• The third book was the “The Image of the Earth”, translated as Geography. It included the coordinates of localities, and assisted in the construction of a world map.

#### Babylonian Scribes:

• Babylonian scribes introduced a new numeral system, developed computational methods, solved linear and quadratic problems, using methods similar like the now used algebra.
• They study what now is called Pythagorean number triples.
• The scribes made clay tablets, which is now the evidence of their work.
• They solved quadratic problems "in terms of a single unknown"(Log in). Almost the same method we use today.
• Babylonian scribes did their works in terms of particular cases, not general formulas. They use sequential procedures instead of formulas.
Clay Tablets, and Pythagorean Triplets

### Summary

The babylonians number system was around the number 60, this means that they grouped numbers into 60s. Today we use 10s instead of 60s. At first they didn't have a zero, which made things difficult. And even when they devised a zero they didn't had a decimal point which complicated things. They use symbols to represent numbers, and then fractions.

### Work Cited

History of Fractions. (n.d.). Retrieved March 31, 2017, from https://nrich.maths.org/2515